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a/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/INSTALLER b/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/INSTALLER new file mode 100644 index 0000000000000000000000000000000000000000..a1b589e38a32041e49332e5e81c2d363dc418d68 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/INSTALLER @@ -0,0 +1 @@ +pip diff --git a/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/LICENSE.txt b/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/LICENSE.txt new file mode 100644 index 0000000000000000000000000000000000000000..5f1c11289f6a54cb07ebdbf31d02e8e81b18b07f --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/LICENSE.txt @@ -0,0 +1,19 @@ +Copyright (c) 2003-2019 Stuart Bishop + +Permission is hereby granted, free of charge, to any person obtaining a +copy of this software and associated documentation files (the "Software"), +to deal in the Software without restriction, including without limitation +the rights to use, copy, modify, merge, publish, distribute, sublicense, +and/or sell copies of the Software, and to permit persons to whom the +Software is furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL +THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +DEALINGS IN THE SOFTWARE. diff --git a/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/METADATA b/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/METADATA new file mode 100644 index 0000000000000000000000000000000000000000..9b1bad2b30b972f27cd5055763c2583a3fd074d4 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/METADATA @@ -0,0 +1,648 @@ +Metadata-Version: 2.1 +Name: pytz +Version: 2026.1.post1 +Summary: World timezone definitions, modern and historical +Home-page: http://pythonhosted.org/pytz +Download-URL: https://pypi.org/project/pytz/ +Author: Stuart Bishop +Author-email: stuart@stuartbishop.net +Maintainer: Stuart Bishop +Maintainer-email: stuart@stuartbishop.net +License: MIT +Keywords: timezone,tzinfo,datetime,olson,time +Platform: Independent +Classifier: Development Status :: 6 - Mature +Classifier: Intended Audience :: Developers +Classifier: License :: OSI Approved :: MIT License +Classifier: Natural Language :: English +Classifier: Operating System :: OS Independent +Classifier: Programming Language :: Python +Classifier: Programming Language :: Python :: 2 +Classifier: Programming Language :: Python :: 2.4 +Classifier: Programming Language :: Python :: 2.5 +Classifier: Programming Language :: Python :: 2.6 +Classifier: Programming Language :: Python :: 2.7 +Classifier: Programming Language :: Python :: 3 +Classifier: Programming Language :: Python :: 3.1 +Classifier: Programming Language :: Python :: 3.2 +Classifier: Programming Language :: Python :: 3.3 +Classifier: Programming Language :: Python :: 3.4 +Classifier: Programming Language :: Python :: 3.5 +Classifier: Programming Language :: Python :: 3.6 +Classifier: Programming Language :: Python :: 3.7 +Classifier: Programming Language :: Python :: 3.8 +Classifier: Programming Language :: Python :: 3.9 +Classifier: Programming Language :: Python :: 3.10 +Classifier: Programming Language :: Python :: 3.11 +Classifier: Programming Language :: Python :: 3.12 +Classifier: Programming Language :: Python :: 3.13 +Classifier: Topic :: Software Development :: Libraries :: Python Modules +License-File: LICENSE.txt + +pytz - World Timezone Definitions for Python +============================================ + +:Author: Stuart Bishop + +Introduction +~~~~~~~~~~~~ + +pytz brings the Olson tz database into Python. This library allows +accurate and cross platform timezone calculations using Python 2.4 +or higher. It also solves the issue of ambiguous times at the end +of daylight saving time, which you can read more about in the Python +Library Reference (``datetime.tzinfo``). + +Almost all of the Olson timezones are supported. + +.. note:: + + Projects using Python 3.9 or later should be using the support + now included as part of the standard library, and third party + packages work with it such as `tzdata `_. + pytz offers no advantages beyond backwards compatibility with + code written for earlier versions of Python. + +.. note:: + + This library differs from the documented Python API for + tzinfo implementations; if you want to create local wallclock + times you need to use the ``localize()`` method documented in this + document. In addition, if you perform date arithmetic on local + times that cross DST boundaries, the result may be in an incorrect + timezone (ie. subtract 1 minute from 2002-10-27 1:00 EST and you get + 2002-10-27 0:59 EST instead of the correct 2002-10-27 1:59 EDT). A + ``normalize()`` method is provided to correct this. Unfortunately these + issues cannot be resolved without modifying the Python datetime + implementation (see PEP-431). + + +Installation +~~~~~~~~~~~~ + +This package can either be installed using ``pip`` or from a tarball using the +standard Python distutils. + +If you are installing using ``pip``, you don't need to download anything as the +latest version will be downloaded for you from PyPI:: + + pip install pytz + +If you are installing from a tarball, run the following command as an +administrative user:: + + python setup.py install + + +pytz for Enterprise +~~~~~~~~~~~~~~~~~~~ + +Available as part of the Tidelift Subscription. + +The maintainers of pytz and thousands of other packages are working with Tidelift to deliver commercial support and maintenance for the open source dependencies you use to build your applications. Save time, reduce risk, and improve code health, while paying the maintainers of the exact dependencies you use. `Learn more. `_. + + +Example & Usage +~~~~~~~~~~~~~~~ + +Localized times and date arithmetic +----------------------------------- + +>>> from datetime import datetime, timedelta +>>> from pytz import timezone +>>> import pytz +>>> utc = pytz.utc +>>> utc.zone +'UTC' +>>> eastern = timezone('US/Eastern') +>>> eastern.zone +'US/Eastern' +>>> amsterdam = timezone('Europe/Amsterdam') +>>> fmt = '%Y-%m-%d %H:%M:%S %Z%z' + +This library only supports two ways of building a localized time. The +first is to use the ``localize()`` method provided by the pytz library. +This is used to localize a naive datetime (datetime with no timezone +information): + +>>> loc_dt = eastern.localize(datetime(2002, 10, 27, 6, 0, 0)) +>>> print(loc_dt.strftime(fmt)) +2002-10-27 06:00:00 EST-0500 + +The second way of building a localized time is by converting an existing +localized time using the standard ``astimezone()`` method: + +>>> ams_dt = loc_dt.astimezone(amsterdam) +>>> ams_dt.strftime(fmt) +'2002-10-27 12:00:00 CET+0100' + +Unfortunately using the tzinfo argument of the standard datetime +constructors ''does not work'' with pytz for many timezones. + +>>> datetime(2002, 10, 27, 12, 0, 0, tzinfo=amsterdam).strftime(fmt) # /!\ Does not work this way! +'2002-10-27 12:00:00 LMT+0018' + +It is safe for timezones without daylight saving transitions though, such +as UTC: + +>>> datetime(2002, 10, 27, 12, 0, 0, tzinfo=pytz.utc).strftime(fmt) # /!\ Not recommended except for UTC +'2002-10-27 12:00:00 UTC+0000' + +The preferred way of dealing with times is to always work in UTC, +converting to localtime only when generating output to be read +by humans. + +>>> utc_dt = datetime(2002, 10, 27, 6, 0, 0, tzinfo=utc) +>>> loc_dt = utc_dt.astimezone(eastern) +>>> loc_dt.strftime(fmt) +'2002-10-27 01:00:00 EST-0500' + +This library also allows you to do date arithmetic using local +times, although it is more complicated than working in UTC as you +need to use the ``normalize()`` method to handle daylight saving time +and other timezone transitions. In this example, ``loc_dt`` is set +to the instant when daylight saving time ends in the US/Eastern +timezone. + +>>> before = loc_dt - timedelta(minutes=10) +>>> before.strftime(fmt) +'2002-10-27 00:50:00 EST-0500' +>>> eastern.normalize(before).strftime(fmt) +'2002-10-27 01:50:00 EDT-0400' +>>> after = eastern.normalize(before + timedelta(minutes=20)) +>>> after.strftime(fmt) +'2002-10-27 01:10:00 EST-0500' + +Creating local times is also tricky, and the reason why working with +local times is not recommended. Unfortunately, you cannot just pass +a ``tzinfo`` argument when constructing a datetime (see the next +section for more details) + +>>> dt = datetime(2002, 10, 27, 1, 30, 0) +>>> dt1 = eastern.localize(dt, is_dst=True) +>>> dt1.strftime(fmt) +'2002-10-27 01:30:00 EDT-0400' +>>> dt2 = eastern.localize(dt, is_dst=False) +>>> dt2.strftime(fmt) +'2002-10-27 01:30:00 EST-0500' + +Converting between timezones is more easily done, using the +standard astimezone method. + +>>> utc_dt = datetime.fromtimestamp(1143408899, tz=utc) +>>> utc_dt.strftime(fmt) +'2006-03-26 21:34:59 UTC+0000' +>>> au_tz = timezone('Australia/Sydney') +>>> au_dt = utc_dt.astimezone(au_tz) +>>> au_dt.strftime(fmt) +'2006-03-27 08:34:59 AEDT+1100' +>>> utc_dt2 = au_dt.astimezone(utc) +>>> utc_dt2.strftime(fmt) +'2006-03-26 21:34:59 UTC+0000' +>>> utc_dt == utc_dt2 +True + +You can take shortcuts when dealing with the UTC side of timezone +conversions. ``normalize()`` and ``localize()`` are not really +necessary when there are no daylight saving time transitions to +deal with. + +>>> utc_dt = datetime.fromtimestamp(1143408899, tz=utc) +>>> utc_dt.strftime(fmt) +'2006-03-26 21:34:59 UTC+0000' +>>> au_tz = timezone('Australia/Sydney') +>>> au_dt = au_tz.normalize(utc_dt.astimezone(au_tz)) +>>> au_dt.strftime(fmt) +'2006-03-27 08:34:59 AEDT+1100' +>>> utc_dt2 = au_dt.astimezone(utc) +>>> utc_dt2.strftime(fmt) +'2006-03-26 21:34:59 UTC+0000' + + +``tzinfo`` API +-------------- + +The ``tzinfo`` instances returned by the ``timezone()`` function have +been extended to cope with ambiguous times by adding an ``is_dst`` +parameter to the ``utcoffset()``, ``dst()`` && ``tzname()`` methods. + +>>> tz = timezone('America/St_Johns') + +>>> normal = datetime(2009, 9, 1) +>>> ambiguous = datetime(2009, 10, 31, 23, 30) + +The ``is_dst`` parameter is ignored for most timestamps. It is only used +during DST transition ambiguous periods to resolve that ambiguity. + +>>> print(tz.utcoffset(normal, is_dst=True)) +-1 day, 21:30:00 +>>> print(tz.dst(normal, is_dst=True)) +1:00:00 +>>> tz.tzname(normal, is_dst=True) +'NDT' + +>>> print(tz.utcoffset(ambiguous, is_dst=True)) +-1 day, 21:30:00 +>>> print(tz.dst(ambiguous, is_dst=True)) +1:00:00 +>>> tz.tzname(ambiguous, is_dst=True) +'NDT' + +>>> print(tz.utcoffset(normal, is_dst=False)) +-1 day, 21:30:00 +>>> tz.dst(normal, is_dst=False).seconds +3600 +>>> tz.tzname(normal, is_dst=False) +'NDT' + +>>> print(tz.utcoffset(ambiguous, is_dst=False)) +-1 day, 20:30:00 +>>> tz.dst(ambiguous, is_dst=False) +datetime.timedelta(0) +>>> tz.tzname(ambiguous, is_dst=False) +'NST' + +If ``is_dst`` is not specified, ambiguous timestamps will raise +an ``pytz.exceptions.AmbiguousTimeError`` exception. + +>>> print(tz.utcoffset(normal)) +-1 day, 21:30:00 +>>> print(tz.dst(normal)) +1:00:00 +>>> tz.tzname(normal) +'NDT' + +>>> import pytz.exceptions +>>> try: +... tz.utcoffset(ambiguous) +... except pytz.exceptions.AmbiguousTimeError: +... print('pytz.exceptions.AmbiguousTimeError: %s' % ambiguous) +pytz.exceptions.AmbiguousTimeError: 2009-10-31 23:30:00 +>>> try: +... tz.dst(ambiguous) +... except pytz.exceptions.AmbiguousTimeError: +... print('pytz.exceptions.AmbiguousTimeError: %s' % ambiguous) +pytz.exceptions.AmbiguousTimeError: 2009-10-31 23:30:00 +>>> try: +... tz.tzname(ambiguous) +... except pytz.exceptions.AmbiguousTimeError: +... print('pytz.exceptions.AmbiguousTimeError: %s' % ambiguous) +pytz.exceptions.AmbiguousTimeError: 2009-10-31 23:30:00 + + +Problems with Localtime +~~~~~~~~~~~~~~~~~~~~~~~ + +The major problem we have to deal with is that certain datetimes +may occur twice in a year. For example, in the US/Eastern timezone +on the last Sunday morning in October, the following sequence +happens: + + - 01:00 EDT occurs + - 1 hour later, instead of 2:00am the clock is turned back 1 hour + and 01:00 happens again (this time 01:00 EST) + +In fact, every instant between 01:00 and 02:00 occurs twice. This means +that if you try and create a time in the 'US/Eastern' timezone +the standard datetime syntax, there is no way to specify if you meant +before of after the end-of-daylight-saving-time transition. Using the +pytz custom syntax, the best you can do is make an educated guess: + +>>> loc_dt = eastern.localize(datetime(2002, 10, 27, 1, 30, 00)) +>>> loc_dt.strftime(fmt) +'2002-10-27 01:30:00 EST-0500' + +As you can see, the system has chosen one for you and there is a 50% +chance of it being out by one hour. For some applications, this does +not matter. However, if you are trying to schedule meetings with people +in different timezones or analyze log files it is not acceptable. + +The best and simplest solution is to stick with using UTC. The pytz +package encourages using UTC for internal timezone representation by +including a special UTC implementation based on the standard Python +reference implementation in the Python documentation. + +The UTC timezone unpickles to be the same instance, and pickles to a +smaller size than other pytz tzinfo instances. The UTC implementation +can be obtained as pytz.utc, pytz.UTC, or pytz.timezone('UTC'). + +>>> import pickle, pytz +>>> dt = datetime(2005, 3, 1, 14, 13, 21, tzinfo=utc) +>>> naive = dt.replace(tzinfo=None) +>>> p = pickle.dumps(dt, 1) +>>> naive_p = pickle.dumps(naive, 1) +>>> len(p) - len(naive_p) +17 +>>> new = pickle.loads(p) +>>> new == dt +True +>>> new is dt +False +>>> new.tzinfo is dt.tzinfo +True +>>> pytz.utc is pytz.UTC is pytz.timezone('UTC') +True + +Note that some other timezones are commonly thought of as the same (GMT, +Greenwich, Universal, etc.). The definition of UTC is distinct from these +other timezones, and they are not equivalent. For this reason, they will +not compare the same in Python. + +>>> utc == pytz.timezone('GMT') +False + +See the section `What is UTC`_, below. + +If you insist on working with local times, this library provides a +facility for constructing them unambiguously: + +>>> loc_dt = datetime(2002, 10, 27, 1, 30, 00) +>>> est_dt = eastern.localize(loc_dt, is_dst=True) +>>> edt_dt = eastern.localize(loc_dt, is_dst=False) +>>> print(est_dt.strftime(fmt) + ' / ' + edt_dt.strftime(fmt)) +2002-10-27 01:30:00 EDT-0400 / 2002-10-27 01:30:00 EST-0500 + +If you pass None as the is_dst flag to localize(), pytz will refuse to +guess and raise exceptions if you try to build ambiguous or non-existent +times. + +For example, 1:30am on 27th Oct 2002 happened twice in the US/Eastern +timezone when the clocks where put back at the end of Daylight Saving +Time: + +>>> dt = datetime(2002, 10, 27, 1, 30, 00) +>>> try: +... eastern.localize(dt, is_dst=None) +... except pytz.exceptions.AmbiguousTimeError: +... print('pytz.exceptions.AmbiguousTimeError: %s' % dt) +pytz.exceptions.AmbiguousTimeError: 2002-10-27 01:30:00 + +Similarly, 2:30am on 7th April 2002 never happened at all in the +US/Eastern timezone, as the clocks where put forward at 2:00am skipping +the entire hour: + +>>> dt = datetime(2002, 4, 7, 2, 30, 00) +>>> try: +... eastern.localize(dt, is_dst=None) +... except pytz.exceptions.NonExistentTimeError: +... print('pytz.exceptions.NonExistentTimeError: %s' % dt) +pytz.exceptions.NonExistentTimeError: 2002-04-07 02:30:00 + +Both of these exceptions share a common base class to make error handling +easier: + +>>> isinstance(pytz.AmbiguousTimeError(), pytz.InvalidTimeError) +True +>>> isinstance(pytz.NonExistentTimeError(), pytz.InvalidTimeError) +True + + +A special case is where countries change their timezone definitions +with no daylight savings time switch. For example, in 1915 Warsaw +switched from Warsaw time to Central European time with no daylight savings +transition. So at the stroke of midnight on August 5th 1915 the clocks +were wound back 24 minutes creating an ambiguous time period that cannot +be specified without referring to the timezone abbreviation or the +actual UTC offset. In this case midnight happened twice, neither time +during a daylight saving time period. pytz handles this transition by +treating the ambiguous period before the switch as daylight savings +time, and the ambiguous period after as standard time. + + +>>> warsaw = pytz.timezone('Europe/Warsaw') +>>> amb_dt1 = warsaw.localize(datetime(1915, 8, 4, 23, 59, 59), is_dst=True) +>>> amb_dt1.strftime(fmt) +'1915-08-04 23:59:59 WMT+0124' +>>> amb_dt2 = warsaw.localize(datetime(1915, 8, 4, 23, 59, 59), is_dst=False) +>>> amb_dt2.strftime(fmt) +'1915-08-04 23:59:59 CET+0100' +>>> switch_dt = warsaw.localize(datetime(1915, 8, 5, 00, 00, 00), is_dst=False) +>>> switch_dt.strftime(fmt) +'1915-08-05 00:00:00 CET+0100' +>>> str(switch_dt - amb_dt1) +'0:24:01' +>>> str(switch_dt - amb_dt2) +'0:00:01' + +The best way of creating a time during an ambiguous time period is +by converting from another timezone such as UTC: + +>>> utc_dt = datetime(1915, 8, 4, 22, 36, tzinfo=pytz.utc) +>>> utc_dt.astimezone(warsaw).strftime(fmt) +'1915-08-04 23:36:00 CET+0100' + +The standard Python way of handling all these ambiguities is not to +handle them, such as demonstrated in this example using the US/Eastern +timezone definition from the Python documentation (Note that this +implementation only works for dates between 1987 and 2006 - it is +included for tests only!): + +>>> from pytz.reference import Eastern # pytz.reference only for tests +>>> dt = datetime(2002, 10, 27, 0, 30, tzinfo=Eastern) +>>> str(dt) +'2002-10-27 00:30:00-04:00' +>>> str(dt + timedelta(hours=1)) +'2002-10-27 01:30:00-05:00' +>>> str(dt + timedelta(hours=2)) +'2002-10-27 02:30:00-05:00' +>>> str(dt + timedelta(hours=3)) +'2002-10-27 03:30:00-05:00' + +Notice the first two results? At first glance you might think they are +correct, but taking the UTC offset into account you find that they are +actually two hours appart instead of the 1 hour we asked for. + +>>> from pytz.reference import UTC # pytz.reference only for tests +>>> str(dt.astimezone(UTC)) +'2002-10-27 04:30:00+00:00' +>>> str((dt + timedelta(hours=1)).astimezone(UTC)) +'2002-10-27 06:30:00+00:00' + + +Country Information +~~~~~~~~~~~~~~~~~~~ + +A mechanism is provided to access the timezones commonly in use +for a particular country, looked up using the ISO 3166 country code. +It returns a list of strings that can be used to retrieve the relevant +tzinfo instance using ``pytz.timezone()``: + +>>> print(' '.join(pytz.country_timezones['nz'])) +Pacific/Auckland Pacific/Chatham + +The Olson database comes with a ISO 3166 country code to English country +name mapping that pytz exposes as a dictionary: + +>>> print(pytz.country_names['nz']) +New Zealand + + +What is UTC +~~~~~~~~~~~ + +'UTC' is `Coordinated Universal Time`_. It is a successor to, but distinct +from, Greenwich Mean Time (GMT) and the various definitions of Universal +Time. UTC is now the worldwide standard for regulating clocks and time +measurement. + +All other timezones are defined relative to UTC, and include offsets like +UTC+0800 - hours to add or subtract from UTC to derive the local time. No +daylight saving time occurs in UTC, making it a useful timezone to perform +date arithmetic without worrying about the confusion and ambiguities caused +by daylight saving time transitions, your country changing its timezone, or +mobile computers that roam through multiple timezones. + +.. _Coordinated Universal Time: https://en.wikipedia.org/wiki/Coordinated_Universal_Time + + +Helpers +~~~~~~~ + +There are two lists of timezones provided. + +``all_timezones`` is the exhaustive list of the timezone names that can +be used. + +>>> from pytz import all_timezones +>>> len(all_timezones) >= 500 +True +>>> 'Etc/Greenwich' in all_timezones +True + +``common_timezones`` is a list of useful, current timezones. It doesn't +contain deprecated zones or historical zones, except for a few I've +deemed in common usage, such as US/Eastern (open a bug report if you +think other timezones are deserving of being included here). It is also +a sequence of strings. + +>>> from pytz import common_timezones +>>> len(common_timezones) < len(all_timezones) +True +>>> 'Etc/Greenwich' in common_timezones +False +>>> 'Australia/Melbourne' in common_timezones +True +>>> 'US/Eastern' in common_timezones +True +>>> 'Canada/Eastern' in common_timezones +True +>>> 'Australia/Yancowinna' in all_timezones +True +>>> 'Australia/Yancowinna' in common_timezones +False + +Both ``common_timezones`` and ``all_timezones`` are alphabetically +sorted: + +>>> common_timezones_dupe = common_timezones[:] +>>> common_timezones_dupe.sort() +>>> common_timezones == common_timezones_dupe +True +>>> all_timezones_dupe = all_timezones[:] +>>> all_timezones_dupe.sort() +>>> all_timezones == all_timezones_dupe +True + +``all_timezones`` and ``common_timezones`` are also available as sets. + +>>> from pytz import all_timezones_set, common_timezones_set +>>> 'US/Eastern' in all_timezones_set +True +>>> 'US/Eastern' in common_timezones_set +True +>>> 'Australia/Victoria' in common_timezones_set +False + +You can also retrieve lists of timezones used by particular countries +using the ``country_timezones()`` function. It requires an ISO-3166 +two letter country code. + +>>> from pytz import country_timezones +>>> print(' '.join(country_timezones('ch'))) +Europe/Zurich +>>> print(' '.join(country_timezones('CH'))) +Europe/Zurich + + +Internationalization - i18n/l10n +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Pytz is an interface to the IANA database, which uses ASCII names. The `Unicode Consortium's Unicode Locales (CLDR) `_ +project provides translations. Python packages such as +`Babel `_ +and Thomas Khyn's `l18n `_ package can be used +to access these translations from Python. + + +License +~~~~~~~ + +MIT license. + +This code is also available as part of Zope 3 under the Zope Public +License, Version 2.1 (ZPL). + +I'm happy to relicense this code if necessary for inclusion in other +open source projects. + + +Latest Versions +~~~~~~~~~~~~~~~ + +This package will be updated after releases of the Olson timezone +database. The latest version can be downloaded from the `Python Package +Index `_. The code that is used +to generate this distribution is hosted on Github and available +using git:: + + git clone https://github.com/stub42/pytz.git + +Announcements of new releases are made on +`Launchpad `_, and the +`Atom feed `_ +hosted there. + + +Bugs, Feature Requests & Patches +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Bugs should be reported on `Github `_. +Feature requests are unlikely to be considered, and efforts instead directed +to timezone support now built into Python or packages that work with it. + + +Security Issues +~~~~~~~~~~~~~~~ + +Reports about security issues can be made via `Tidelift `_. + + +Issues & Limitations +~~~~~~~~~~~~~~~~~~~~ + +- This project is in maintenance mode. Projects using Python 3.9 or later + are best served by using the timezone functionaly now included in core + Python and packages that work with it such as `tzdata `_. + +- Offsets from UTC are rounded to the nearest whole minute, so timezones + such as Europe/Amsterdam pre 1937 will be up to 30 seconds out. This + was a limitation of the Python datetime library. + +- If you think a timezone definition is incorrect, I probably can't fix + it. pytz is a direct translation of the Olson timezone database, and + changes to the timezone definitions need to be made to this source. + If you find errors they should be reported to the time zone mailing + list, linked from http://www.iana.org/time-zones. + + +Further Reading +~~~~~~~~~~~~~~~ + +More info than you want to know about timezones: +https://data.iana.org/time-zones/tz-link.html + + +Contact +~~~~~~~ + +Stuart Bishop diff --git a/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/RECORD b/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/RECORD new file mode 100644 index 0000000000000000000000000000000000000000..ff7b5d3017fcf1aa5e6b7f9bbc552d56f53e37a0 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pytz-2026.1.post1.dist-info/RECORD @@ -0,0 +1,623 @@ 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Columns are +# separated by a single tab. Lines beginning with ‘#’ are comments. +# All text uses UTF-8 encoding. The columns of the table are as follows: +# +# 1. ISO 3166-1 alpha-2 country code, current as of +# ISO/TC 46 N1127 (2024-02-29). See: ISO/TC 46 Documents +# https://www.iso.org/committee/48750.html?view=documents +# 2. The usual English name for the coded region. This sometimes +# departs from ISO-listed names, sometimes so that sorted subsets +# of names are useful (e.g., “Samoa (American)” and “Samoa +# (western)” rather than “American Samoa” and “Samoa”), +# sometimes to avoid confusion among non-experts (e.g., +# “Czech Republic” and “Turkey” rather than “Czechia” and “Türkiye”), +# and sometimes to omit needless detail or churn (e.g., “Netherlands” +# rather than “Netherlands (the)” or “Netherlands (Kingdom of the)”). +# +# The table is sorted by country code. +# +# This table is intended as an aid for users, to help them select time +# zone data appropriate for their practical needs. It is not intended +# to take or endorse any position on legal or territorial claims. +# +#country- +#code name of country, territory, area, or subdivision +AD Andorra +AE United Arab Emirates +AF Afghanistan +AG Antigua & Barbuda +AI Anguilla +AL Albania +AM Armenia +AO Angola +AQ Antarctica +AR Argentina +AS Samoa (American) +AT Austria +AU Australia +AW Aruba +AX Åland Islands +AZ Azerbaijan +BA Bosnia & Herzegovina +BB Barbados +BD Bangladesh +BE Belgium +BF Burkina Faso +BG Bulgaria +BH Bahrain +BI Burundi +BJ Benin +BL St Barthelemy +BM Bermuda +BN Brunei +BO Bolivia +BQ Caribbean NL +BR Brazil +BS Bahamas +BT Bhutan +BV Bouvet Island +BW Botswana +BY Belarus +BZ Belize +CA Canada +CC Cocos (Keeling) Islands +CD Congo (Dem. Rep.) +CF Central African Rep. +CG Congo (Rep.) +CH Switzerland +CI Côte d’Ivoire +CK Cook Islands +CL Chile +CM Cameroon +CN China +CO Colombia +CR Costa Rica +CU Cuba +CV Cape Verde +CW Curaçao +CX Christmas Island +CY Cyprus +CZ Czech Republic +DE Germany +DJ Djibouti +DK Denmark +DM Dominica +DO Dominican Republic +DZ Algeria +EC Ecuador +EE Estonia +EG Egypt +EH Western Sahara +ER Eritrea +ES Spain +ET Ethiopia +FI Finland +FJ Fiji +FK Falkland Islands +FM Micronesia +FO Faroe Islands +FR France +GA Gabon +GB Britain (UK) +GD Grenada +GE Georgia +GF French Guiana +GG Guernsey +GH Ghana +GI Gibraltar +GL Greenland +GM Gambia +GN Guinea +GP Guadeloupe +GQ Equatorial Guinea +GR Greece +GS South Georgia & the South Sandwich Islands +GT Guatemala +GU Guam +GW Guinea-Bissau +GY Guyana +HK Hong Kong +HM Heard Island & McDonald Islands +HN Honduras +HR Croatia +HT Haiti +HU Hungary +ID Indonesia +IE Ireland +IL Israel +IM Isle of Man +IN India +IO British Indian Ocean Territory +IQ Iraq +IR Iran +IS Iceland +IT Italy +JE Jersey +JM Jamaica +JO Jordan +JP Japan +KE Kenya +KG Kyrgyzstan +KH Cambodia +KI Kiribati +KM Comoros +KN St Kitts & Nevis +KP Korea (North) +KR Korea (South) +KW Kuwait +KY Cayman Islands +KZ Kazakhstan +LA Laos +LB Lebanon +LC St Lucia +LI Liechtenstein +LK Sri Lanka +LR Liberia +LS Lesotho +LT Lithuania +LU Luxembourg +LV Latvia +LY Libya +MA Morocco +MC Monaco +MD Moldova +ME Montenegro +MF St Martin (French) +MG Madagascar +MH Marshall Islands +MK North Macedonia +ML Mali +MM Myanmar (Burma) +MN Mongolia +MO Macau +MP Northern Mariana Islands +MQ Martinique +MR Mauritania +MS Montserrat +MT Malta +MU Mauritius +MV Maldives +MW Malawi +MX Mexico +MY Malaysia +MZ Mozambique +NA Namibia +NC New Caledonia +NE Niger +NF Norfolk Island +NG Nigeria +NI Nicaragua +NL Netherlands +NO Norway +NP Nepal +NR Nauru +NU Niue +NZ New Zealand +OM Oman +PA Panama +PE Peru +PF French Polynesia +PG Papua New Guinea +PH Philippines +PK Pakistan +PL Poland +PM St Pierre & Miquelon +PN Pitcairn +PR Puerto Rico +PS Palestine +PT Portugal +PW Palau +PY Paraguay +QA Qatar +RE Réunion +RO Romania +RS Serbia +RU Russia +RW Rwanda +SA Saudi Arabia +SB Solomon Islands +SC Seychelles +SD Sudan +SE Sweden +SG Singapore +SH St Helena +SI Slovenia +SJ Svalbard & Jan Mayen +SK Slovakia +SL Sierra Leone +SM San Marino +SN Senegal +SO Somalia +SR Suriname +SS South Sudan +ST Sao Tome & Principe +SV El Salvador +SX St Maarten (Dutch) +SY Syria +SZ Eswatini (Swaziland) +TC Turks & Caicos Is +TD Chad +TF French S. Terr. +TG Togo +TH Thailand +TJ Tajikistan +TK Tokelau +TL East Timor +TM Turkmenistan +TN Tunisia +TO Tonga +TR Turkey +TT Trinidad & Tobago +TV Tuvalu +TW Taiwan +TZ Tanzania +UA Ukraine +UG Uganda +UM US minor outlying islands +US United States +UY Uruguay +UZ Uzbekistan +VA Vatican City +VC St Vincent +VE Venezuela +VG Virgin Islands (UK) +VI Virgin Islands (US) +VN Vietnam +VU Vanuatu +WF Wallis & Futuna +WS Samoa (western) +YE Yemen +YT Mayotte +ZA South Africa +ZM Zambia +ZW Zimbabwe diff --git a/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/leapseconds b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/leapseconds new file mode 100644 index 0000000000000000000000000000000000000000..a796e4b4e22e2d4bd28c1763bced1a154172409f --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/leapseconds @@ -0,0 +1,86 @@ +# Allowance for leap seconds added to each time zone file. + +# This file is in the public domain. + +# This file is generated automatically from the data in the public-domain +# NIST/IERS format leap-seconds.list file, which can be copied from +# +# or via a less-secure protocol and with different comments and +# less volatile last-modified and expiration timestamps, from +# . +# For more about leap-seconds.list, please see +# The NTP Timescale and Leap Seconds +# . + +# The rules for leap seconds are specified in Annex 1 (Time scales) of: +# Standard-frequency and time-signal emissions. +# International Telecommunication Union - Radiocommunication Sector +# (ITU-R) Recommendation TF.460-6 (02/2002) +# . +# The International Earth Rotation and Reference Systems Service (IERS) +# periodically uses leap seconds to keep UTC to within 0.9 s of UT1 +# (a proxy for Earth's angle in space as measured by astronomers) +# and publishes leap second data in a copyrighted file +# . +# See: Levine J. Coordinated Universal Time and the leap second. +# URSI Radio Sci Bull. 2016;89(4):30-6. doi:10.23919/URSIRSB.2016.7909995 +# . + +# There were no leap seconds before 1972, as no official mechanism +# accounted for the discrepancy between atomic time (TAI) and the earth's +# rotation. The first ("1 Jan 1972") data line in leap-seconds.list +# does not denote a leap second; it denotes the start of the current definition +# of UTC. + +# All leap-seconds are Stationary (S) at the given UTC time. +# The correction (+ or -) is made at the given time, so in the unlikely +# event of a negative leap second, a line would look like this: +# Leap YEAR MON DAY 23:59:59 - S +# Typical lines look like this: +# Leap YEAR MON DAY 23:59:60 + S +Leap 1972 Jun 30 23:59:60 + S +Leap 1972 Dec 31 23:59:60 + S +Leap 1973 Dec 31 23:59:60 + S +Leap 1974 Dec 31 23:59:60 + S +Leap 1975 Dec 31 23:59:60 + S +Leap 1976 Dec 31 23:59:60 + S +Leap 1977 Dec 31 23:59:60 + S +Leap 1978 Dec 31 23:59:60 + S +Leap 1979 Dec 31 23:59:60 + S +Leap 1981 Jun 30 23:59:60 + S +Leap 1982 Jun 30 23:59:60 + S +Leap 1983 Jun 30 23:59:60 + S +Leap 1985 Jun 30 23:59:60 + S +Leap 1987 Dec 31 23:59:60 + S +Leap 1989 Dec 31 23:59:60 + S +Leap 1990 Dec 31 23:59:60 + S +Leap 1992 Jun 30 23:59:60 + S +Leap 1993 Jun 30 23:59:60 + S +Leap 1994 Jun 30 23:59:60 + S +Leap 1995 Dec 31 23:59:60 + S +Leap 1997 Jun 30 23:59:60 + S +Leap 1998 Dec 31 23:59:60 + S +Leap 2005 Dec 31 23:59:60 + S +Leap 2008 Dec 31 23:59:60 + S +Leap 2012 Jun 30 23:59:60 + S +Leap 2015 Jun 30 23:59:60 + S +Leap 2016 Dec 31 23:59:60 + S + +# UTC timestamp when this leap second list expires. +# Any additional leap seconds will come after this. +# This Expires line is commented out for now, +# so that pre-2020a zic implementations do not reject this file. +#Expires 2026 Dec 28 00:00:00 + +# Here are POSIX timestamps for the data in this file. +# "#updated" gives the last time the leap seconds data changed +# or, if this file was derived from the IERS leap-seconds.list, +# the last time that file changed in any way. +# "#expires" gives the first time this file might be wrong; +# if this file was derived from the IERS leap-seconds.list, +# this is typically a bit less than one year after "updated". +#updated 1767698058 (2026-01-06 11:14:18 UTC) +#expires 1798416000 (2026-12-28 00:00:00 UTC) + +# Updated through IERS Bulletin C (https://hpiers.obspm.fr/iers/bul/bulc/bulletinc.dat) +# File expires on 28 December 2026 diff --git a/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/tzdata.zi b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/tzdata.zi new file mode 100644 index 0000000000000000000000000000000000000000..28ffb729356c4c468f3f3c974c0010a18da1b734 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/tzdata.zi @@ -0,0 +1,4300 @@ +# version unknown +# redo posix_only +# This zic input file is in the public domain. +R d 1916 o - Jun 14 23s 1 S +R d 1916 1919 - O Su>=1 23s 0 - +R d 1917 o - Mar 24 23s 1 S +R d 1918 o - Mar 9 23s 1 S +R d 1919 o - Mar 1 23s 1 S +R d 1920 o - F 14 23s 1 S +R d 1920 o - O 23 23s 0 - +R d 1921 o - Mar 14 23s 1 S +R d 1921 o - Jun 21 23s 0 - +R d 1939 o - S 11 23s 1 S +R d 1939 o - N 19 1 0 - +R d 1944 1945 - Ap M>=1 2 1 S +R d 1944 o - O 8 2 0 - +R d 1945 o - S 16 1 0 - +R d 1971 o - Ap 25 23s 1 S +R d 1971 o - S 26 23s 0 - +R d 1977 o - May 6 0 1 S +R d 1977 o - O 21 0 0 - +R d 1978 o - Mar 24 1 1 S +R d 1978 o - S 22 3 0 - +R d 1980 o - Ap 25 0 1 S +R d 1980 o - O 31 2 0 - +R K 1940 o - Jul 15 0 1 S +R K 1940 o - O 1 0 0 - +R K 1941 o - Ap 15 0 1 S +R K 1941 o - S 16 0 0 - +R K 1942 1944 - Ap 1 0 1 S +R K 1942 o - O 27 0 0 - +R K 1943 1945 - N 1 0 0 - +R K 1945 o - Ap 16 0 1 S +R K 1957 o - May 10 0 1 S +R K 1957 1958 - O 1 0 0 - +R K 1958 o - May 1 0 1 S +R K 1959 1981 - May 1 1 1 S +R K 1959 1965 - S 30 3 0 - +R K 1966 1994 - O 1 3 0 - +R K 1982 o - Jul 25 1 1 S +R K 1983 o - Jul 12 1 1 S +R K 1984 1988 - May 1 1 1 S +R K 1989 o - May 6 1 1 S +R K 1990 1994 - May 1 1 1 S +R K 1995 2010 - Ap lastF 0s 1 S +R K 1995 2005 - S lastTh 24 0 - +R K 2006 o - S 21 24 0 - +R K 2007 o - S Th>=1 24 0 - +R K 2008 o - Au lastTh 24 0 - +R K 2009 o - Au 20 24 0 - +R K 2010 o - Au 10 24 0 - +R K 2010 o - S 9 24 1 S +R K 2010 o - S lastTh 24 0 - +R K 2014 o - May 15 24 1 S +R K 2014 o - Jun 26 24 0 - +R K 2014 o - Jul 31 24 1 S +R K 2014 o - S lastTh 24 0 - +R K 2023 ma - Ap lastF 0 1 S +R K 2023 ma - O lastTh 24 0 - +R L 1951 o - O 14 2 1 S +R L 1952 o - Ja 1 0 0 - +R L 1953 o - O 9 2 1 S +R L 1954 o - Ja 1 0 0 - +R L 1955 o - S 30 0 1 S +R L 1956 o - Ja 1 0 0 - +R L 1982 1984 - Ap 1 0 1 S +R L 1982 1985 - O 1 0 0 - +R L 1985 o - Ap 6 0 1 S +R L 1986 o - Ap 4 0 1 S +R L 1986 o - O 3 0 0 - +R L 1987 1989 - Ap 1 0 1 S +R L 1987 1989 - O 1 0 0 - +R L 1997 o - Ap 4 0 1 S +R L 1997 o - O 4 0 0 - +R L 2013 o - Mar lastF 1 1 S +R L 2013 o - O lastF 2 0 - +R MU 1982 o - O 10 0 1 - +R MU 1983 o - Mar 21 0 0 - +R MU 2008 o - O lastSu 2 1 - +R MU 2009 o - Mar lastSu 2 0 - +R M 1939 o - S 12 0 1 - +R M 1939 o - N 19 0 0 - +R M 1940 o - F 25 0 1 - +R M 1945 o - N 18 0 0 - +R M 1950 o - Jun 11 0 1 - +R M 1950 o - O 29 0 0 - +R M 1967 o - Jun 3 12 1 - +R M 1967 o - O 1 0 0 - +R M 1974 o - Jun 24 0 1 - +R M 1974 o - S 1 0 0 - +R M 1976 1977 - May 1 0 1 - +R M 1976 o - Au 1 0 0 - +R M 1977 o - S 28 0 0 - +R M 1978 o - Jun 1 0 1 - +R M 1978 o - Au 4 0 0 - +R M 2008 o - Jun 1 0 1 - +R M 2008 o - S 1 0 0 - +R M 2009 o - Jun 1 0 1 - +R M 2009 o - Au 21 0 0 - +R M 2010 o - May 2 0 1 - +R M 2010 o - Au 8 0 0 - +R M 2011 o - Ap 3 0 1 - +R M 2011 o - Jul 31 0 0 - +R M 2012 2013 - Ap lastSu 2 1 - +R M 2012 o - Jul 20 3 0 - +R M 2012 o - Au 20 2 1 - +R M 2012 o - S 30 3 0 - +R M 2013 o - Jul 7 3 0 - +R M 2013 o - Au 10 2 1 - +R M 2013 2018 - O lastSu 3 0 - +R M 2014 2018 - Mar lastSu 2 1 - +R M 2014 o - Jun 28 3 0 - +R M 2014 o - Au 2 2 1 - +R M 2015 o - Jun 14 3 0 - +R M 2015 o - Jul 19 2 1 - +R M 2016 o - Jun 5 3 0 - +R M 2016 o - Jul 10 2 1 - +R M 2017 o - May 21 3 0 - +R M 2017 o - Jul 2 2 1 - +R M 2018 o - May 13 3 0 - +R M 2018 o - Jun 17 2 1 - +R M 2019 o - May 5 3 -1 - +R M 2019 o - Jun 9 2 0 - +R M 2020 o - Ap 19 3 -1 - +R M 2020 o - May 31 2 0 - +R M 2021 o - Ap 11 3 -1 - +R M 2021 o - May 16 2 0 - +R M 2022 o - Mar 27 3 -1 - +R M 2022 o - May 8 2 0 - +R M 2023 o - Mar 19 3 -1 - +R M 2023 o - Ap 23 2 0 - +R M 2024 o - Mar 10 3 -1 - +R M 2024 o - Ap 14 2 0 - +R M 2025 o - F 23 3 -1 - +R M 2025 o - Ap 6 2 0 - +R M 2026 o - F 15 3 -1 - +R M 2026 o - Mar 22 2 0 - +R M 2027 o - F 7 3 -1 - +R M 2027 o - Mar 14 2 0 - +R M 2028 o - Ja 23 3 -1 - +R M 2028 o - Mar 5 2 0 - +R M 2029 o - Ja 14 3 -1 - +R M 2029 o - F 18 2 0 - +R M 2029 o - D 30 3 -1 - +R M 2030 o - F 10 2 0 - +R M 2030 o - D 22 3 -1 - +R M 2031 o - Ja 26 2 0 - +R M 2031 o - D 14 3 -1 - +R M 2032 o - Ja 18 2 0 - +R M 2032 o - N 28 3 -1 - +R M 2033 o - Ja 9 2 0 - +R M 2033 o - N 20 3 -1 - +R M 2033 o - D 25 2 0 - +R M 2034 o - N 5 3 -1 - +R M 2034 o - D 17 2 0 - +R M 2035 o - O 28 3 -1 - +R M 2035 o - D 9 2 0 - +R M 2036 o - O 19 3 -1 - +R M 2036 o - N 23 2 0 - +R M 2037 o - O 4 3 -1 - +R M 2037 o - N 15 2 0 - +R M 2038 o - S 26 3 -1 - +R M 2038 o - O 31 2 0 - +R M 2039 o - S 18 3 -1 - +R M 2039 o - O 23 2 0 - +R M 2040 o - S 2 3 -1 - +R M 2040 o - O 14 2 0 - +R M 2041 o - Au 25 3 -1 - +R M 2041 o - S 29 2 0 - +R M 2042 o - Au 10 3 -1 - +R M 2042 o - S 21 2 0 - +R M 2043 o - Au 2 3 -1 - +R M 2043 o - S 13 2 0 - +R M 2044 o - Jul 24 3 -1 - +R M 2044 o - Au 28 2 0 - +R M 2045 o - Jul 9 3 -1 - +R M 2045 o - Au 20 2 0 - +R M 2046 o - Jul 1 3 -1 - +R M 2046 o - Au 5 2 0 - +R M 2047 o - Jun 23 3 -1 - +R M 2047 o - Jul 28 2 0 - +R M 2048 o - Jun 7 3 -1 - +R M 2048 o - Jul 19 2 0 - +R M 2049 o - May 30 3 -1 - +R M 2049 o - Jul 4 2 0 - +R M 2050 o - May 15 3 -1 - +R M 2050 o - Jun 26 2 0 - +R M 2051 o - May 7 3 -1 - +R M 2051 o - Jun 18 2 0 - +R M 2052 o - Ap 28 3 -1 - +R M 2052 o - Jun 2 2 0 - +R M 2053 o - Ap 13 3 -1 - +R M 2053 o - May 25 2 0 - +R M 2054 o - Ap 5 3 -1 - +R M 2054 o - May 10 2 0 - +R M 2055 o - Mar 28 3 -1 - +R M 2055 o - May 2 2 0 - +R M 2056 o - Mar 12 3 -1 - +R M 2056 o - Ap 23 2 0 - +R M 2057 o - Mar 4 3 -1 - +R M 2057 o - Ap 8 2 0 - +R M 2058 o - F 17 3 -1 - +R M 2058 o - Mar 31 2 0 - +R M 2059 o - F 9 3 -1 - +R M 2059 o - Mar 23 2 0 - +R M 2060 o - F 1 3 -1 - +R M 2060 o - Mar 7 2 0 - +R M 2061 o - Ja 16 3 -1 - +R M 2061 o - F 27 2 0 - +R M 2062 o - Ja 8 3 -1 - +R M 2062 o - F 12 2 0 - +R M 2062 o - D 31 3 -1 - +R M 2063 o - F 4 2 0 - +R M 2063 o - D 16 3 -1 - +R M 2064 o - Ja 27 2 0 - +R M 2064 o - D 7 3 -1 - +R M 2065 o - Ja 11 2 0 - +R M 2065 o - N 22 3 -1 - +R M 2066 o - Ja 3 2 0 - +R M 2066 o - N 14 3 -1 - +R M 2066 o - D 26 2 0 - +R M 2067 o - N 6 3 -1 - +R M 2067 o - D 11 2 0 - +R M 2068 o - O 21 3 -1 - +R M 2068 o - D 2 2 0 - +R M 2069 o - O 13 3 -1 - +R M 2069 o - N 17 2 0 - +R M 2070 o - O 5 3 -1 - +R M 2070 o - N 9 2 0 - +R M 2071 o - S 20 3 -1 - +R M 2071 o - N 1 2 0 - +R M 2072 o - S 11 3 -1 - +R M 2072 o - O 16 2 0 - +R M 2073 o - Au 27 3 -1 - +R M 2073 o - O 8 2 0 - +R M 2074 o - Au 19 3 -1 - +R M 2074 o - S 30 2 0 - +R M 2075 o - Au 11 3 -1 - +R M 2075 o - S 15 2 0 - +R M 2076 o - Jul 26 3 -1 - +R M 2076 o - S 6 2 0 - +R M 2077 o - Jul 18 3 -1 - +R M 2077 o - Au 22 2 0 - +R M 2078 o - Jul 10 3 -1 - +R M 2078 o - Au 14 2 0 - +R M 2079 o - Jun 25 3 -1 - +R M 2079 o - Au 6 2 0 - +R M 2080 o - Jun 16 3 -1 - +R M 2080 o - Jul 21 2 0 - +R M 2081 o - Jun 1 3 -1 - +R M 2081 o - Jul 13 2 0 - +R M 2082 o - May 24 3 -1 - +R M 2082 o - Jun 28 2 0 - +R M 2083 o - May 16 3 -1 - +R M 2083 o - Jun 20 2 0 - +R M 2084 o - Ap 30 3 -1 - +R M 2084 o - Jun 11 2 0 - +R M 2085 o - Ap 22 3 -1 - +R M 2085 o - May 27 2 0 - +R M 2086 o - Ap 14 3 -1 - +R M 2086 o - May 19 2 0 - +R M 2087 o - Mar 30 3 -1 - +R M 2087 o - May 11 2 0 - +R NA 1994 o - Mar 21 0 -1 WAT +R NA 1994 2017 - S Su>=1 2 0 CAT +R NA 1995 2017 - Ap Su>=1 2 -1 WAT +R SA 1942 1943 - S Su>=15 2 1 - +R SA 1943 1944 - Mar Su>=15 2 0 - +R SD 1970 o - May 1 0 1 S +R SD 1970 1985 - O 15 0 0 - +R SD 1971 o - Ap 30 0 1 S +R SD 1972 1985 - Ap lastSu 0 1 S +R n 1939 o - Ap 15 23s 1 S +R n 1939 o - N 18 23s 0 - +R n 1940 o - F 25 23s 1 S +R n 1941 o - O 6 0 0 - +R n 1942 o - Mar 9 0 1 S +R n 1942 o - N 2 3 0 - +R n 1943 o - Mar 29 2 1 S +R n 1943 o - Ap 17 2 0 - +R n 1943 o - Ap 25 2 1 S +R n 1943 o - O 4 2 0 - +R n 1944 1945 - Ap M>=1 2 1 S +R n 1944 o - O 8 0 0 - +R n 1945 o - S 16 0 0 - +R n 1977 o - Ap 30 0s 1 S +R n 1977 o - S 24 0s 0 - +R n 1978 o - May 1 0s 1 S +R n 1978 o - O 1 0s 0 - +R n 1988 o - Jun 1 0s 1 S +R n 1988 1990 - S lastSu 0s 0 - +R n 1989 o - Mar 26 0s 1 S +R n 1990 o - May 1 0s 1 S +R n 2005 o - May 1 0s 1 S +R n 2005 o - S 30 1s 0 - +R n 2006 2008 - Mar lastSu 2s 1 S +R n 2006 2008 - O lastSu 2s 0 - +R Tr 2005 ma - Mar lastSu 1u 2 +02 +R Tr 2004 ma - O lastSu 1u 0 +00 +R AM 2011 o - Mar lastSu 2s 1 - +R AM 2011 o - O lastSu 2s 0 - +R AZ 1997 2015 - Mar lastSu 4 1 - +R AZ 1997 2015 - O lastSu 5 0 - +R BD 2009 o - Jun 19 23 1 - +R BD 2009 o - D 31 24 0 - +R Sh 1919 o - Ap 12 24 1 D +R Sh 1919 o - S 30 24 0 S +R Sh 1940 o - Jun 1 0 1 D +R Sh 1940 o - O 12 24 0 S +R Sh 1941 o - Mar 15 0 1 D +R Sh 1941 o - N 1 24 0 S +R Sh 1942 o - Ja 31 0 1 D +R Sh 1945 o - S 1 24 0 S +R Sh 1946 o - May 15 0 1 D +R Sh 1946 o - S 30 24 0 S +R Sh 1947 o - Ap 15 0 1 D +R Sh 1947 o - O 31 24 0 S +R Sh 1948 1949 - May 1 0 1 D +R Sh 1948 1949 - S 30 24 0 S +R CN 1986 o - May 4 2 1 D +R CN 1986 1991 - S Su>=11 2 0 S +R CN 1987 1991 - Ap Su>=11 2 1 D +R HK 1946 o - Ap 21 0 1 S +R HK 1946 o - D 1 3:30s 0 - +R HK 1947 o - Ap 13 3:30s 1 S +R HK 1947 o - N 30 3:30s 0 - +R HK 1948 o - May 2 3:30s 1 S +R HK 1948 1952 - O Su>=28 3:30s 0 - +R HK 1949 1953 - Ap Su>=1 3:30 1 S +R HK 1953 1964 - O Su>=31 3:30 0 - +R HK 1954 1964 - Mar Su>=18 3:30 1 S +R HK 1965 1976 - Ap Su>=16 3:30 1 S +R HK 1965 1976 - O Su>=16 3:30 0 - +R HK 1973 o - D 30 3:30 1 S +R HK 1979 o - May 13 3:30 1 S +R HK 1979 o - O 21 3:30 0 - +R f 1946 o - May 15 0 1 D +R f 1946 o - O 1 0 0 S +R f 1947 o - Ap 15 0 1 D +R f 1947 o - N 1 0 0 S +R f 1948 1951 - May 1 0 1 D +R f 1948 1951 - O 1 0 0 S +R f 1952 o - Mar 1 0 1 D +R f 1952 1954 - N 1 0 0 S +R f 1953 1959 - Ap 1 0 1 D +R f 1955 1961 - O 1 0 0 S +R f 1960 1961 - Jun 1 0 1 D +R f 1974 1975 - Ap 1 0 1 D +R f 1974 1975 - O 1 0 0 S +R f 1979 o - Jul 1 0 1 D +R f 1979 o - O 1 0 0 S +R _ 1942 1943 - Ap 30 23 1 - +R _ 1942 o - N 17 23 0 - +R _ 1943 o - S 30 23 0 S +R _ 1946 o - Ap 30 23s 1 D +R _ 1946 o - S 30 23s 0 S +R _ 1947 o - Ap 19 23s 1 D +R _ 1947 o - N 30 23s 0 S +R _ 1948 o - May 2 23s 1 D +R _ 1948 o - O 31 23s 0 S +R _ 1949 1950 - Ap Sa>=1 23s 1 D +R _ 1949 1950 - O lastSa 23s 0 S +R _ 1951 o - Mar 31 23s 1 D +R _ 1951 o - O 28 23s 0 S +R _ 1952 1953 - Ap Sa>=1 23s 1 D +R _ 1952 o - N 1 23s 0 S +R _ 1953 1954 - O lastSa 23s 0 S +R _ 1954 1956 - Mar Sa>=17 23s 1 D +R _ 1955 o - N 5 23s 0 S +R _ 1956 1964 - N Su>=1 3:30 0 S +R _ 1957 1964 - Mar Su>=18 3:30 1 D +R _ 1965 1973 - Ap Su>=16 3:30 1 D +R _ 1965 1966 - O Su>=16 2:30 0 S +R _ 1967 1976 - O Su>=16 3:30 0 S +R _ 1973 o - D 30 3:30 1 D +R _ 1975 1976 - Ap Su>=16 3:30 1 D +R _ 1979 o - May 13 3:30 1 D +R _ 1979 o - O Su>=16 3:30 0 S +R CY 1975 o - Ap 13 0 1 S +R CY 1975 o - O 12 0 0 - +R CY 1976 o - May 15 0 1 S +R CY 1976 o - O 11 0 0 - +R CY 1977 1980 - Ap Su>=1 0 1 S +R CY 1977 o - S 25 0 0 - +R CY 1978 o - O 2 0 0 - +R CY 1979 1997 - S lastSu 0 0 - +R CY 1981 1998 - Mar lastSu 0 1 S +R i 1910 o - Ja 1 0 0 - +R i 1977 o - Mar 21 23 1 - +R i 1977 o - O 20 24 0 - +R i 1978 o - Mar 24 24 1 - +R i 1978 o - Au 5 1 0 - +R i 1979 o - May 26 24 1 - +R i 1979 o - S 18 24 0 - +R i 1980 o - Mar 20 24 1 - +R i 1980 o - S 22 24 0 - +R i 1991 o - May 2 24 1 - +R i 1992 1995 - Mar 21 24 1 - +R i 1991 1995 - S 21 24 0 - +R i 1996 o - Mar 20 24 1 - +R i 1996 o - S 20 24 0 - +R i 1997 1999 - Mar 21 24 1 - +R i 1997 1999 - S 21 24 0 - +R i 2000 o - Mar 20 24 1 - +R i 2000 o - S 20 24 0 - +R i 2001 2003 - Mar 21 24 1 - +R i 2001 2003 - S 21 24 0 - +R i 2004 o - Mar 20 24 1 - +R i 2004 o - S 20 24 0 - +R i 2005 o - Mar 21 24 1 - +R i 2005 o - S 21 24 0 - +R i 2008 o - Mar 20 24 1 - +R i 2008 o - S 20 24 0 - +R i 2009 2011 - Mar 21 24 1 - +R i 2009 2011 - S 21 24 0 - +R i 2012 o - Mar 20 24 1 - +R i 2012 o - S 20 24 0 - +R i 2013 2015 - Mar 21 24 1 - +R i 2013 2015 - S 21 24 0 - +R i 2016 o - Mar 20 24 1 - +R i 2016 o - S 20 24 0 - +R i 2017 2019 - Mar 21 24 1 - +R i 2017 2019 - S 21 24 0 - +R i 2020 o - Mar 20 24 1 - +R i 2020 o - S 20 24 0 - +R i 2021 2022 - Mar 21 24 1 - +R i 2021 2022 - S 21 24 0 - +R IQ 1982 o - May 1 0 1 - +R IQ 1982 1984 - O 1 0 0 - +R IQ 1983 o - Mar 31 0 1 - +R IQ 1984 1985 - Ap 1 0 1 - +R IQ 1985 1990 - S lastSu 1s 0 - +R IQ 1986 1990 - Mar lastSu 1s 1 - +R IQ 1991 2007 - Ap 1 3s 1 - +R IQ 1991 2007 - O 1 3s 0 - +R Z 1940 o - May 31 24u 1 D +R Z 1940 o - S 30 24u 0 S +R Z 1940 o - N 16 24u 1 D +R Z 1942 1946 - O 31 24u 0 S +R Z 1943 1944 - Mar 31 24u 1 D +R Z 1945 1946 - Ap 15 24u 1 D +R Z 1948 o - May 22 24u 2 DD +R Z 1948 o - Au 31 24u 1 D +R Z 1948 1949 - O 31 24u 0 S +R Z 1949 o - Ap 30 24u 1 D +R Z 1950 o - Ap 15 24u 1 D +R Z 1950 o - S 14 24u 0 S +R Z 1951 o - Mar 31 24u 1 D +R Z 1951 o - N 10 24u 0 S +R Z 1952 o - Ap 19 24u 1 D +R Z 1952 o - O 18 24u 0 S +R Z 1953 o - Ap 11 24u 1 D +R Z 1953 o - S 12 24u 0 S +R Z 1954 o - Jun 12 24u 1 D +R Z 1954 o - S 11 24u 0 S +R Z 1955 o - Jun 11 24u 1 D +R Z 1955 o - S 10 24u 0 S +R Z 1956 o - Jun 2 24u 1 D +R Z 1956 o - S 29 24u 0 S +R Z 1957 o - Ap 27 24u 1 D +R Z 1957 o - S 21 24u 0 S +R Z 1974 o - Jul 6 24 1 D +R Z 1974 o - O 12 24 0 S +R Z 1975 o - Ap 19 24 1 D +R Z 1975 o - Au 30 24 0 S +R Z 1980 o - Au 2 24s 1 D +R Z 1980 o - S 13 24s 0 S +R Z 1984 o - May 5 24s 1 D +R Z 1984 o - Au 25 24s 0 S +R Z 1985 o - Ap 13 24 1 D +R Z 1985 o - Au 31 24 0 S +R Z 1986 o - May 17 24 1 D +R Z 1986 o - S 6 24 0 S +R Z 1987 o - Ap 14 24 1 D +R Z 1987 o - S 12 24 0 S +R Z 1988 o - Ap 9 24 1 D +R Z 1988 o - S 3 24 0 S +R Z 1989 o - Ap 29 24 1 D +R Z 1989 o - S 2 24 0 S +R Z 1990 o - Mar 24 24 1 D +R Z 1990 o - Au 25 24 0 S +R Z 1991 o - Mar 23 24 1 D +R Z 1991 o - Au 31 24 0 S +R Z 1992 o - Mar 28 24 1 D +R Z 1992 o - S 5 24 0 S +R Z 1993 o - Ap 2 0 1 D +R Z 1993 o - S 5 0 0 S +R Z 1994 o - Ap 1 0 1 D +R Z 1994 o - Au 28 0 0 S +R Z 1995 o - Mar 31 0 1 D +R Z 1995 o - S 3 0 0 S +R Z 1996 o - Mar 14 24 1 D +R Z 1996 o - S 15 24 0 S +R Z 1997 o - Mar 20 24 1 D +R Z 1997 o - S 13 24 0 S +R Z 1998 o - Mar 20 0 1 D +R Z 1998 o - S 6 0 0 S +R Z 1999 o - Ap 2 2 1 D +R Z 1999 o - S 3 2 0 S +R Z 2000 o - Ap 14 2 1 D +R Z 2000 o - O 6 1 0 S +R Z 2001 o - Ap 9 1 1 D +R Z 2001 o - S 24 1 0 S +R Z 2002 o - Mar 29 1 1 D +R Z 2002 o - O 7 1 0 S +R Z 2003 o - Mar 28 1 1 D +R Z 2003 o - O 3 1 0 S +R Z 2004 o - Ap 7 1 1 D +R Z 2004 o - S 22 1 0 S +R Z 2005 2012 - Ap F<=1 2 1 D +R Z 2005 o - O 9 2 0 S +R Z 2006 o - O 1 2 0 S +R Z 2007 o - S 16 2 0 S +R Z 2008 o - O 5 2 0 S +R Z 2009 o - S 27 2 0 S +R Z 2010 o - S 12 2 0 S +R Z 2011 o - O 2 2 0 S +R Z 2012 o - S 23 2 0 S +R Z 2013 ma - Mar F>=23 2 1 D +R Z 2013 ma - O lastSu 2 0 S +R JP 1948 o - May Sa>=1 24 1 D +R JP 1948 1951 - S Sa>=8 25 0 S +R JP 1949 o - Ap Sa>=1 24 1 D +R JP 1950 1951 - May Sa>=1 24 1 D +R J 1973 o - Jun 6 0 1 S +R J 1973 1975 - O 1 0 0 - +R J 1974 1977 - May 1 0 1 S +R J 1976 o - N 1 0 0 - +R J 1977 o - O 1 0 0 - +R J 1978 o - Ap 30 0 1 S +R J 1978 o - S 30 0 0 - +R J 1985 o - Ap 1 0 1 S +R J 1985 o - O 1 0 0 - +R J 1986 1988 - Ap F>=1 0 1 S +R J 1986 1990 - O F>=1 0 0 - +R J 1989 o - May 8 0 1 S +R J 1990 o - Ap 27 0 1 S +R J 1991 o - Ap 17 0 1 S +R J 1991 o - S 27 0 0 - +R J 1992 o - Ap 10 0 1 S +R J 1992 1993 - O F>=1 0 0 - +R J 1993 1998 - Ap F>=1 0 1 S +R J 1994 o - S F>=15 0 0 - +R J 1995 1998 - S F>=15 0s 0 - +R J 1999 o - Jul 1 0s 1 S +R J 1999 2002 - S lastF 0s 0 - +R J 2000 2001 - Mar lastTh 0s 1 S +R J 2002 2012 - Mar lastTh 24 1 S +R J 2003 o - O 24 0s 0 - +R J 2004 o - O 15 0s 0 - +R J 2005 o - S lastF 0s 0 - +R J 2006 2011 - O lastF 0s 0 - +R J 2013 o - D 20 0 0 - +R J 2014 2021 - Mar lastTh 24 1 S +R J 2014 2022 - O lastF 0s 0 - +R J 2022 o - F lastTh 24 1 S +R KG 1992 1996 - Ap Su>=7 0s 1 - +R KG 1992 1996 - S lastSu 0 0 - +R KG 1997 2005 - Mar lastSu 2:30 1 - +R KG 1997 2004 - O lastSu 2:30 0 - +R KR 1948 o - Jun 1 0 1 D +R KR 1948 o - S 12 24 0 S +R KR 1949 o - Ap 3 0 1 D +R KR 1949 1951 - S Sa>=7 24 0 S +R KR 1950 o - Ap 1 0 1 D +R KR 1951 o - May 6 0 1 D +R KR 1955 o - May 5 0 1 D +R KR 1955 o - S 8 24 0 S +R KR 1956 o - May 20 0 1 D +R KR 1956 o - S 29 24 0 S +R KR 1957 1960 - May Su>=1 0 1 D +R KR 1957 1960 - S Sa>=17 24 0 S +R KR 1987 1988 - May Su>=8 2 1 D +R KR 1987 1988 - O Su>=8 3 0 S +R l 1920 o - Mar 28 0 1 S +R l 1920 o - O 25 0 0 - +R l 1921 o - Ap 3 0 1 S +R l 1921 o - O 3 0 0 - +R l 1922 o - Mar 26 0 1 S +R l 1922 o - O 8 0 0 - +R l 1923 o - Ap 22 0 1 S +R l 1923 o - S 16 0 0 - +R l 1957 1961 - May 1 0 1 S +R l 1957 1961 - O 1 0 0 - +R l 1972 o - Jun 22 0 1 S +R l 1972 1977 - O 1 0 0 - +R l 1973 1977 - May 1 0 1 S +R l 1978 o - Ap 30 0 1 S +R l 1978 o - S 30 0 0 - +R l 1984 1987 - May 1 0 1 S +R l 1984 1991 - O 16 0 0 - +R l 1988 o - Jun 1 0 1 S +R l 1989 o - May 10 0 1 S +R l 1990 1992 - May 1 0 1 S +R l 1992 o - O 4 0 0 - +R l 1993 ma - Mar lastSu 0 1 S +R l 1993 1998 - S lastSu 0 0 - +R l 1999 ma - O lastSu 0 0 - +R NB 1935 1941 - S 14 0 0:20 - +R NB 1935 1941 - D 14 0 0 - +R X 1983 1984 - Ap 1 0 1 - +R X 1983 o - O 1 0 0 - +R X 1985 1998 - Mar lastSu 0 1 - +R X 1984 1998 - S lastSu 0 0 - +R X 2001 o - Ap lastSa 2 1 - +R X 2001 2006 - S lastSa 2 0 - +R X 2002 2006 - Mar lastSa 2 1 - +R X 2015 2016 - Mar lastSa 2 1 - +R X 2015 2016 - S lastSa 0 0 - +R PK 2002 o - Ap Su>=2 0 1 S +R PK 2002 o - O Su>=2 0 0 - +R PK 2008 o - Jun 1 0 1 S +R PK 2008 2009 - N 1 0 0 - +R PK 2009 o - Ap 15 0 1 S +R P 1999 2005 - Ap F>=15 0 1 S +R P 1999 2003 - O F>=15 0 0 - +R P 2004 o - O 1 1 0 - +R P 2005 o - O 4 2 0 - +R P 2006 2007 - Ap 1 0 1 S +R P 2006 o - S 22 0 0 - +R P 2007 o - S 13 2 0 - +R P 2008 2009 - Mar lastF 0 1 S +R P 2008 o - S 1 0 0 - +R P 2009 o - S 4 1 0 - +R P 2010 o - Mar 26 0 1 S +R P 2010 o - Au 11 0 0 - +R P 2011 o - Ap 1 0:1 1 S +R P 2011 o - Au 1 0 0 - +R P 2011 o - Au 30 0 1 S +R P 2011 o - S 30 0 0 - +R P 2012 2014 - Mar lastTh 24 1 S +R P 2012 o - S 21 1 0 - +R P 2013 o - S 27 0 0 - +R P 2014 o - O 24 0 0 - +R P 2015 o - Mar 28 0 1 S +R P 2015 o - O 23 1 0 - +R P 2016 2018 - Mar Sa<=30 1 1 S +R P 2016 2018 - O Sa<=30 1 0 - +R P 2019 o - Mar 29 0 1 S +R P 2019 o - O Sa<=30 0 0 - +R P 2020 2021 - Mar Sa<=30 0 1 S +R P 2020 o - O 24 1 0 - +R P 2021 o - O 29 1 0 - +R P 2022 o - Mar 27 0 1 S +R P 2022 2035 - O Sa<=30 2 0 - +R P 2023 o - Ap 29 2 1 S +R P 2024 o - Ap 20 2 1 S +R P 2025 o - Ap 12 2 1 S +R P 2026 2054 - Mar Sa<=30 2 1 S +R P 2036 o - O 18 2 0 - +R P 2037 o - O 10 2 0 - +R P 2038 o - S 25 2 0 - +R P 2039 o - S 17 2 0 - +R P 2040 o - S 1 2 0 - +R P 2040 o - O 20 2 1 S +R P 2040 2067 - O Sa<=30 2 0 - +R P 2041 o - Au 24 2 0 - +R P 2041 o - O 5 2 1 S +R P 2042 o - Au 16 2 0 - +R P 2042 o - S 27 2 1 S +R P 2043 o - Au 1 2 0 - +R P 2043 o - S 19 2 1 S +R P 2044 o - Jul 23 2 0 - +R P 2044 o - S 3 2 1 S +R P 2045 o - Jul 15 2 0 - +R P 2045 o - Au 26 2 1 S +R P 2046 o - Jun 30 2 0 - +R P 2046 o - Au 18 2 1 S +R P 2047 o - Jun 22 2 0 - +R P 2047 o - Au 3 2 1 S +R P 2048 o - Jun 6 2 0 - +R P 2048 o - Jul 25 2 1 S +R P 2049 o - May 29 2 0 - +R P 2049 o - Jul 10 2 1 S +R P 2050 o - May 21 2 0 - +R P 2050 o - Jul 2 2 1 S +R P 2051 o - May 6 2 0 - +R P 2051 o - Jun 24 2 1 S +R P 2052 o - Ap 27 2 0 - +R P 2052 o - Jun 8 2 1 S +R P 2053 o - Ap 12 2 0 - +R P 2053 o - May 31 2 1 S +R P 2054 o - Ap 4 2 0 - +R P 2054 o - May 23 2 1 S +R P 2055 o - May 8 2 1 S +R P 2056 o - Ap 29 2 1 S +R P 2057 o - Ap 14 2 1 S +R P 2058 o - Ap 6 2 1 S +R P 2059 ma - Mar Sa<=30 2 1 S +R P 2068 o - O 20 2 0 - +R P 2069 o - O 12 2 0 - +R P 2070 o - O 4 2 0 - +R P 2071 o - S 19 2 0 - +R P 2072 o - S 10 2 0 - +R P 2072 o - O 22 2 1 S +R P 2072 ma - O Sa<=30 2 0 - +R P 2073 o - S 2 2 0 - +R P 2073 o - O 14 2 1 S +R P 2074 o - Au 18 2 0 - +R P 2074 o - O 6 2 1 S +R P 2075 o - Au 10 2 0 - +R P 2075 o - S 21 2 1 S +R P 2076 o - Jul 25 2 0 - +R P 2076 o - S 12 2 1 S +R P 2077 o - Jul 17 2 0 - +R P 2077 o - S 4 2 1 S +R P 2078 o - Jul 9 2 0 - +R P 2078 o - Au 20 2 1 S +R P 2079 o - Jun 24 2 0 - +R P 2079 o - Au 12 2 1 S +R P 2080 o - Jun 15 2 0 - +R P 2080 o - Jul 27 2 1 S +R P 2081 o - Jun 7 2 0 - +R P 2081 o - Jul 19 2 1 S +R P 2082 o - May 23 2 0 - +R P 2082 o - Jul 11 2 1 S +R P 2083 o - May 15 2 0 - +R P 2083 o - Jun 26 2 1 S +R P 2084 o - Ap 29 2 0 - +R P 2084 o - Jun 17 2 1 S +R P 2085 o - Ap 21 2 0 - +R P 2085 o - Jun 9 2 1 S +R P 2086 o - Ap 13 2 0 - +R P 2086 o - May 25 2 1 S +R PH 1936 o - O 31 24 1 D +R PH 1937 o - Ja 15 24 0 S +R PH 1941 o - D 15 24 1 D +R PH 1945 o - N 30 24 0 S +R PH 1954 o - Ap 11 24 1 D +R PH 1954 o - Jun 4 24 0 S +R PH 1977 o - Mar 27 24 1 D +R PH 1977 o - S 21 24 0 S +R PH 1990 o - May 21 0 1 D +R PH 1990 o - Jul 28 24 0 S +R S 1920 1923 - Ap Su>=15 2 1 S +R S 1920 1923 - O Su>=1 2 0 - +R S 1962 o - Ap 29 2 1 S +R S 1962 o - O 1 2 0 - +R S 1963 1965 - May 1 2 1 S +R S 1963 o - S 30 2 0 - +R S 1964 o - O 1 2 0 - +R S 1965 o - S 30 2 0 - +R S 1966 o - Ap 24 2 1 S +R S 1966 1976 - O 1 2 0 - +R S 1967 1978 - May 1 2 1 S +R S 1977 1978 - S 1 2 0 - +R S 1983 1984 - Ap 9 2 1 S +R S 1983 1984 - O 1 2 0 - +R S 1986 o - F 16 2 1 S +R S 1986 o - O 9 2 0 - +R S 1987 o - Mar 1 2 1 S +R S 1987 1988 - O 31 2 0 - +R S 1988 o - Mar 15 2 1 S +R S 1989 o - Mar 31 2 1 S +R S 1989 o - O 1 2 0 - +R S 1990 o - Ap 1 2 1 S +R S 1990 o - S 30 2 0 - +R S 1991 o - Ap 1 0 1 S +R S 1991 1992 - O 1 0 0 - +R S 1992 o - Ap 8 0 1 S +R S 1993 o - Mar 26 0 1 S +R S 1993 o - S 25 0 0 - +R S 1994 1996 - Ap 1 0 1 S +R S 1994 2005 - O 1 0 0 - +R S 1997 1998 - Mar lastM 0 1 S +R S 1999 2006 - Ap 1 0 1 S +R S 2006 o - S 22 0 0 - +R S 2007 o - Mar lastF 0 1 S +R S 2007 o - N F>=1 0 0 - +R S 2008 o - Ap F>=1 0 1 S +R S 2008 o - N 1 0 0 - +R S 2009 o - Mar lastF 0 1 S +R S 2010 2011 - Ap F>=1 0 1 S +R S 2012 2022 - Mar lastF 0 1 S +R S 2009 2022 - O lastF 0 0 - +R AU 1917 o - Ja 1 2s 1 D +R AU 1917 o - Mar lastSu 2s 0 S +R AU 1942 o - Ja 1 2s 1 D +R AU 1942 o - Mar lastSu 2s 0 S +R AU 1942 o - S 27 2s 1 D +R AU 1943 1944 - Mar lastSu 2s 0 S +R AU 1943 o - O 3 2s 1 D +R AW 1974 o - O lastSu 2s 1 D +R AW 1975 o - Mar Su>=1 2s 0 S +R AW 1983 o - O lastSu 2s 1 D +R AW 1984 o - Mar Su>=1 2s 0 S +R AW 1991 o - N 17 2s 1 D +R AW 1992 o - Mar Su>=1 2s 0 S +R AW 2006 o - D 3 2s 1 D +R AW 2007 2009 - Mar lastSu 2s 0 S +R AW 2007 2008 - O lastSu 2s 1 D +R AQ 1971 o - O lastSu 2s 1 D +R AQ 1972 o - F lastSu 2s 0 S +R AQ 1989 1991 - O lastSu 2s 1 D +R AQ 1990 1992 - Mar Su>=1 2s 0 S +R Ho 1992 1993 - O lastSu 2s 1 D +R Ho 1993 1994 - Mar Su>=1 2s 0 S +R AS 1971 1985 - O lastSu 2s 1 D +R AS 1986 o - O 19 2s 1 D +R AS 1987 2007 - O lastSu 2s 1 D +R AS 1972 o - F 27 2s 0 S +R AS 1973 1985 - Mar Su>=1 2s 0 S +R AS 1986 1990 - Mar Su>=15 2s 0 S +R AS 1991 o - Mar 3 2s 0 S +R AS 1992 o - Mar 22 2s 0 S +R AS 1993 o - Mar 7 2s 0 S +R AS 1994 o - Mar 20 2s 0 S +R AS 1995 2005 - Mar lastSu 2s 0 S +R AS 2006 o - Ap 2 2s 0 S +R AS 2007 o - Mar lastSu 2s 0 S +R AS 2008 ma - Ap Su>=1 2s 0 S +R AS 2008 ma - O Su>=1 2s 1 D +R AT 1916 o - O Su>=1 2s 1 D +R AT 1917 o - Mar lastSu 2s 0 S +R AT 1917 1918 - O Su>=22 2s 1 D +R AT 1918 1919 - Mar Su>=1 2s 0 S +R AT 1967 o - O Su>=1 2s 1 D +R AT 1968 o - Mar Su>=29 2s 0 S +R AT 1968 1985 - O lastSu 2s 1 D +R AT 1969 1971 - Mar Su>=8 2s 0 S +R AT 1972 o - F lastSu 2s 0 S +R AT 1973 1981 - Mar Su>=1 2s 0 S +R AT 1982 1983 - Mar lastSu 2s 0 S +R AT 1984 1986 - Mar Su>=1 2s 0 S +R AT 1986 o - O Su>=15 2s 1 D +R AT 1987 1990 - Mar Su>=15 2s 0 S +R AT 1987 o - O Su>=22 2s 1 D +R AT 1988 1990 - O lastSu 2s 1 D +R AT 1991 1999 - O Su>=1 2s 1 D +R AT 1991 2005 - Mar lastSu 2s 0 S +R AT 2000 o - Au lastSu 2s 1 D +R AT 2001 ma - O Su>=1 2s 1 D +R AT 2006 o - Ap Su>=1 2s 0 S +R AT 2007 o - Mar lastSu 2s 0 S +R AT 2008 ma - Ap Su>=1 2s 0 S +R AV 1971 1985 - O lastSu 2s 1 D +R AV 1972 o - F lastSu 2s 0 S +R AV 1973 1985 - Mar Su>=1 2s 0 S +R AV 1986 1990 - Mar Su>=15 2s 0 S +R AV 1986 1987 - O Su>=15 2s 1 D +R AV 1988 1999 - O lastSu 2s 1 D +R AV 1991 1994 - Mar Su>=1 2s 0 S +R AV 1995 2005 - Mar lastSu 2s 0 S +R AV 2000 o - Au lastSu 2s 1 D +R AV 2001 2007 - O lastSu 2s 1 D +R AV 2006 o - Ap Su>=1 2s 0 S +R AV 2007 o - Mar lastSu 2s 0 S +R AV 2008 ma - Ap Su>=1 2s 0 S +R AV 2008 ma - O Su>=1 2s 1 D +R AN 1971 1985 - O lastSu 2s 1 D +R AN 1972 o - F 27 2s 0 S +R AN 1973 1981 - Mar Su>=1 2s 0 S +R AN 1982 o - Ap Su>=1 2s 0 S +R AN 1983 1985 - Mar Su>=1 2s 0 S +R AN 1986 1989 - Mar Su>=15 2s 0 S +R AN 1986 o - O 19 2s 1 D +R AN 1987 1999 - O lastSu 2s 1 D +R AN 1990 1995 - Mar Su>=1 2s 0 S +R AN 1996 2005 - Mar lastSu 2s 0 S +R AN 2000 o - Au lastSu 2s 1 D +R AN 2001 2007 - O lastSu 2s 1 D +R AN 2006 o - Ap Su>=1 2s 0 S +R AN 2007 o - Mar lastSu 2s 0 S +R AN 2008 ma - Ap Su>=1 2s 0 S +R AN 2008 ma - O Su>=1 2s 1 D +R LH 1981 1984 - O lastSu 2 1 - +R LH 1982 1985 - Mar Su>=1 2 0 - +R LH 1985 o - O lastSu 2 0:30 - +R LH 1986 1989 - Mar Su>=15 2 0 - +R LH 1986 o - O 19 2 0:30 - +R LH 1987 1999 - O lastSu 2 0:30 - +R LH 1990 1995 - Mar Su>=1 2 0 - +R LH 1996 2005 - Mar lastSu 2 0 - +R LH 2000 o - Au lastSu 2 0:30 - +R LH 2001 2007 - O lastSu 2 0:30 - +R LH 2006 o - Ap Su>=1 2 0 - +R LH 2007 o - Mar lastSu 2 0 - +R LH 2008 ma - Ap Su>=1 2 0 - +R LH 2008 ma - O Su>=1 2 0:30 - +R FJ 1998 1999 - N Su>=1 2 1 - +R FJ 1999 2000 - F lastSu 3 0 - +R FJ 2009 o - N 29 2 1 - +R FJ 2010 o - Mar lastSu 3 0 - +R FJ 2010 2013 - O Su>=21 2 1 - +R FJ 2011 o - Mar Su>=1 3 0 - +R FJ 2012 2013 - Ja Su>=18 3 0 - +R FJ 2014 o - Ja Su>=18 2 0 - +R FJ 2014 2018 - N Su>=1 2 1 - +R FJ 2015 2021 - Ja Su>=12 3 0 - +R FJ 2019 o - N Su>=8 2 1 - +R FJ 2020 o - D 20 2 1 - +R Gu 1959 o - Jun 27 2 1 D +R Gu 1961 o - Ja 29 2 0 S +R Gu 1967 o - S 1 2 1 D +R Gu 1969 o - Ja 26 0:1 0 S +R Gu 1969 o - Jun 22 2 1 D +R Gu 1969 o - Au 31 2 0 S +R Gu 1970 1971 - Ap lastSu 2 1 D +R Gu 1970 1971 - S Su>=1 2 0 S +R Gu 1973 o - D 16 2 1 D +R Gu 1974 o - F 24 2 0 S +R Gu 1976 o - May 26 2 1 D +R Gu 1976 o - Au 22 2:1 0 S +R Gu 1977 o - Ap 24 2 1 D +R Gu 1977 o - Au 28 2 0 S +R NC 1977 1978 - D Su>=1 0 1 - +R NC 1978 1979 - F 27 0 0 - +R NC 1996 o - D 1 2s 1 - +R NC 1997 o - Mar 2 2s 0 - +R NZ 1927 o - N 6 2 1 S +R NZ 1928 o - Mar 4 2 0 M +R NZ 1928 1933 - O Su>=8 2 0:30 S +R NZ 1929 1933 - Mar Su>=15 2 0 M +R NZ 1934 1940 - Ap lastSu 2 0 M +R NZ 1934 1940 - S lastSu 2 0:30 S +R NZ 1946 o - Ja 1 0 0 S +R NZ 1974 o - N Su>=1 2s 1 D +R k 1974 o - N Su>=1 2:45s 1 - +R NZ 1975 o - F lastSu 2s 0 S +R k 1975 o - F lastSu 2:45s 0 - +R NZ 1975 1988 - O lastSu 2s 1 D +R k 1975 1988 - O lastSu 2:45s 1 - +R NZ 1976 1989 - Mar Su>=1 2s 0 S +R k 1976 1989 - Mar Su>=1 2:45s 0 - +R NZ 1989 o - O Su>=8 2s 1 D +R k 1989 o - O Su>=8 2:45s 1 - +R NZ 1990 2006 - O Su>=1 2s 1 D +R k 1990 2006 - O Su>=1 2:45s 1 - +R NZ 1990 2007 - Mar Su>=15 2s 0 S +R k 1990 2007 - Mar Su>=15 2:45s 0 - +R NZ 2007 ma - S lastSu 2s 1 D +R k 2007 ma - S lastSu 2:45s 1 - +R NZ 2008 ma - Ap Su>=1 2s 0 S +R k 2008 ma - Ap Su>=1 2:45s 0 - +R CK 1978 o - N 12 0 0:30 - +R CK 1979 1991 - Mar Su>=1 0 0 - +R CK 1979 1990 - O lastSu 0 0:30 - +R WS 2010 o - S lastSu 0 1 - +R WS 2011 o - Ap Sa>=1 4 0 - +R WS 2011 o - S lastSa 3 1 - +R WS 2012 2021 - Ap Su>=1 4 0 - +R WS 2012 2020 - S lastSu 3 1 - +R TO 1999 o - O 7 2s 1 - +R TO 2000 o - Mar 19 2s 0 - +R TO 2000 2001 - N Su>=1 2 1 - +R TO 2001 2002 - Ja lastSu 2 0 - +R TO 2016 o - N Su>=1 2 1 - +R TO 2017 o - Ja Su>=15 3 0 - +R VU 1973 o - D 22 12u 1 - +R VU 1974 o - Mar 30 12u 0 - +R VU 1983 1991 - S Sa>=22 24 1 - +R VU 1984 1991 - Mar Sa>=22 24 0 - +R VU 1992 1993 - Ja Sa>=22 24 0 - +R VU 1992 o - O Sa>=22 24 1 - +R G 1916 o - May 21 2s 1 BST +R G 1916 o - O 1 2s 0 GMT +R G 1917 o - Ap 8 2s 1 BST +R G 1917 o - S 17 2s 0 GMT +R G 1918 o - Mar 24 2s 1 BST +R G 1918 o - S 30 2s 0 GMT +R G 1919 o - Mar 30 2s 1 BST +R G 1919 o - S 29 2s 0 GMT +R G 1920 o - Mar 28 2s 1 BST +R G 1920 o - O 25 2s 0 GMT +R G 1921 o - Ap 3 2s 1 BST +R G 1921 o - O 3 2s 0 GMT +R G 1922 o - Mar 26 2s 1 BST +R G 1922 o - O 8 2s 0 GMT +R G 1923 o - Ap Su>=16 2s 1 BST +R G 1923 1924 - S Su>=16 2s 0 GMT +R G 1924 o - Ap Su>=9 2s 1 BST +R G 1925 1926 - Ap Su>=16 2s 1 BST +R G 1925 1938 - O Su>=2 2s 0 GMT +R G 1927 o - Ap Su>=9 2s 1 BST +R G 1928 1929 - Ap Su>=16 2s 1 BST +R G 1930 o - Ap Su>=9 2s 1 BST +R G 1931 1932 - Ap Su>=16 2s 1 BST +R G 1933 o - Ap Su>=9 2s 1 BST +R G 1934 o - Ap Su>=16 2s 1 BST +R G 1935 o - Ap Su>=9 2s 1 BST +R G 1936 1937 - Ap Su>=16 2s 1 BST +R G 1938 o - Ap Su>=9 2s 1 BST +R G 1939 o - Ap Su>=16 2s 1 BST +R G 1939 o - N Su>=16 2s 0 GMT +R G 1940 o - F Su>=23 2s 1 BST +R G 1941 o - May Su>=2 1s 2 BDST +R G 1941 1943 - Au Su>=9 1s 1 BST +R G 1942 1944 - Ap Su>=2 1s 2 BDST +R G 1944 o - S Su>=16 1s 1 BST +R G 1945 o - Ap M>=2 1s 2 BDST +R G 1945 o - Jul Su>=9 1s 1 BST +R G 1945 1946 - O Su>=2 2s 0 GMT +R G 1946 o - Ap Su>=9 2s 1 BST +R G 1947 o - Mar 16 2s 1 BST +R G 1947 o - Ap 13 1s 2 BDST +R G 1947 o - Au 10 1s 1 BST +R G 1947 o - N 2 2s 0 GMT +R G 1948 o - Mar 14 2s 1 BST +R G 1948 o - O 31 2s 0 GMT +R G 1949 o - Ap 3 2s 1 BST +R G 1949 o - O 30 2s 0 GMT +R G 1950 1952 - Ap Su>=14 2s 1 BST +R G 1950 1952 - O Su>=21 2s 0 GMT +R G 1953 o - Ap Su>=16 2s 1 BST +R G 1953 1960 - O Su>=2 2s 0 GMT +R G 1954 o - Ap Su>=9 2s 1 BST +R G 1955 1956 - Ap Su>=16 2s 1 BST +R G 1957 o - Ap Su>=9 2s 1 BST +R G 1958 1959 - Ap Su>=16 2s 1 BST +R G 1960 o - Ap Su>=9 2s 1 BST +R G 1961 1963 - Mar lastSu 2s 1 BST +R G 1961 1968 - O Su>=23 2s 0 GMT +R G 1964 1967 - Mar Su>=19 2s 1 BST +R G 1968 o - F 18 2s 1 BST +R G 1972 1980 - Mar Su>=16 2s 1 BST +R G 1972 1980 - O Su>=23 2s 0 GMT +R G 1981 1995 - Mar lastSu 1u 1 BST +R G 1981 1989 - O Su>=23 1u 0 GMT +R G 1990 1995 - O Su>=22 1u 0 GMT +R IE 1971 o - O 31 2u -1 - +R IE 1972 1980 - Mar Su>=16 2u 0 - +R IE 1972 1980 - O Su>=23 2u -1 - +R IE 1981 ma - Mar lastSu 1u 0 - +R IE 1981 1989 - O Su>=23 1u -1 - +R IE 1990 1995 - O Su>=22 1u -1 - +R IE 1996 ma - O lastSu 1u -1 - +R E 1977 1980 - Ap Su>=1 1u 1 S +R E 1977 o - S lastSu 1u 0 - +R E 1978 o - O 1 1u 0 - +R E 1979 1995 - S lastSu 1u 0 - +R E 1981 ma - Mar lastSu 1u 1 S +R E 1996 ma - O lastSu 1u 0 - +R W- 1977 1980 - Ap Su>=1 1s 1 S +R W- 1977 o - S lastSu 1s 0 - +R W- 1978 o - O 1 1s 0 - +R W- 1979 1995 - S lastSu 1s 0 - +R W- 1981 ma - Mar lastSu 1s 1 S +R W- 1996 ma - O lastSu 1s 0 - +R c 1916 o - Ap 30 23 1 S +R c 1916 o - O 1 1 0 - +R c 1917 1918 - Ap M>=15 2s 1 S +R c 1917 1918 - S M>=15 2s 0 - +R c 1940 o - Ap 1 2s 1 S +R c 1942 o - N 2 2s 0 - +R c 1943 o - Mar 29 2s 1 S +R c 1943 o - O 4 2s 0 - +R c 1944 1945 - Ap M>=1 2s 1 S +R c 1944 o - O 2 2s 0 - +R c 1945 o - S 16 2s 0 - +R c 1977 1980 - Ap Su>=1 2s 1 S +R c 1977 o - S lastSu 2s 0 - +R c 1978 o - O 1 2s 0 - +R c 1979 1995 - S lastSu 2s 0 - +R c 1981 ma - Mar lastSu 2s 1 S +R c 1996 ma - O lastSu 2s 0 - +R e 1977 1980 - Ap Su>=1 0 1 S +R e 1977 o - S lastSu 0 0 - +R e 1978 o - O 1 0 0 - +R e 1979 1995 - S lastSu 0 0 - +R e 1981 ma - Mar lastSu 0 1 S +R e 1996 ma - O lastSu 0 0 - +R R 1917 o - Jul 1 23 1 MST +R R 1917 o - D 28 0 0 MMT +R R 1918 o - May 31 22 2 MDST +R R 1918 o - S 16 1 1 MST +R R 1919 o - May 31 23 2 MDST +R R 1919 o - Jul 1 0u 1 MSD +R R 1919 o - Au 16 0 0 MSK +R R 1921 o - F 14 23 1 MSD +R R 1921 o - Mar 20 23 2 +05 +R R 1921 o - S 1 0 1 MSD +R R 1921 o - O 1 0 0 - +R R 1981 1984 - Ap 1 0 1 S +R R 1981 1983 - O 1 0 0 - +R R 1984 1995 - S lastSu 2s 0 - +R R 1985 2010 - Mar lastSu 2s 1 S +R R 1996 2010 - O lastSu 2s 0 - +R q 1940 o - Jun 16 0 1 S +R q 1942 o - N 2 3 0 - +R q 1943 o - Mar 29 2 1 S +R q 1943 o - Ap 10 3 0 - +R q 1974 o - May 4 0 1 S +R q 1974 o - O 2 0 0 - +R q 1975 o - May 1 0 1 S +R q 1975 o - O 2 0 0 - +R q 1976 o - May 2 0 1 S +R q 1976 o - O 3 0 0 - +R q 1977 o - May 8 0 1 S +R q 1977 o - O 2 0 0 - +R q 1978 o - May 6 0 1 S +R q 1978 o - O 1 0 0 - +R q 1979 o - May 5 0 1 S +R q 1979 o - S 30 0 0 - +R q 1980 o - May 3 0 1 S +R q 1980 o - O 4 0 0 - +R q 1981 o - Ap 26 0 1 S +R q 1981 o - S 27 0 0 - +R q 1982 o - May 2 0 1 S +R q 1982 o - O 3 0 0 - +R q 1983 o - Ap 18 0 1 S +R q 1983 o - O 1 0 0 - +R q 1984 o - Ap 1 0 1 S +R a 1920 o - Ap 5 2s 1 S +R a 1920 o - S 13 2s 0 - +R a 1946 o - Ap 14 2s 1 S +R a 1946 o - O 7 2s 0 - +R a 1947 1948 - O Su>=1 2s 0 - +R a 1947 o - Ap 6 2s 1 S +R a 1948 o - Ap 18 2s 1 S +R a 1980 o - Ap 6 0 1 S +R a 1980 o - S 28 0 0 - +R b 1918 o - Mar 9 0s 1 S +R b 1918 1919 - O Sa>=1 23s 0 - +R b 1919 o - Mar 1 23s 1 S +R b 1920 o - F 14 23s 1 S +R b 1920 o - O 23 23s 0 - +R b 1921 o - Mar 14 23s 1 S +R b 1921 o - O 25 23s 0 - +R b 1922 o - Mar 25 23s 1 S +R b 1922 1927 - O Sa>=1 23s 0 - +R b 1923 o - Ap 21 23s 1 S +R b 1924 o - Mar 29 23s 1 S +R b 1925 o - Ap 4 23s 1 S +R b 1926 o - Ap 17 23s 1 S +R b 1927 o - Ap 9 23s 1 S +R b 1928 o - Ap 14 23s 1 S +R b 1928 1938 - O Su>=2 2s 0 - +R b 1929 o - Ap 21 2s 1 S +R b 1930 o - Ap 13 2s 1 S +R b 1931 o - Ap 19 2s 1 S +R b 1932 o - Ap 3 2s 1 S +R b 1933 o - Mar 26 2s 1 S +R b 1934 o - Ap 8 2s 1 S +R b 1935 o - Mar 31 2s 1 S +R b 1936 o - Ap 19 2s 1 S +R b 1937 o - Ap 4 2s 1 S +R b 1938 o - Mar 27 2s 1 S +R b 1939 o - Ap 16 2s 1 S +R b 1939 o - N 19 2s 0 - +R b 1940 o - F 25 2s 1 S +R b 1944 o - S 17 2s 0 - +R b 1945 o - Ap 2 2s 1 S +R b 1945 o - S 16 2s 0 - +R b 1946 o - May 19 2s 1 S +R b 1946 o - O 7 2s 0 - +R BG 1979 o - Mar 31 23 1 S +R BG 1979 o - O 1 1 0 - +R BG 1980 1982 - Ap Sa>=1 23 1 S +R BG 1980 o - S 29 1 0 - +R BG 1981 o - S 27 2 0 - +R CZ 1945 o - Ap M>=1 2s 1 S +R CZ 1945 o - O 1 2s 0 - +R CZ 1946 o - May 6 2s 1 S +R CZ 1946 1949 - O Su>=1 2s 0 - +R CZ 1947 1948 - Ap Su>=15 2s 1 S +R CZ 1949 o - Ap 9 2s 1 S +R Th 1991 1992 - Mar lastSu 2 1 D +R Th 1991 1992 - S lastSu 2 0 S +R Th 1993 2006 - Ap Su>=1 2 1 D +R Th 1993 2006 - O lastSu 2 0 S +R Th 2007 ma - Mar Su>=8 2 1 D +R Th 2007 ma - N Su>=1 2 0 S +R FI 1942 o - Ap 2 24 1 S +R FI 1942 o - O 4 1 0 - +R FI 1981 1982 - Mar lastSu 2 1 S +R FI 1981 1982 - S lastSu 3 0 - +R F 1916 o - Jun 14 23s 1 S +R F 1916 1919 - O Su>=1 23s 0 - +R F 1917 o - Mar 24 23s 1 S +R F 1918 o - Mar 9 23s 1 S +R F 1919 o - Mar 1 23s 1 S +R F 1920 o - F 14 23s 1 S +R F 1920 o - O 23 23s 0 - +R F 1921 o - Mar 14 23s 1 S +R F 1921 o - O 25 23s 0 - +R F 1922 o - Mar 25 23s 1 S +R F 1922 1938 - O Sa>=1 23s 0 - +R F 1923 o - May 26 23s 1 S +R F 1924 o - Mar 29 23s 1 S +R F 1925 o - Ap 4 23s 1 S +R F 1926 o - Ap 17 23s 1 S +R F 1927 o - Ap 9 23s 1 S +R F 1928 o - Ap 14 23s 1 S +R F 1929 o - Ap 20 23s 1 S +R F 1930 o - Ap 12 23s 1 S +R F 1931 o - Ap 18 23s 1 S +R F 1932 o - Ap 2 23s 1 S +R F 1933 o - Mar 25 23s 1 S +R F 1934 o - Ap 7 23s 1 S +R F 1935 o - Mar 30 23s 1 S +R F 1936 o - Ap 18 23s 1 S +R F 1937 o - Ap 3 23s 1 S +R F 1938 o - Mar 26 23s 1 S +R F 1939 o - Ap 15 23s 1 S +R F 1939 o - N 18 23s 0 - +R F 1940 o - F 25 2 1 S +R F 1941 o - May 5 0 2 M +R F 1941 o - O 6 0 1 S +R F 1942 o - Mar 9 0 2 M +R F 1942 o - N 2 3 1 S +R F 1943 o - Mar 29 2 2 M +R F 1943 o - O 4 3 1 S +R F 1944 o - Ap 3 2 2 M +R F 1944 o - O 8 1 1 S +R F 1945 o - Ap 2 2 2 M +R F 1945 o - S 16 3 0 - +R F 1976 o - Mar 28 1 1 S +R F 1976 o - S 26 1 0 - +R DE 1946 o - Ap 14 2s 1 S +R DE 1946 o - O 7 2s 0 - +R DE 1947 1949 - O Su>=1 2s 0 - +R DE 1947 o - Ap 6 3s 1 S +R DE 1947 o - May 11 2s 2 M +R DE 1947 o - Jun 29 3 1 S +R DE 1948 o - Ap 18 2s 1 S +R DE 1949 o - Ap 10 2s 1 S +R So 1945 o - May 24 2 2 M +R So 1945 o - S 24 3 1 S +R So 1945 o - N 18 2s 0 - +R g 1932 o - Jul 7 0 1 S +R g 1932 o - S 1 0 0 - +R g 1941 o - Ap 7 0 1 S +R g 1942 o - N 2 3 0 - +R g 1943 o - Mar 30 0 1 S +R g 1943 o - O 4 0 0 - +R g 1952 o - Jul 1 0 1 S +R g 1952 o - N 2 0 0 - +R g 1975 o - Ap 12 0s 1 S +R g 1975 o - N 26 0s 0 - +R g 1976 o - Ap 11 2s 1 S +R g 1976 o - O 10 2s 0 - +R g 1977 1978 - Ap Su>=1 2s 1 S +R g 1977 o - S 26 2s 0 - +R g 1978 o - S 24 4 0 - +R g 1979 o - Ap 1 9 1 S +R g 1979 o - S 29 2 0 - +R g 1980 o - Ap 1 0 1 S +R g 1980 o - S 28 0 0 - +R h 1918 1919 - Ap 15 2 1 S +R h 1918 1920 - S M>=15 3 0 - +R h 1920 o - Ap 5 2 1 S +R h 1945 o - May 1 23 1 S +R h 1945 o - N 1 1 0 - +R h 1946 o - Mar 31 2s 1 S +R h 1946 o - O 7 2 0 - +R h 1947 1949 - Ap Su>=4 2s 1 S +R h 1947 1949 - O Su>=1 2s 0 - +R h 1954 o - May 23 0 1 S +R h 1954 o - O 3 0 0 - +R h 1955 o - May 22 2 1 S +R h 1955 o - O 2 3 0 - +R h 1956 1957 - Jun Su>=1 2 1 S +R h 1956 1957 - S lastSu 3 0 - +R h 1980 o - Ap 6 0 1 S +R h 1980 o - S 28 1 0 - +R h 1981 1983 - Mar lastSu 0 1 S +R h 1981 1983 - S lastSu 1 0 - +R I 1916 o - Jun 3 24 1 S +R I 1916 1917 - S 30 24 0 - +R I 1917 o - Mar 31 24 1 S +R I 1918 o - Mar 9 24 1 S +R I 1918 o - O 6 24 0 - +R I 1919 o - Mar 1 24 1 S +R I 1919 o - O 4 24 0 - +R I 1920 o - Mar 20 24 1 S +R I 1920 o - S 18 24 0 - +R I 1940 o - Jun 14 24 1 S +R I 1942 o - N 2 2s 0 - +R I 1943 o - Mar 29 2s 1 S +R I 1943 o - O 4 2s 0 - +R I 1944 o - Ap 2 2s 1 S +R I 1944 o - S 17 2s 0 - +R I 1945 o - Ap 2 2 1 S +R I 1945 o - S 15 1 0 - +R I 1946 o - Mar 17 2s 1 S +R I 1946 o - O 6 2s 0 - +R I 1947 o - Mar 16 0s 1 S +R I 1947 o - O 5 0s 0 - +R I 1948 o - F 29 2s 1 S +R I 1948 o - O 3 2s 0 - +R I 1966 1968 - May Su>=22 0s 1 S +R I 1966 o - S 24 24 0 - +R I 1967 1969 - S Su>=22 0s 0 - +R I 1969 o - Jun 1 0s 1 S +R I 1970 o - May 31 0s 1 S +R I 1970 o - S lastSu 0s 0 - +R I 1971 1972 - May Su>=22 0s 1 S +R I 1971 o - S lastSu 0s 0 - +R I 1972 o - O 1 0s 0 - +R I 1973 o - Jun 3 0s 1 S +R I 1973 1974 - S lastSu 0s 0 - +R I 1974 o - May 26 0s 1 S +R I 1975 o - Jun 1 0s 1 S +R I 1975 1977 - S lastSu 0s 0 - +R I 1976 o - May 30 0s 1 S +R I 1977 1979 - May Su>=22 0s 1 S +R I 1978 o - O 1 0s 0 - +R I 1979 o - S 30 0s 0 - +R LV 1989 1996 - Mar lastSu 2s 1 S +R LV 1989 1996 - S lastSu 2s 0 - +R MT 1973 o - Mar 31 0s 1 S +R MT 1973 o - S 29 0s 0 - +R MT 1974 o - Ap 21 0s 1 S +R MT 1974 o - S 16 0s 0 - +R MT 1975 1979 - Ap Su>=15 2 1 S +R MT 1975 1980 - S Su>=15 2 0 - +R MT 1980 o - Mar 31 2 1 S +R MD 1997 2021 - Mar lastSu 2 1 S +R MD 1997 2021 - O lastSu 3 0 - +R O 1918 1919 - S 16 2s 0 - +R O 1919 o - Ap 15 2s 1 S +R O 1944 o - Ap 3 2s 1 S +R O 1944 o - O 4 2 0 - +R O 1945 o - Ap 29 0 1 S +R O 1945 o - N 1 0 0 - +R O 1946 o - Ap 14 0s 1 S +R O 1946 o - O 7 2s 0 - +R O 1947 o - May 4 2s 1 S +R O 1947 1949 - O Su>=1 2s 0 - +R O 1948 o - Ap 18 2s 1 S +R O 1949 o - Ap 10 2s 1 S +R O 1957 o - Jun 2 1s 1 S +R O 1957 1958 - S lastSu 1s 0 - +R O 1958 o - Mar 30 1s 1 S +R O 1959 o - May 31 1s 1 S +R O 1959 1961 - O Su>=1 1s 0 - +R O 1960 o - Ap 3 1s 1 S +R O 1961 1964 - May lastSu 1s 1 S +R O 1962 1964 - S lastSu 1s 0 - +R p 1916 o - Jun 17 23 1 S +R p 1916 o - N 1 1 0 - +R p 1917 1921 - Mar 1 0 1 S +R p 1917 1921 - O 14 24 0 - +R p 1924 o - Ap 16 23s 1 S +R p 1924 o - O 4 23s 0 - +R p 1926 o - Ap 17 23s 1 S +R p 1926 1929 - O Sa>=1 23s 0 - +R p 1927 o - Ap 9 23s 1 S +R p 1928 o - Ap 14 23s 1 S +R p 1929 o - Ap 20 23s 1 S +R p 1931 o - Ap 18 23s 1 S +R p 1931 1932 - O Sa>=1 23s 0 - +R p 1932 o - Ap 2 23s 1 S +R p 1934 o - Ap 7 23s 1 S +R p 1934 1938 - O Sa>=1 23s 0 - +R p 1935 o - Mar 30 23s 1 S +R p 1936 o - Ap 18 23s 1 S +R p 1937 o - Ap 3 23s 1 S +R p 1938 o - Mar 26 23s 1 S +R p 1939 o - Ap 15 23s 1 S +R p 1939 o - N 18 23s 0 - +R p 1940 o - F 24 23s 1 S +R p 1940 o - O 7 23s 0 - +R p 1941 o - Ap 5 23s 1 S +R p 1941 o - O 5 23s 0 - +R p 1942 1945 - Mar Sa>=8 23s 1 S +R p 1942 o - Ap 25 22s 2 M +R p 1942 o - Au 15 22s 1 S +R p 1942 1945 - O Sa>=24 23s 0 - +R p 1943 o - Ap 17 22s 2 M +R p 1943 1945 - Au Sa>=25 22s 1 S +R p 1944 1945 - Ap Sa>=21 22s 2 M +R p 1946 o - Ap Sa>=1 23s 1 S +R p 1946 o - O Sa>=1 23s 0 - +R p 1947 1966 - Ap Su>=1 2s 1 S +R p 1947 1965 - O Su>=1 2s 0 - +R p 1976 o - S lastSu 1 0 - +R p 1977 o - Mar lastSu 0s 1 S +R p 1977 o - S lastSu 0s 0 - +R p 1978 1980 - Ap Su>=1 1s 1 S +R p 1978 o - O 1 1s 0 - +R p 1979 1980 - S lastSu 1s 0 - +R p 1981 1986 - Mar lastSu 0s 1 S +R p 1981 1985 - S lastSu 0s 0 - +R z 1932 o - May 21 0s 1 S +R z 1932 1939 - O Su>=1 0s 0 - +R z 1933 1939 - Ap Su>=2 0s 1 S +R z 1979 o - May 27 0 1 S +R z 1979 o - S lastSu 0 0 - +R z 1980 o - Ap 5 23 1 S +R z 1980 o - S lastSu 1 0 - +R z 1991 1993 - Mar lastSu 0s 1 S +R z 1991 1993 - S lastSu 0s 0 - +R s 1918 o - Ap 15 23 1 S +R s 1918 1919 - O 6 24s 0 - +R s 1919 o - Ap 6 23 1 S +R s 1924 o - Ap 16 23 1 S +R s 1924 o - O 4 24s 0 - +R s 1926 o - Ap 17 23 1 S +R s 1926 1929 - O Sa>=1 24s 0 - +R s 1927 o - Ap 9 23 1 S +R s 1928 o - Ap 15 0 1 S +R s 1929 o - Ap 20 23 1 S +R s 1937 o - Jun 16 23 1 S +R s 1937 o - O 2 24s 0 - +R s 1938 o - Ap 2 23 1 S +R s 1938 o - Ap 30 23 2 M +R s 1938 o - O 2 24 1 S +R s 1939 o - O 7 24s 0 - +R s 1942 o - May 2 23 1 S +R s 1942 o - S 1 1 0 - +R s 1943 1946 - Ap Sa>=13 23 1 S +R s 1943 1944 - O Su>=1 1 0 - +R s 1945 1946 - S lastSu 1 0 - +R s 1949 o - Ap 30 23 1 S +R s 1949 o - O 2 1 0 - +R s 1974 1975 - Ap Sa>=12 23 1 S +R s 1974 1975 - O Su>=1 1 0 - +R s 1976 o - Mar 27 23 1 S +R s 1976 1977 - S lastSu 1 0 - +R s 1977 o - Ap 2 23 1 S +R s 1978 o - Ap 2 2s 1 S +R s 1978 o - O 1 2s 0 - +R Sp 1967 o - Jun 3 12 1 S +R Sp 1967 o - O 1 0 0 - +R Sp 1974 o - Jun 24 0 1 S +R Sp 1974 o - S 1 0 0 - +R Sp 1976 1977 - May 1 0 1 S +R Sp 1976 o - Au 1 0 0 - +R Sp 1977 o - S 28 0 0 - +R Sp 1978 o - Jun 1 0 1 S +R Sp 1978 o - Au 4 0 0 - +R CH 1941 1942 - May M>=1 1 1 S +R CH 1941 1942 - O M>=1 2 0 - +R T 1916 o - May 1 0 1 S +R T 1916 o - O 1 0 0 - +R T 1920 o - Mar 28 0 1 S +R T 1920 o - O 25 0 0 - +R T 1921 o - Ap 3 0 1 S +R T 1921 o - O 3 0 0 - +R T 1922 o - Mar 26 0 1 S +R T 1922 o - O 8 0 0 - +R T 1924 o - May 13 0 1 S +R T 1924 1925 - O 1 0 0 - +R T 1925 o - May 1 0 1 S +R T 1940 o - Jul 1 0 1 S +R T 1940 o - O 6 0 0 - +R T 1940 o - D 1 0 1 S +R T 1941 o - S 21 0 0 - +R T 1942 o - Ap 1 0 1 S +R T 1945 o - O 8 0 0 - +R T 1946 o - Jun 1 0 1 S +R T 1946 o - O 1 0 0 - +R T 1947 1948 - Ap Su>=16 0 1 S +R T 1947 1951 - O Su>=2 0 0 - +R T 1949 o - Ap 10 0 1 S +R T 1950 o - Ap 16 0 1 S +R T 1951 o - Ap 22 0 1 S +R T 1962 o - Jul 15 0 1 S +R T 1963 o - O 30 0 0 - +R T 1964 o - May 15 0 1 S +R T 1964 o - O 1 0 0 - +R T 1973 o - Jun 3 1 1 S +R T 1973 1976 - O Su>=31 2 0 - +R T 1974 o - Mar 31 2 1 S +R T 1975 o - Mar 22 2 1 S +R T 1976 o - Mar 21 2 1 S +R T 1977 1978 - Ap Su>=1 2 1 S +R T 1977 1978 - O Su>=15 2 0 - +R T 1978 o - Jun 29 0 0 - +R T 1983 o - Jul 31 2 1 S +R T 1983 o - O 2 2 0 - +R T 1985 o - Ap 20 1s 1 S +R T 1985 o - S 28 1s 0 - +R T 1986 1993 - Mar lastSu 1s 1 S +R T 1986 1995 - S lastSu 1s 0 - +R T 1994 o - Mar 20 1s 1 S +R T 1995 2006 - Mar lastSu 1s 1 S +R T 1996 2006 - O lastSu 1s 0 - +R u 1918 1919 - Mar lastSu 2 1 D +R u 1918 1919 - O lastSu 2 0 S +R u 1942 o - F 9 2 1 W +R u 1945 o - Au 14 23u 1 P +R u 1945 o - S 30 2 0 S +R u 1967 2006 - O lastSu 2 0 S +R u 1967 1973 - Ap lastSu 2 1 D +R u 1974 o - Ja 6 2 1 D +R u 1975 o - F lastSu 2 1 D +R u 1976 1986 - Ap lastSu 2 1 D +R u 1987 2006 - Ap Su>=1 2 1 D +R u 2007 ma - Mar Su>=8 2 1 D +R u 2007 ma - N Su>=1 2 0 S +R NY 1920 o - Mar lastSu 2 1 D +R NY 1920 o - O lastSu 2 0 S +R NY 1921 1966 - Ap lastSu 2 1 D +R NY 1921 1954 - S lastSu 2 0 S +R NY 1955 1966 - O lastSu 2 0 S +R Ch 1920 o - Jun 13 2 1 D +R Ch 1920 1921 - O lastSu 2 0 S +R Ch 1921 o - Mar lastSu 2 1 D +R Ch 1922 1966 - Ap lastSu 2 1 D +R Ch 1922 1954 - S lastSu 2 0 S +R Ch 1955 1966 - O lastSu 2 0 S +R De 1920 1921 - Mar lastSu 2 1 D +R De 1920 o - O lastSu 2 0 S +R De 1921 o - May 22 2 0 S +R De 1965 1966 - Ap lastSu 2 1 D +R De 1965 1966 - O lastSu 2 0 S +R CA 1948 o - Mar 14 2:1 1 D +R CA 1949 o - Ja 1 2 0 S +R CA 1950 1966 - Ap lastSu 1 1 D +R CA 1950 1961 - S lastSu 2 0 S +R CA 1962 1966 - O lastSu 2 0 S +R In 1941 o - Jun 22 2 1 D +R In 1941 1954 - S lastSu 2 0 S +R In 1946 1954 - Ap lastSu 2 1 D +R Ma 1951 o - Ap lastSu 2 1 D +R Ma 1951 o - S lastSu 2 0 S +R Ma 1954 1960 - Ap lastSu 2 1 D +R Ma 1954 1960 - S lastSu 2 0 S +R V 1946 o - Ap lastSu 2 1 D +R V 1946 o - S lastSu 2 0 S +R V 1953 1954 - Ap lastSu 2 1 D +R V 1953 1959 - S lastSu 2 0 S +R V 1955 o - May 1 0 1 D +R V 1956 1963 - Ap lastSu 2 1 D +R V 1960 o - O lastSu 2 0 S +R V 1961 o - S lastSu 2 0 S +R V 1962 1963 - O lastSu 2 0 S +R Pe 1955 o - May 1 0 1 D +R Pe 1955 1960 - S lastSu 2 0 S +R Pe 1956 1963 - Ap lastSu 2 1 D +R Pe 1961 1963 - O lastSu 2 0 S +R Pi 1955 o - May 1 0 1 D +R Pi 1955 1960 - S lastSu 2 0 S +R Pi 1956 1964 - Ap lastSu 2 1 D +R Pi 1961 1964 - O lastSu 2 0 S +R St 1947 1961 - Ap lastSu 2 1 D +R St 1947 1954 - S lastSu 2 0 S +R St 1955 1956 - O lastSu 2 0 S +R St 1957 1958 - S lastSu 2 0 S +R St 1959 1961 - O lastSu 2 0 S +R Pu 1946 1960 - Ap lastSu 2 1 D +R Pu 1946 1954 - S lastSu 2 0 S +R Pu 1955 1956 - O lastSu 2 0 S +R Pu 1957 1960 - S lastSu 2 0 S +R v 1921 o - May 1 2 1 D +R v 1921 o - S 1 2 0 S +R v 1941 o - Ap lastSu 2 1 D +R v 1941 o - S lastSu 2 0 S +R v 1946 o - Ap lastSu 0:1 1 D +R v 1946 o - Jun 2 2 0 S +R v 1950 1961 - Ap lastSu 2 1 D +R v 1950 1955 - S lastSu 2 0 S +R v 1956 1961 - O lastSu 2 0 S +R Dt 1948 o - Ap lastSu 2 1 D +R Dt 1948 o - S lastSu 2 0 S +R Me 1946 o - Ap lastSu 2 1 D +R Me 1946 o - S lastSu 2 0 S +R Me 1966 o - Ap lastSu 2 1 D +R Me 1966 o - O lastSu 2 0 S +R C 1918 o - Ap 14 2 1 D +R C 1918 o - O 27 2 0 S +R C 1942 o - F 9 2 1 W +R C 1945 o - Au 14 23u 1 P +R C 1945 o - S 30 2 0 S +R C 1974 1986 - Ap lastSu 2 1 D +R C 1974 2006 - O lastSu 2 0 S +R C 1987 2006 - Ap Su>=1 2 1 D +R C 2007 ma - Mar Su>=8 2 1 D +R C 2007 ma - N Su>=1 2 0 S +R j 1917 o - Ap 8 2 1 D +R j 1917 o - S 17 2 0 S +R j 1919 o - May 5 23 1 D +R j 1919 o - Au 12 23 0 S +R j 1920 1935 - May Su>=1 23 1 D +R j 1920 1935 - O lastSu 23 0 S +R j 1936 1941 - May M>=9 0 1 D +R j 1936 1941 - O M>=2 0 0 S +R j 1946 1950 - May Su>=8 2 1 D +R j 1946 1950 - O Su>=2 2 0 S +R j 1951 1986 - Ap lastSu 2 1 D +R j 1951 1959 - S lastSu 2 0 S +R j 1960 1986 - O lastSu 2 0 S +R j 1987 o - Ap Su>=1 0:1 1 D +R j 1987 2006 - O lastSu 0:1 0 S +R j 1988 o - Ap Su>=1 0:1 2 DD +R j 1989 2006 - Ap Su>=1 0:1 1 D +R j 2007 2011 - Mar Su>=8 0:1 1 D +R j 2007 2010 - N Su>=1 0:1 0 S +R H 1916 o - Ap 1 0 1 D +R H 1916 o - O 1 0 0 S +R H 1920 o - May 9 0 1 D +R H 1920 o - Au 29 0 0 S +R H 1921 o - May 6 0 1 D +R H 1921 1922 - S 5 0 0 S +R H 1922 o - Ap 30 0 1 D +R H 1923 1925 - May Su>=1 0 1 D +R H 1923 o - S 4 0 0 S +R H 1924 o - S 15 0 0 S +R H 1925 o - S 28 0 0 S +R H 1926 o - May 16 0 1 D +R H 1926 o - S 13 0 0 S +R H 1927 o - May 1 0 1 D +R H 1927 o - S 26 0 0 S +R H 1928 1931 - May Su>=8 0 1 D +R H 1928 o - S 9 0 0 S +R H 1929 o - S 3 0 0 S +R H 1930 o - S 15 0 0 S +R H 1931 1932 - S M>=24 0 0 S +R H 1932 o - May 1 0 1 D +R H 1933 o - Ap 30 0 1 D +R H 1933 o - O 2 0 0 S +R H 1934 o - May 20 0 1 D +R H 1934 o - S 16 0 0 S +R H 1935 o - Jun 2 0 1 D +R H 1935 o - S 30 0 0 S +R H 1936 o - Jun 1 0 1 D +R H 1936 o - S 14 0 0 S +R H 1937 1938 - May Su>=1 0 1 D +R H 1937 1941 - S M>=24 0 0 S +R H 1939 o - May 28 0 1 D +R H 1940 1941 - May Su>=1 0 1 D +R H 1946 1949 - Ap lastSu 2 1 D +R H 1946 1949 - S lastSu 2 0 S +R H 1951 1954 - Ap lastSu 2 1 D +R H 1951 1954 - S lastSu 2 0 S +R H 1956 1959 - Ap lastSu 2 1 D +R H 1956 1959 - S lastSu 2 0 S +R H 1962 1973 - Ap lastSu 2 1 D +R H 1962 1973 - O lastSu 2 0 S +R o 1933 1935 - Jun Su>=8 1 1 D +R o 1933 1935 - S Su>=8 1 0 S +R o 1936 1938 - Jun Su>=1 1 1 D +R o 1936 1938 - S Su>=1 1 0 S +R o 1939 o - May 27 1 1 D +R o 1939 1941 - S Sa>=21 1 0 S +R o 1940 o - May 19 1 1 D +R o 1941 o - May 4 1 1 D +R o 1946 1972 - Ap lastSu 2 1 D +R o 1946 1956 - S lastSu 2 0 S +R o 1957 1972 - O lastSu 2 0 S +R o 1993 2006 - Ap Su>=1 0:1 1 D +R o 1993 2006 - O lastSu 0:1 0 S +R t 1919 o - Mar 30 23:30 1 D +R t 1919 o - O 26 0 0 S +R t 1920 o - May 2 2 1 D +R t 1920 o - S 26 0 0 S +R t 1921 o - May 15 2 1 D +R t 1921 o - S 15 2 0 S +R t 1922 1923 - May Su>=8 2 1 D +R t 1922 1926 - S Su>=15 2 0 S +R t 1924 1927 - May Su>=1 2 1 D +R t 1927 1937 - S Su>=25 2 0 S +R t 1928 1937 - Ap Su>=25 2 1 D +R t 1938 1940 - Ap lastSu 2 1 D +R t 1938 1939 - S lastSu 2 0 S +R t 1945 1948 - S lastSu 2 0 S +R t 1946 1973 - Ap lastSu 2 1 D +R t 1949 1950 - N lastSu 2 0 S +R t 1951 1956 - S lastSu 2 0 S +R t 1957 1973 - O lastSu 2 0 S +R W 1916 o - Ap 23 0 1 D +R W 1916 o - S 17 0 0 S +R W 1918 o - Ap 14 2 1 D +R W 1918 o - O 27 2 0 S +R W 1937 o - May 16 2 1 D +R W 1937 o - S 26 2 0 S +R W 1942 o - F 9 2 1 W +R W 1945 o - Au 14 23u 1 P +R W 1945 o - S lastSu 2 0 S +R W 1946 o - May 12 2 1 D +R W 1946 o - O 13 2 0 S +R W 1947 1949 - Ap lastSu 2 1 D +R W 1947 1949 - S lastSu 2 0 S +R W 1950 o - May 1 2 1 D +R W 1950 o - S 30 2 0 S +R W 1951 1960 - Ap lastSu 2 1 D +R W 1951 1958 - S lastSu 2 0 S +R W 1959 o - O lastSu 2 0 S +R W 1960 o - S lastSu 2 0 S +R W 1963 o - Ap lastSu 2 1 D +R W 1963 o - S 22 2 0 S +R W 1966 1986 - Ap lastSu 2s 1 D +R W 1966 2005 - O lastSu 2s 0 S +R W 1987 2005 - Ap Su>=1 2s 1 D +R r 1918 o - Ap 14 2 1 D +R r 1918 o - O 27 2 0 S +R r 1930 1934 - May Su>=1 0 1 D +R r 1930 1934 - O Su>=1 0 0 S +R r 1937 1941 - Ap Su>=8 0 1 D +R r 1937 o - O Su>=8 0 0 S +R r 1938 o - O Su>=1 0 0 S +R r 1939 1941 - O Su>=8 0 0 S +R r 1942 o - F 9 2 1 W +R r 1945 o - Au 14 23u 1 P +R r 1945 o - S lastSu 2 0 S +R r 1946 o - Ap Su>=8 2 1 D +R r 1946 o - O Su>=8 2 0 S +R r 1947 1957 - Ap lastSu 2 1 D +R r 1947 1957 - S lastSu 2 0 S +R r 1959 o - Ap lastSu 2 1 D +R r 1959 o - O lastSu 2 0 S +R Sw 1957 o - Ap lastSu 2 1 D +R Sw 1957 o - O lastSu 2 0 S +R Sw 1959 1961 - Ap lastSu 2 1 D +R Sw 1959 o - O lastSu 2 0 S +R Sw 1960 1961 - S lastSu 2 0 S +R Ed 1918 1919 - Ap Su>=8 2 1 D +R Ed 1918 o - O 27 2 0 S +R Ed 1919 o - May 27 2 0 S +R Ed 1920 1923 - Ap lastSu 2 1 D +R Ed 1920 o - O lastSu 2 0 S +R Ed 1921 1923 - S lastSu 2 0 S +R Ed 1942 o - F 9 2 1 W +R Ed 1945 o - Au 14 23u 1 P +R Ed 1945 o - S lastSu 2 0 S +R Ed 1947 o - Ap lastSu 2 1 D +R Ed 1947 o - S lastSu 2 0 S +R Ed 1972 1986 - Ap lastSu 2 1 D +R Ed 1972 2006 - O lastSu 2 0 S +R Va 1918 o - Ap 14 2 1 D +R Va 1918 o - O 27 2 0 S +R Va 1942 o - F 9 2 1 W +R Va 1945 o - Au 14 23u 1 P +R Va 1945 o - S 30 2 0 S +R Va 1946 1986 - Ap lastSu 2 1 D +R Va 1946 o - S 29 2 0 S +R Va 1947 1961 - S lastSu 2 0 S +R Va 1962 2006 - O lastSu 2 0 S +R Y 1918 o - Ap 14 2 1 D +R Y 1918 o - O 27 2 0 S +R Y 1919 o - May 25 2 1 D +R Y 1919 o - N 1 0 0 S +R Y 1942 o - F 9 2 1 W +R Y 1945 o - Au 14 23u 1 P +R Y 1945 o - S 30 2 0 S +R Y 1972 1986 - Ap lastSu 2 1 D +R Y 1972 2006 - O lastSu 2 0 S +R Y 1987 2006 - Ap Su>=1 2 1 D +R Yu 1965 o - Ap lastSu 0 2 DD +R Yu 1965 o - O lastSu 2 0 S +R m 1931 o - Ap 30 0 1 D +R m 1931 o - O 1 0 0 S +R m 1939 o - F 5 0 1 D +R m 1939 o - Jun 25 0 0 S +R m 1940 o - D 9 0 1 D +R m 1941 o - Ap 1 0 0 S +R m 1943 o - D 16 0 1 W +R m 1944 o - May 1 0 0 S +R m 1950 o - F 12 0 1 D +R m 1950 o - Jul 30 0 0 S +R m 1996 2000 - Ap Su>=1 2 1 D +R m 1996 2000 - O lastSu 2 0 S +R m 2001 o - May Su>=1 2 1 D +R m 2001 o - S lastSu 2 0 S +R m 2002 2022 - Ap Su>=1 2 1 D +R m 2002 2022 - O lastSu 2 0 S +R BB 1942 o - Ap 19 5u 1 D +R BB 1942 o - Au 31 6u 0 S +R BB 1943 o - May 2 5u 1 D +R BB 1943 o - S 5 6u 0 S +R BB 1944 o - Ap 10 5u 0:30 - +R BB 1944 o - S 10 6u 0 S +R BB 1977 o - Jun 12 2 1 D +R BB 1977 1978 - O Su>=1 2 0 S +R BB 1978 1980 - Ap Su>=15 2 1 D +R BB 1979 o - S 30 2 0 S +R BB 1980 o - S 25 2 0 S +R BZ 1918 1941 - O Sa>=1 24 0:30 -0530 +R BZ 1919 1942 - F Sa>=8 24 0 CST +R BZ 1942 o - Jun 27 24 1 CWT +R BZ 1945 o - Au 14 23u 1 CPT +R BZ 1945 o - D 15 24 0 CST +R BZ 1947 1967 - O Sa>=1 24 0:30 -0530 +R BZ 1948 1968 - F Sa>=8 24 0 CST +R BZ 1973 o - D 5 0 1 CDT +R BZ 1974 o - F 9 0 0 CST +R BZ 1982 o - D 18 0 1 CDT +R BZ 1983 o - F 12 0 0 CST +R Be 1917 o - Ap 5 24 1 - +R Be 1917 o - S 30 24 0 - +R Be 1918 o - Ap 13 24 1 - +R Be 1918 o - S 15 24 0 S +R Be 1942 o - Ja 11 2 1 D +R Be 1942 o - O 18 2 0 S +R Be 1943 o - Mar 21 2 1 D +R Be 1943 o - O 31 2 0 S +R Be 1944 1945 - Mar Su>=8 2 1 D +R Be 1944 1945 - N Su>=1 2 0 S +R Be 1947 o - May Su>=15 2 1 D +R Be 1947 o - S Su>=8 2 0 S +R Be 1948 1952 - May Su>=22 2 1 D +R Be 1948 1952 - S Su>=1 2 0 S +R Be 1956 o - May Su>=22 2 1 D +R Be 1956 o - O lastSu 2 0 S +R CR 1979 1980 - F lastSu 0 1 D +R CR 1979 1980 - Jun Su>=1 0 0 S +R CR 1991 1992 - Ja Sa>=15 0 1 D +R CR 1991 o - Jul 1 0 0 S +R CR 1992 o - Mar 15 0 0 S +R Q 1928 o - Jun 10 0 1 D +R Q 1928 o - O 10 0 0 S +R Q 1940 1942 - Jun Su>=1 0 1 D +R Q 1940 1942 - S Su>=1 0 0 S +R Q 1945 1946 - Jun Su>=1 0 1 D +R Q 1945 1946 - S Su>=1 0 0 S +R Q 1965 o - Jun 1 0 1 D +R Q 1965 o - S 30 0 0 S +R Q 1966 o - May 29 0 1 D +R Q 1966 o - O 2 0 0 S +R Q 1967 o - Ap 8 0 1 D +R Q 1967 1968 - S Su>=8 0 0 S +R Q 1968 o - Ap 14 0 1 D +R Q 1969 1977 - Ap lastSu 0 1 D +R Q 1969 1971 - O lastSu 0 0 S +R Q 1972 1974 - O 8 0 0 S +R Q 1975 1977 - O lastSu 0 0 S +R Q 1978 o - May 7 0 1 D +R Q 1978 1990 - O Su>=8 0 0 S +R Q 1979 1980 - Mar Su>=15 0 1 D +R Q 1981 1985 - May Su>=5 0 1 D +R Q 1986 1989 - Mar Su>=14 0 1 D +R Q 1990 1997 - Ap Su>=1 0 1 D +R Q 1991 1995 - O Su>=8 0s 0 S +R Q 1996 o - O 6 0s 0 S +R Q 1997 o - O 12 0s 0 S +R Q 1998 1999 - Mar lastSu 0s 1 D +R Q 1998 2003 - O lastSu 0s 0 S +R Q 2000 2003 - Ap Su>=1 0s 1 D +R Q 2004 o - Mar lastSu 0s 1 D +R Q 2006 2010 - O lastSu 0s 0 S +R Q 2007 o - Mar Su>=8 0s 1 D +R Q 2008 o - Mar Su>=15 0s 1 D +R Q 2009 2010 - Mar Su>=8 0s 1 D +R Q 2011 o - Mar Su>=15 0s 1 D +R Q 2011 o - N 13 0s 0 S +R Q 2012 o - Ap 1 0s 1 D +R Q 2012 ma - N Su>=1 0s 0 S +R Q 2013 ma - Mar Su>=8 0s 1 D +R DO 1966 o - O 30 0 1 EDT +R DO 1967 o - F 28 0 0 EST +R DO 1969 1973 - O lastSu 0 0:30 -0430 +R DO 1970 o - F 21 0 0 EST +R DO 1971 o - Ja 20 0 0 EST +R DO 1972 1974 - Ja 21 0 0 EST +R SV 1987 1988 - May Su>=1 0 1 D +R SV 1987 1988 - S lastSu 0 0 S +R GT 1973 o - N 25 0 1 D +R GT 1974 o - F 24 0 0 S +R GT 1983 o - May 21 0 1 D +R GT 1983 o - S 22 0 0 S +R GT 1991 o - Mar 23 0 1 D +R GT 1991 o - S 7 0 0 S +R GT 2006 o - Ap 30 0 1 D +R GT 2006 o - O 1 0 0 S +R HT 1983 o - May 8 0 1 D +R HT 1984 1987 - Ap lastSu 0 1 D +R HT 1983 1987 - O lastSu 0 0 S +R HT 1988 1997 - Ap Su>=1 1s 1 D +R HT 1988 1997 - O lastSu 1s 0 S +R HT 2005 2006 - Ap Su>=1 0 1 D +R HT 2005 2006 - O lastSu 0 0 S +R HT 2012 2015 - Mar Su>=8 2 1 D +R HT 2012 2015 - N Su>=1 2 0 S +R HT 2017 ma - Mar Su>=8 2 1 D +R HT 2017 ma - N Su>=1 2 0 S +R HN 1987 1988 - May Su>=1 0 1 D +R HN 1987 1988 - S lastSu 0 0 S +R HN 2006 o - May Su>=1 0 1 D +R HN 2006 o - Au M>=1 0 0 S +R NI 1979 1980 - Mar Su>=16 0 1 D +R NI 1979 1980 - Jun M>=23 0 0 S +R NI 2005 o - Ap 10 0 1 D +R NI 2005 o - O Su>=1 0 0 S +R NI 2006 o - Ap 30 2 1 D +R NI 2006 o - O Su>=1 1 0 S +R A 1930 o - D 1 0 1 - +R A 1931 o - Ap 1 0 0 - +R A 1931 o - O 15 0 1 - +R A 1932 1940 - Mar 1 0 0 - +R A 1932 1939 - N 1 0 1 - +R A 1940 o - Jul 1 0 1 - +R A 1941 o - Jun 15 0 0 - +R A 1941 o - O 15 0 1 - +R A 1943 o - Au 1 0 0 - +R A 1943 o - O 15 0 1 - +R A 1946 o - Mar 1 0 0 - +R A 1946 o - O 1 0 1 - +R A 1963 o - O 1 0 0 - +R A 1963 o - D 15 0 1 - +R A 1964 1966 - Mar 1 0 0 - +R A 1964 1966 - O 15 0 1 - +R A 1967 o - Ap 2 0 0 - +R A 1967 1968 - O Su>=1 0 1 - +R A 1968 1969 - Ap Su>=1 0 0 - +R A 1974 o - Ja 23 0 1 - +R A 1974 o - May 1 0 0 - +R A 1988 o - D 1 0 1 - +R A 1989 1993 - Mar Su>=1 0 0 - +R A 1989 1992 - O Su>=15 0 1 - +R A 1999 o - O Su>=1 0 1 - +R A 2000 o - Mar 3 0 0 - +R A 2007 o - D 30 0 1 - +R A 2008 2009 - Mar Su>=15 0 0 - +R A 2008 o - O Su>=15 0 1 - +R Sa 2008 2009 - Mar Su>=8 0 0 - +R Sa 2007 2008 - O Su>=8 0 1 - +R B 1931 o - O 3 11 1 - +R B 1932 1933 - Ap 1 0 0 - +R B 1932 o - O 3 0 1 - +R B 1949 1952 - D 1 0 1 - +R B 1950 o - Ap 16 1 0 - +R B 1951 1952 - Ap 1 0 0 - +R B 1953 o - Mar 1 0 0 - +R B 1963 o - D 9 0 1 - +R B 1964 o - Mar 1 0 0 - +R B 1965 o - Ja 31 0 1 - +R B 1965 o - Mar 31 0 0 - +R B 1965 o - D 1 0 1 - +R B 1966 1968 - Mar 1 0 0 - +R B 1966 1967 - N 1 0 1 - +R B 1985 o - N 2 0 1 - +R B 1986 o - Mar 15 0 0 - +R B 1986 o - O 25 0 1 - +R B 1987 o - F 14 0 0 - +R B 1987 o - O 25 0 1 - +R B 1988 o - F 7 0 0 - +R B 1988 o - O 16 0 1 - +R B 1989 o - Ja 29 0 0 - +R B 1989 o - O 15 0 1 - +R B 1990 o - F 11 0 0 - +R B 1990 o - O 21 0 1 - +R B 1991 o - F 17 0 0 - +R B 1991 o - O 20 0 1 - +R B 1992 o - F 9 0 0 - +R B 1992 o - O 25 0 1 - +R B 1993 o - Ja 31 0 0 - +R B 1993 1995 - O Su>=11 0 1 - +R B 1994 1995 - F Su>=15 0 0 - +R B 1996 o - F 11 0 0 - +R B 1996 o - O 6 0 1 - +R B 1997 o - F 16 0 0 - +R B 1997 o - O 6 0 1 - +R B 1998 o - Mar 1 0 0 - +R B 1998 o - O 11 0 1 - +R B 1999 o - F 21 0 0 - +R B 1999 o - O 3 0 1 - +R B 2000 o - F 27 0 0 - +R B 2000 2001 - O Su>=8 0 1 - +R B 2001 2006 - F Su>=15 0 0 - +R B 2002 o - N 3 0 1 - +R B 2003 o - O 19 0 1 - +R B 2004 o - N 2 0 1 - +R B 2005 o - O 16 0 1 - +R B 2006 o - N 5 0 1 - +R B 2007 o - F 25 0 0 - +R B 2007 o - O Su>=8 0 1 - +R B 2008 2017 - O Su>=15 0 1 - +R B 2008 2011 - F Su>=15 0 0 - +R B 2012 o - F Su>=22 0 0 - +R B 2013 2014 - F Su>=15 0 0 - +R B 2015 o - F Su>=22 0 0 - +R B 2016 2019 - F Su>=15 0 0 - +R B 2018 o - N Su>=1 0 1 - +R x 1927 1931 - S 1 0 1 - +R x 1928 1932 - Ap 1 0 0 - +R x 1968 o - N 3 4u 1 - +R x 1969 o - Mar 30 3u 0 - +R x 1969 o - N 23 4u 1 - +R x 1970 o - Mar 29 3u 0 - +R x 1971 o - Mar 14 3u 0 - +R x 1970 1972 - O Su>=9 4u 1 - +R x 1972 1986 - Mar Su>=9 3u 0 - +R x 1973 o - S 30 4u 1 - +R x 1974 1987 - O Su>=9 4u 1 - +R x 1987 o - Ap 12 3u 0 - +R x 1988 1990 - Mar Su>=9 3u 0 - +R x 1988 1989 - O Su>=9 4u 1 - +R x 1990 o - S 16 4u 1 - +R x 1991 1996 - Mar Su>=9 3u 0 - +R x 1991 1997 - O Su>=9 4u 1 - +R x 1997 o - Mar 30 3u 0 - +R x 1998 o - Mar Su>=9 3u 0 - +R x 1998 o - S 27 4u 1 - +R x 1999 o - Ap 4 3u 0 - +R x 1999 2010 - O Su>=9 4u 1 - +R x 2000 2007 - Mar Su>=9 3u 0 - +R x 2008 o - Mar 30 3u 0 - +R x 2009 o - Mar Su>=9 3u 0 - +R x 2010 o - Ap Su>=1 3u 0 - +R x 2011 o - May Su>=2 3u 0 - +R x 2011 o - Au Su>=16 4u 1 - +R x 2012 2014 - Ap Su>=23 3u 0 - +R x 2012 2014 - S Su>=2 4u 1 - +R x 2016 2018 - May Su>=9 3u 0 - +R x 2016 2018 - Au Su>=9 4u 1 - +R x 2019 ma - Ap Su>=2 3u 0 - +R x 2019 2021 - S Su>=2 4u 1 - +R x 2022 o - S Su>=9 4u 1 - +R x 2023 ma - S Su>=2 4u 1 - +R CO 1992 o - May 3 0 1 - +R CO 1993 o - F 6 24 0 - +R EC 1992 o - N 28 0 1 - +R EC 1993 o - F 5 0 0 - +R FK 1937 1938 - S lastSu 0 1 - +R FK 1938 1942 - Mar Su>=19 0 0 - +R FK 1939 o - O 1 0 1 - +R FK 1940 1942 - S lastSu 0 1 - +R FK 1943 o - Ja 1 0 0 - +R FK 1983 o - S lastSu 0 1 - +R FK 1984 1985 - Ap lastSu 0 0 - +R FK 1984 o - S 16 0 1 - +R FK 1985 2000 - S Su>=9 0 1 - +R FK 1986 2000 - Ap Su>=16 0 0 - +R FK 2001 2010 - Ap Su>=15 2 0 - +R FK 2001 2010 - S Su>=1 2 1 - +R y 1975 1988 - O 1 0 1 - +R y 1975 1978 - Mar 1 0 0 - +R y 1979 1991 - Ap 1 0 0 - +R y 1989 o - O 22 0 1 - +R y 1990 o - O 1 0 1 - +R y 1991 o - O 6 0 1 - +R y 1992 o - Mar 1 0 0 - +R y 1992 o - O 5 0 1 - +R y 1993 o - Mar 31 0 0 - +R y 1993 1995 - O 1 0 1 - +R y 1994 1995 - F lastSu 0 0 - +R y 1996 o - Mar 1 0 0 - +R y 1996 2001 - O Su>=1 0 1 - +R y 1997 o - F lastSu 0 0 - +R y 1998 2001 - Mar Su>=1 0 0 - +R y 2002 2004 - Ap Su>=1 0 0 - +R y 2002 2003 - S Su>=1 0 1 - +R y 2004 2009 - O Su>=15 0 1 - +R y 2005 2009 - Mar Su>=8 0 0 - +R y 2010 2024 - O Su>=1 0 1 - +R y 2010 2012 - Ap Su>=8 0 0 - +R y 2013 2024 - Mar Su>=22 0 0 - +R PE 1938 o - Ja 1 0 1 - +R PE 1938 o - Ap 1 0 0 - +R PE 1938 1939 - S lastSu 0 1 - +R PE 1939 1940 - Mar Su>=24 0 0 - +R PE 1986 1987 - Ja 1 0 1 - +R PE 1986 1987 - Ap 1 0 0 - +R PE 1990 o - Ja 1 0 1 - +R PE 1990 o - Ap 1 0 0 - +R PE 1994 o - Ja 1 0 1 - +R PE 1994 o - Ap 1 0 0 - +R U 1923 1925 - O 1 0 0:30 - +R U 1924 1926 - Ap 1 0 0 - +R U 1933 1938 - O lastSu 0 0:30 - +R U 1934 1941 - Mar lastSa 24 0 - +R U 1939 o - O 1 0 0:30 - +R U 1940 o - O 27 0 0:30 - +R U 1941 o - Au 1 0 0:30 - +R U 1942 o - D 14 0 0:30 - +R U 1943 o - Mar 14 0 0 - +R U 1959 o - May 24 0 0:30 - +R U 1959 o - N 15 0 0 - +R U 1960 o - Ja 17 0 1 - +R U 1960 o - Mar 6 0 0 - +R U 1965 o - Ap 4 0 1 - +R U 1965 o - S 26 0 0 - +R U 1968 o - May 27 0 0:30 - +R U 1968 o - D 1 0 0 - +R U 1970 o - Ap 25 0 1 - +R U 1970 o - Jun 14 0 0 - +R U 1972 o - Ap 23 0 1 - +R U 1972 o - Jul 16 0 0 - +R U 1974 o - Ja 13 0 1:30 - +R U 1974 o - Mar 10 0 0:30 - +R U 1974 o - S 1 0 0 - +R U 1974 o - D 22 0 1 - +R U 1975 o - Mar 30 0 0 - +R U 1976 o - D 19 0 1 - +R U 1977 o - Mar 6 0 0 - +R U 1977 o - D 4 0 1 - +R U 1978 1979 - Mar Su>=1 0 0 - +R U 1978 o - D 17 0 1 - +R U 1979 o - Ap 29 0 1 - +R U 1980 o - Mar 16 0 0 - +R U 1987 o - D 14 0 1 - +R U 1988 o - F 28 0 0 - +R U 1988 o - D 11 0 1 - +R U 1989 o - Mar 5 0 0 - +R U 1989 o - O 29 0 1 - +R U 1990 o - F 25 0 0 - +R U 1990 1991 - O Su>=21 0 1 - +R U 1991 1992 - Mar Su>=1 0 0 - +R U 1992 o - O 18 0 1 - +R U 1993 o - F 28 0 0 - +R U 2004 o - S 19 0 1 - +R U 2005 o - Mar 27 2 0 - +R U 2005 o - O 9 2 1 - +R U 2006 2015 - Mar Su>=8 2 0 - +R U 2006 2014 - O Su>=1 2 1 - +Z Africa/Abidjan -0:16:8 - LMT 1912 +0 - GMT +Z Africa/Algiers 0:12:12 - LMT 1891 Mar 16 +0:9:21 - PMT 1911 Mar 11 +0 d WE%sT 1940 F 25 2 +1 d CE%sT 1946 O 7 +0 - WET 1956 Ja 29 +1 - CET 1963 Ap 14 +0 d WE%sT 1977 O 21 +1 d CE%sT 1979 O 26 +0 d WE%sT 1981 May +1 - CET +Z Africa/Bissau -1:2:20 - LMT 1912 Ja 1 1u +-1 - %z 1975 +0 - GMT +Z Africa/Cairo 2:5:9 - LMT 1900 O +2 K EE%sT +Z Africa/Casablanca -0:30:20 - LMT 1913 O 26 +0 M %z 1984 Mar 16 +1 - %z 1986 +0 M %z 2018 O 28 3 +1 M %z +Z Africa/Ceuta -0:21:16 - LMT 1901 Ja 1 0u +0 - WET 1918 May 6 23 +0 1 WEST 1918 O 7 23 +0 - WET 1924 +0 s WE%sT 1929 +0 - WET 1967 +0 Sp WE%sT 1984 Mar 16 +1 - CET 1986 +1 E CE%sT +Z Africa/El_Aaiun -0:52:48 - LMT 1934 +-1 - %z 1976 Ap 14 +0 M %z 2018 O 28 3 +1 M %z +Z Africa/Johannesburg 1:52 - LMT 1892 F 8 +1:30 - SAST 1903 Mar +2 SA SAST +Z Africa/Juba 2:6:28 - LMT 1931 +2 SD CA%sT 2000 Ja 15 12 +3 - EAT 2021 F +2 - CAT +Z Africa/Khartoum 2:10:8 - LMT 1931 +2 SD CA%sT 2000 Ja 15 12 +3 - EAT 2017 N +2 - CAT +Z Africa/Lagos 0:13:35 - LMT 1905 Jul +0 - GMT 1908 Jul +0:13:35 - LMT 1914 +0:30 - %z 1919 S +1 - WAT +Z Africa/Maputo 2:10:18 - LMT 1909 +2 - CAT +Z Africa/Monrovia -0:43:8 - LMT 1882 +-0:43:8 - MMT 1919 Mar +-0:44:30 - MMT 1972 Ja 7 +0 - GMT +Z Africa/Nairobi 2:27:16 - LMT 1908 May +2:30 - %z 1928 Jun 30 24 +3 - EAT 1930 Ja 4 24 +2:30 - %z 1936 D 31 24 +2:45 - %z 1942 Jul 31 24 +3 - EAT +Z Africa/Ndjamena 1:0:12 - LMT 1912 +1 - WAT 1979 O 14 +1 1 WAST 1980 Mar 8 +1 - WAT +Z Africa/Sao_Tome 0:26:56 - LMT 1884 +-0:36:45 - LMT 1912 Ja 1 0u +0 - GMT 2018 Ja 1 1 +1 - WAT 2019 Ja 1 2 +0 - GMT +Z Africa/Tripoli 0:52:44 - LMT 1920 +1 L CE%sT 1959 +2 - EET 1982 +1 L CE%sT 1990 May 4 +2 - EET 1996 S 30 +1 L CE%sT 1997 O 4 +2 - EET 2012 N 10 2 +1 L CE%sT 2013 O 25 2 +2 - EET +Z Africa/Tunis 0:40:44 - LMT 1881 May 12 +0:9:21 - PMT 1911 Mar 11 +1 n CE%sT +Z Africa/Windhoek 1:8:24 - LMT 1892 F 8 +1:30 - %z 1903 Mar +2 - SAST 1942 S 20 2 +2 1 SAST 1943 Mar 21 2 +2 - SAST 1990 Mar 21 +2 NA %s +Z America/Adak 12:13:22 - LMT 1867 O 19 12:44:35 +-11:46:38 - LMT 1900 Au 20 12 +-11 - NST 1942 +-11 u N%sT 1946 +-11 - NST 1967 Ap +-11 - BST 1969 +-11 u B%sT 1983 O 30 2 +-10 u AH%sT 1983 N 30 +-10 u H%sT +Z America/Anchorage 14:0:24 - LMT 1867 O 19 14:31:37 +-9:59:36 - LMT 1900 Au 20 12 +-10 - AST 1942 +-10 u A%sT 1967 Ap +-10 - AHST 1969 +-10 u AH%sT 1983 O 30 2 +-9 u Y%sT 1983 N 30 +-9 u AK%sT +Z America/Araguaina -3:12:48 - LMT 1914 +-3 B %z 1990 S 17 +-3 - %z 1995 S 14 +-3 B %z 2003 S 24 +-3 - %z 2012 O 21 +-3 B %z 2013 S +-3 - %z +Z America/Argentina/Buenos_Aires -3:53:48 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 A %z +Z America/Argentina/Catamarca -4:23:8 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1991 Mar 3 +-4 - %z 1991 O 20 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 - %z 2004 Jun +-4 - %z 2004 Jun 20 +-3 A %z 2008 O 18 +-3 - %z +Z America/Argentina/Cordoba -4:16:48 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1991 Mar 3 +-4 - %z 1991 O 20 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 A %z +Z America/Argentina/Jujuy -4:21:12 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1990 Mar 4 +-4 - %z 1990 O 28 +-4 1 %z 1991 Mar 17 +-4 - %z 1991 O 6 +-3 1 %z 1992 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 A %z 2008 O 18 +-3 - %z +Z America/Argentina/La_Rioja -4:27:24 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1991 Mar +-4 - %z 1991 May 7 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 - %z 2004 Jun +-4 - %z 2004 Jun 20 +-3 A %z 2008 O 18 +-3 - %z +Z America/Argentina/Mendoza -4:35:16 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1990 Mar 4 +-4 - %z 1990 O 15 +-4 1 %z 1991 Mar +-4 - %z 1991 O 15 +-4 1 %z 1992 Mar +-4 - %z 1992 O 18 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 - %z 2004 May 23 +-4 - %z 2004 S 26 +-3 A %z 2008 O 18 +-3 - %z +Z America/Argentina/Rio_Gallegos -4:36:52 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 - %z 2004 Jun +-4 - %z 2004 Jun 20 +-3 A %z 2008 O 18 +-3 - %z +Z America/Argentina/Salta -4:21:40 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1991 Mar 3 +-4 - %z 1991 O 20 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 A %z 2008 O 18 +-3 - %z +Z America/Argentina/San_Juan -4:34:4 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1991 Mar +-4 - %z 1991 May 7 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 - %z 2004 May 31 +-4 - %z 2004 Jul 25 +-3 A %z 2008 O 18 +-3 - %z +Z America/Argentina/San_Luis -4:25:24 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1990 +-3 1 %z 1990 Mar 14 +-4 - %z 1990 O 15 +-4 1 %z 1991 Mar +-4 - %z 1991 Jun +-3 - %z 1999 O 3 +-4 1 %z 2000 Mar 3 +-3 - %z 2004 May 31 +-4 - %z 2004 Jul 25 +-3 A %z 2008 Ja 21 +-4 Sa %z 2009 O 11 +-3 - %z +Z America/Argentina/Tucuman -4:20:52 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1991 Mar 3 +-4 - %z 1991 O 20 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 - %z 2004 Jun +-4 - %z 2004 Jun 13 +-3 A %z +Z America/Argentina/Ushuaia -4:33:12 - LMT 1894 O 31 +-4:16:48 - CMT 1920 May +-4 - %z 1930 D +-4 A %z 1969 O 5 +-3 A %z 1999 O 3 +-4 A %z 2000 Mar 3 +-3 - %z 2004 May 30 +-4 - %z 2004 Jun 20 +-3 A %z 2008 O 18 +-3 - %z +Z America/Asuncion -3:50:40 - LMT 1890 +-3:50:40 - AMT 1931 O 10 +-4 - %z 1972 O +-3 - %z 1974 Ap +-4 y %z 2024 O 15 +-3 - %z +Z America/Bahia -2:34:4 - LMT 1914 +-3 B %z 2003 S 24 +-3 - %z 2011 O 16 +-3 B %z 2012 O 21 +-3 - %z +Z America/Bahia_Banderas -7:1 - LMT 1922 Ja 1 7u +-7 - MST 1927 Jun 10 +-6 - CST 1930 N 15 +-7 m M%sT 1932 Ap +-6 - CST 1942 Ap 24 +-7 - MST 1970 +-7 m M%sT 2010 Ap 4 2 +-6 m C%sT +Z America/Barbados -3:58:29 - LMT 1911 Au 28 +-4 BB A%sT 1944 +-4 BB AST/-0330 1945 +-4 BB A%sT +Z America/Belem -3:13:56 - LMT 1914 +-3 B %z 1988 S 12 +-3 - %z +Z America/Belize -5:52:48 - LMT 1912 Ap +-6 BZ %s +Z America/Boa_Vista -4:2:40 - LMT 1914 +-4 B %z 1988 S 12 +-4 - %z 1999 S 30 +-4 B %z 2000 O 15 +-4 - %z +Z America/Bogota -4:56:16 - LMT 1884 Mar 13 +-4:56:16 - BMT 1914 N 23 +-5 CO %z +Z America/Boise -7:44:49 - LMT 1883 N 18 20u +-8 u P%sT 1923 May 13 2 +-7 u M%sT 1974 +-7 - MST 1974 F 3 2 +-7 u M%sT +Z America/Cambridge_Bay 0 - -00 1920 +-7 Y M%sT 1999 O 31 2 +-6 C C%sT 2000 O 29 2 +-5 - EST 2000 N 5 +-6 - CST 2001 Ap 1 3 +-7 C M%sT +Z America/Campo_Grande -3:38:28 - LMT 1914 +-4 B %z +Z America/Cancun -5:47:4 - LMT 1922 Ja 1 6u +-6 - CST 1981 D 26 2 +-5 - EST 1983 Ja 4 +-6 m C%sT 1997 O 26 2 +-5 m E%sT 1998 Au 2 2 +-6 m C%sT 2015 F 1 2 +-5 - EST +Z America/Caracas -4:27:44 - LMT 1890 +-4:27:40 - CMT 1912 F 12 +-4:30 - %z 1965 +-4 - %z 2007 D 9 3 +-4:30 - %z 2016 May 1 2:30 +-4 - %z +Z America/Cayenne -3:29:20 - LMT 1911 Jul +-4 - %z 1967 O +-3 - %z +Z America/Chicago -5:50:36 - LMT 1883 N 18 18u +-6 u C%sT 1920 +-6 Ch C%sT 1936 Mar 1 2 +-5 - EST 1936 N 15 2 +-6 Ch C%sT 1942 +-6 u C%sT 1946 +-6 Ch C%sT 1967 +-6 u C%sT +Z America/Chihuahua -7:4:20 - LMT 1922 Ja 1 7u +-7 - MST 1927 Jun 10 +-6 - CST 1930 N 15 +-7 m M%sT 1932 Ap +-6 - CST 1996 +-6 m C%sT 1998 +-6 - CST 1998 Ap Su>=1 3 +-7 m M%sT 2022 O 30 2 +-6 - CST +Z America/Ciudad_Juarez -7:5:56 - LMT 1922 Ja 1 7u +-7 - MST 1927 Jun 10 +-6 - CST 1930 N 15 +-7 m M%sT 1932 Ap +-6 - CST 1996 +-6 m C%sT 1998 +-6 - CST 1998 Ap Su>=1 3 +-7 m M%sT 2010 +-7 u M%sT 2022 O 30 2 +-6 - CST 2022 N 30 +-7 u M%sT +Z America/Costa_Rica -5:36:13 - LMT 1890 +-5:36:13 - SJMT 1921 Ja 15 +-6 CR C%sT +Z America/Coyhaique -4:48:16 - LMT 1890 +-4:42:45 - SMT 1910 Ja 10 +-5 - %z 1916 Jul +-4:42:45 - SMT 1918 S 10 +-4 - %z 1919 Jul +-4:42:45 - SMT 1927 S +-5 x %z 1932 S +-4 - %z 1942 Jun +-5 - %z 1942 Au +-4 - %z 1946 Au 28 24 +-5 1 %z 1947 Mar 31 24 +-5 - %z 1947 May 21 23 +-4 x %z 2025 Mar 20 +-3 - %z +Z America/Cuiaba -3:44:20 - LMT 1914 +-4 B %z 2003 S 24 +-4 - %z 2004 O +-4 B %z +Z America/Danmarkshavn -1:14:40 - LMT 1916 Jul 28 +-3 - %z 1980 Ap 6 2 +-3 E %z 1996 +0 - GMT +Z America/Dawson -9:17:40 - LMT 1900 Au 20 +-9 Y Y%sT 1965 +-9 Yu Y%sT 1973 O 28 +-8 - PST 1980 +-8 C P%sT 2020 N +-7 - MST +Z America/Dawson_Creek -8:0:56 - LMT 1884 +-8 C P%sT 1947 +-8 Va P%sT 1972 Au 30 2 +-7 - MST +Z America/Denver -6:59:56 - LMT 1883 N 18 19u +-7 u M%sT 1920 +-7 De M%sT 1942 +-7 u M%sT 1946 +-7 De M%sT 1967 +-7 u M%sT +Z America/Detroit -5:32:11 - LMT 1905 +-6 - CST 1915 May 15 2 +-5 - EST 1942 +-5 u E%sT 1946 +-5 Dt E%sT 1967 Jun 14 0:1 +-5 u E%sT 1969 +-5 - EST 1973 +-5 u E%sT 1975 +-5 - EST 1975 Ap 27 2 +-5 u E%sT +Z America/Edmonton -7:33:52 - LMT 1906 S +-7 Ed M%sT 1987 +-7 C M%sT +Z America/Eirunepe -4:39:28 - LMT 1914 +-5 B %z 1988 S 12 +-5 - %z 1993 S 28 +-5 B %z 1994 S 22 +-5 - %z 2008 Jun 24 +-4 - %z 2013 N 10 +-5 - %z +Z America/El_Salvador -5:56:48 - LMT 1921 +-6 SV C%sT +Z America/Fort_Nelson -8:10:47 - LMT 1884 +-8 Va P%sT 1946 +-8 - PST 1947 +-8 Va P%sT 1987 +-8 C P%sT 2015 Mar 8 2 +-7 - MST +Z America/Fortaleza -2:34 - LMT 1914 +-3 B %z 1990 S 17 +-3 - %z 1999 S 30 +-3 B %z 2000 O 22 +-3 - %z 2001 S 13 +-3 B %z 2002 O +-3 - %z +Z America/Glace_Bay -3:59:48 - LMT 1902 Jun 15 +-4 C A%sT 1953 +-4 H A%sT 1954 +-4 - AST 1972 +-4 H A%sT 1974 +-4 C A%sT +Z America/Goose_Bay -4:1:40 - LMT 1884 +-3:30:52 - NST 1918 +-3:30:52 C N%sT 1919 +-3:30:52 - NST 1935 Mar 30 +-3:30 - NST 1936 +-3:30 j N%sT 1942 May 11 +-3:30 C N%sT 1946 +-3:30 j N%sT 1966 Mar 15 2 +-4 j A%sT 2011 N +-4 C A%sT +Z America/Grand_Turk -4:44:32 - LMT 1890 +-5:7:10 - KMT 1912 F +-5 - EST 1979 +-5 u E%sT 2015 Mar 8 2 +-4 - AST 2018 Mar 11 3 +-5 u E%sT +Z America/Guatemala -6:2:4 - LMT 1918 O 5 +-6 GT C%sT +Z America/Guayaquil -5:19:20 - LMT 1890 +-5:14 - QMT 1931 +-5 EC %z +Z America/Guyana -3:52:39 - LMT 1911 Au +-4 - %z 1915 Mar +-3:45 - %z 1975 Au +-3 - %z 1992 Mar 29 1 +-4 - %z +Z America/Halifax -4:14:24 - LMT 1902 Jun 15 +-4 H A%sT 1918 +-4 C A%sT 1919 +-4 H A%sT 1942 F 9 2s +-4 C A%sT 1946 +-4 H A%sT 1974 +-4 C A%sT +Z America/Havana -5:29:28 - LMT 1890 +-5:29:36 - HMT 1925 Jul 19 12 +-5 Q C%sT +Z America/Hermosillo -7:23:52 - LMT 1922 Ja 1 7u +-7 - MST 1927 Jun 10 +-6 - CST 1930 N 15 +-7 m M%sT 1932 Ap +-6 - CST 1942 Ap 24 +-7 - MST 1996 +-7 m M%sT 1999 +-7 - MST +Z America/Indiana/Indianapolis -5:44:38 - LMT 1883 N 18 18u +-6 u C%sT 1920 +-6 In C%sT 1942 +-6 u C%sT 1946 +-6 In C%sT 1955 Ap 24 2 +-5 - EST 1957 S 29 2 +-6 - CST 1958 Ap 27 2 +-5 - EST 1969 +-5 u E%sT 1971 +-5 - EST 2006 +-5 u E%sT +Z America/Indiana/Knox -5:46:30 - LMT 1883 N 18 18u +-6 u C%sT 1947 +-6 St C%sT 1962 Ap 29 2 +-5 - EST 1963 O 27 2 +-6 u C%sT 1991 O 27 2 +-5 - EST 2006 Ap 2 2 +-6 u C%sT +Z America/Indiana/Marengo -5:45:23 - LMT 1883 N 18 18u +-6 u C%sT 1951 +-6 Ma C%sT 1961 Ap 30 2 +-5 - EST 1969 +-5 u E%sT 1974 Ja 6 2 +-6 1 CDT 1974 O 27 2 +-5 u E%sT 1976 +-5 - EST 2006 +-5 u E%sT +Z America/Indiana/Petersburg -5:49:7 - LMT 1883 N 18 18u +-6 u C%sT 1955 +-6 Pi C%sT 1965 Ap 25 2 +-5 - EST 1966 O 30 2 +-6 u C%sT 1977 O 30 2 +-5 - EST 2006 Ap 2 2 +-6 u C%sT 2007 N 4 2 +-5 u E%sT +Z America/Indiana/Tell_City -5:47:3 - LMT 1883 N 18 18u +-6 u C%sT 1946 +-6 Pe C%sT 1964 Ap 26 2 +-5 - EST 1967 O 29 2 +-6 u C%sT 1969 Ap 27 2 +-5 u E%sT 1971 +-5 - EST 2006 Ap 2 2 +-6 u C%sT +Z America/Indiana/Vevay -5:40:16 - LMT 1883 N 18 18u +-6 u C%sT 1954 Ap 25 2 +-5 - EST 1969 +-5 u E%sT 1973 +-5 - EST 2006 +-5 u E%sT +Z America/Indiana/Vincennes -5:50:7 - LMT 1883 N 18 18u +-6 u C%sT 1946 +-6 V C%sT 1964 Ap 26 2 +-5 - EST 1969 +-5 u E%sT 1971 +-5 - EST 2006 Ap 2 2 +-6 u C%sT 2007 N 4 2 +-5 u E%sT +Z America/Indiana/Winamac -5:46:25 - LMT 1883 N 18 18u +-6 u C%sT 1946 +-6 Pu C%sT 1961 Ap 30 2 +-5 - EST 1969 +-5 u E%sT 1971 +-5 - EST 2006 Ap 2 2 +-6 u C%sT 2007 Mar 11 2 +-5 u E%sT +Z America/Inuvik 0 - -00 1953 +-8 Y P%sT 1979 Ap lastSu 2 +-7 Y M%sT 1980 +-7 C M%sT +Z America/Iqaluit 0 - -00 1942 Au +-5 Y E%sT 1999 O 31 2 +-6 C C%sT 2000 O 29 2 +-5 C E%sT +Z America/Jamaica -5:7:10 - LMT 1890 +-5:7:10 - KMT 1912 F +-5 - EST 1974 +-5 u E%sT 1984 +-5 - EST +Z America/Juneau 15:2:19 - LMT 1867 O 19 15:33:32 +-8:57:41 - LMT 1900 Au 20 12 +-8 - PST 1942 +-8 u P%sT 1946 +-8 - PST 1969 +-8 u P%sT 1980 Ap 27 2 +-9 u Y%sT 1980 O 26 2 +-8 u P%sT 1983 O 30 2 +-9 u Y%sT 1983 N 30 +-9 u AK%sT +Z America/Kentucky/Louisville -5:43:2 - LMT 1883 N 18 18u +-6 u C%sT 1921 +-6 v C%sT 1942 +-6 u C%sT 1946 +-6 v C%sT 1961 Jul 23 2 +-5 - EST 1968 +-5 u E%sT 1974 Ja 6 2 +-6 1 CDT 1974 O 27 2 +-5 u E%sT +Z America/Kentucky/Monticello -5:39:24 - LMT 1883 N 18 18u +-6 u C%sT 1946 +-6 - CST 1968 +-6 u C%sT 2000 O 29 2 +-5 u E%sT +Z America/La_Paz -4:32:36 - LMT 1890 +-4:32:36 - CMT 1931 O 15 +-4:32:36 1 BST 1932 Mar 21 +-4 - %z +Z America/Lima -5:8:12 - LMT 1890 +-5:8:36 - LMT 1908 Jul 28 +-5 PE %z +Z America/Los_Angeles -7:52:58 - LMT 1883 N 18 20u +-8 u P%sT 1946 +-8 CA P%sT 1967 +-8 u P%sT +Z America/Maceio -2:22:52 - LMT 1914 +-3 B %z 1990 S 17 +-3 - %z 1995 O 13 +-3 B %z 1996 S 4 +-3 - %z 1999 S 30 +-3 B %z 2000 O 22 +-3 - %z 2001 S 13 +-3 B %z 2002 O +-3 - %z +Z America/Managua -5:45:8 - LMT 1890 +-5:45:12 - MMT 1934 Jun 23 +-6 - CST 1973 May +-5 - EST 1975 F 16 +-6 NI C%sT 1992 Ja 1 4 +-5 - EST 1992 S 24 +-6 - CST 1993 +-5 - EST 1997 +-6 NI C%sT +Z America/Manaus -4:0:4 - LMT 1914 +-4 B %z 1988 S 12 +-4 - %z 1993 S 28 +-4 B %z 1994 S 22 +-4 - %z +Z America/Martinique -4:4:20 - LMT 1890 +-4:4:20 - FFMT 1911 May +-4 - AST 1980 Ap 6 +-4 1 ADT 1980 S 28 +-4 - AST +Z America/Matamoros -6:30 - LMT 1922 Ja 1 6u +-6 - CST 1988 +-6 u C%sT 1989 +-6 m C%sT 2010 +-6 u C%sT +Z America/Mazatlan -7:5:40 - LMT 1922 Ja 1 7u +-7 - MST 1927 Jun 10 +-6 - CST 1930 N 15 +-7 m M%sT 1932 Ap +-6 - CST 1942 Ap 24 +-7 - MST 1970 +-7 m M%sT +Z America/Menominee -5:50:27 - LMT 1885 S 18 12 +-6 u C%sT 1946 +-6 Me C%sT 1969 Ap 27 2 +-5 - EST 1973 Ap 29 2 +-6 u C%sT +Z America/Merida -5:58:28 - LMT 1922 Ja 1 6u +-6 - CST 1981 D 26 2 +-5 - EST 1982 N 2 2 +-6 m C%sT +Z America/Metlakatla 15:13:42 - LMT 1867 O 19 15:44:55 +-8:46:18 - LMT 1900 Au 20 12 +-8 - PST 1942 +-8 u P%sT 1946 +-8 - PST 1969 +-8 u P%sT 1983 O 30 2 +-8 - PST 2015 N 1 2 +-9 u AK%sT 2018 N 4 2 +-8 - PST 2019 Ja 20 2 +-9 u AK%sT +Z America/Mexico_City -6:36:36 - LMT 1922 Ja 1 7u +-7 - MST 1927 Jun 10 +-6 - CST 1930 N 15 +-7 m M%sT 1932 Ap +-6 m C%sT 2001 S 30 2 +-6 - CST 2002 F 20 +-6 m C%sT +Z America/Miquelon -3:44:40 - LMT 1911 Jun 15 +-4 - AST 1980 May +-3 - %z 1987 +-3 C %z +Z America/Moncton -4:19:8 - LMT 1883 D 9 +-5 - EST 1902 Jun 15 +-4 C A%sT 1933 +-4 o A%sT 1942 +-4 C A%sT 1946 +-4 o A%sT 1973 +-4 C A%sT 1993 +-4 o A%sT 2007 +-4 C A%sT +Z America/Monterrey -6:41:16 - LMT 1922 Ja 1 6u +-7 - MST 1927 Jun 10 +-6 - CST 1930 N 15 +-7 m M%sT 1932 Ap +-6 - CST 1988 +-6 u C%sT 1989 +-6 m C%sT +Z America/Montevideo -3:44:51 - LMT 1908 Jun 10 +-3:44:51 - MMT 1920 May +-4 - %z 1923 O +-3:30 U %z 1942 D 14 +-3 U %z 1960 +-3 U %z 1968 +-3 U %z 1970 +-3 U %z 1974 +-3 U %z 1974 Mar 10 +-3 U %z 1974 D 22 +-3 U %z +Z America/New_York -4:56:2 - LMT 1883 N 18 17u +-5 u E%sT 1920 +-5 NY E%sT 1942 +-5 u E%sT 1946 +-5 NY E%sT 1967 +-5 u E%sT +Z America/Nome 12:58:22 - LMT 1867 O 19 13:29:35 +-11:1:38 - LMT 1900 Au 20 12 +-11 - NST 1942 +-11 u N%sT 1946 +-11 - NST 1967 Ap +-11 - BST 1969 +-11 u B%sT 1983 O 30 2 +-9 u Y%sT 1983 N 30 +-9 u AK%sT +Z America/Noronha -2:9:40 - LMT 1914 +-2 B %z 1990 S 17 +-2 - %z 1999 S 30 +-2 B %z 2000 O 15 +-2 - %z 2001 S 13 +-2 B %z 2002 O +-2 - %z +Z America/North_Dakota/Beulah -6:47:7 - LMT 1883 N 18 19u +-7 u M%sT 2010 N 7 2 +-6 u C%sT +Z America/North_Dakota/Center -6:45:12 - LMT 1883 N 18 19u +-7 u M%sT 1992 O 25 2 +-6 u C%sT +Z America/North_Dakota/New_Salem -6:45:39 - LMT 1883 N 18 19u +-7 u M%sT 2003 O 26 2 +-6 u C%sT +Z America/Nuuk -3:26:56 - LMT 1916 Jul 28 +-3 - %z 1980 Ap 6 2 +-3 E %z 2023 Mar 26 1u +-2 - %z 2023 O 29 1u +-2 E %z +Z America/Ojinaga -6:57:40 - LMT 1922 Ja 1 7u +-7 - MST 1927 Jun 10 +-6 - CST 1930 N 15 +-7 m M%sT 1932 Ap +-6 - CST 1996 +-6 m C%sT 1998 +-6 - CST 1998 Ap Su>=1 3 +-7 m M%sT 2010 +-7 u M%sT 2022 O 30 2 +-6 - CST 2022 N 30 +-6 u C%sT +Z America/Panama -5:18:8 - LMT 1890 +-5:19:36 - CMT 1908 Ap 22 +-5 - EST +Z America/Paramaribo -3:40:40 - LMT 1911 +-3:40:52 - PMT 1935 +-3:40:36 - PMT 1945 O +-3:30 - %z 1984 O +-3 - %z +Z America/Phoenix -7:28:18 - LMT 1883 N 18 19u +-7 u M%sT 1944 Ja 1 0:1 +-7 - MST 1944 Ap 1 0:1 +-7 u M%sT 1944 O 1 0:1 +-7 - MST 1967 +-7 u M%sT 1968 Mar 21 +-7 - MST +Z America/Port-au-Prince -4:49:20 - LMT 1890 +-4:49 - PPMT 1917 Ja 24 12 +-5 HT E%sT +Z America/Porto_Velho -4:15:36 - LMT 1914 +-4 B %z 1988 S 12 +-4 - %z +Z America/Puerto_Rico -4:24:25 - LMT 1899 Mar 28 12 +-4 - AST 1942 May 3 +-4 u A%sT 1946 +-4 - AST +Z America/Punta_Arenas -4:43:40 - LMT 1890 +-4:42:45 - SMT 1910 Ja 10 +-5 - %z 1916 Jul +-4:42:45 - SMT 1918 S 10 +-4 - %z 1919 Jul +-4:42:45 - SMT 1927 S +-5 x %z 1932 S +-4 - %z 1942 Jun +-5 - %z 1942 Au +-4 - %z 1946 Au 28 24 +-5 1 %z 1947 Mar 31 24 +-5 - %z 1947 May 21 23 +-4 x %z 2016 D 4 +-3 - %z +Z America/Rankin_Inlet 0 - -00 1957 +-6 Y C%sT 2000 O 29 2 +-5 - EST 2001 Ap 1 3 +-6 C C%sT +Z America/Recife -2:19:36 - LMT 1914 +-3 B %z 1990 S 17 +-3 - %z 1999 S 30 +-3 B %z 2000 O 15 +-3 - %z 2001 S 13 +-3 B %z 2002 O +-3 - %z +Z America/Regina -6:58:36 - LMT 1905 S +-7 r M%sT 1960 Ap lastSu 2 +-6 - CST +Z America/Resolute 0 - -00 1947 Au 31 +-6 Y C%sT 2000 O 29 2 +-5 - EST 2001 Ap 1 3 +-6 C C%sT 2006 O 29 2 +-5 - EST 2007 Mar 11 3 +-6 C C%sT +Z America/Rio_Branco -4:31:12 - LMT 1914 +-5 B %z 1988 S 12 +-5 - %z 2008 Jun 24 +-4 - %z 2013 N 10 +-5 - %z +Z America/Santarem -3:38:48 - LMT 1914 +-4 B %z 1988 S 12 +-4 - %z 2008 Jun 24 +-3 - %z +Z America/Santiago -4:42:45 - LMT 1890 +-4:42:45 - SMT 1910 Ja 10 +-5 - %z 1916 Jul +-4:42:45 - SMT 1918 S 10 +-4 - %z 1919 Jul +-4:42:45 - SMT 1927 S +-5 x %z 1932 S +-4 - %z 1942 Jun +-5 - %z 1942 Au +-4 - %z 1946 Jul 14 24 +-4 1 %z 1946 Au 28 24 +-5 1 %z 1947 Mar 31 24 +-5 - %z 1947 May 21 23 +-4 x %z +Z America/Santo_Domingo -4:39:36 - LMT 1890 +-4:40 - SDMT 1933 Ap 1 12 +-5 DO %s 1974 O 27 +-4 - AST 2000 O 29 2 +-5 u E%sT 2000 D 3 1 +-4 - AST +Z America/Sao_Paulo -3:6:28 - LMT 1914 +-3 B %z 1963 O 23 +-3 1 %z 1964 +-3 B %z +Z America/Scoresbysund -1:27:52 - LMT 1916 Jul 28 +-2 - %z 1980 Ap 6 2 +-2 c %z 1981 Mar 29 +-1 E %z 2024 Mar 31 +-2 E %z +Z America/Sitka 14:58:47 - LMT 1867 O 19 15:30 +-9:1:13 - LMT 1900 Au 20 12 +-8 - PST 1942 +-8 u P%sT 1946 +-8 - PST 1969 +-8 u P%sT 1983 O 30 2 +-9 u Y%sT 1983 N 30 +-9 u AK%sT +Z America/St_Johns -3:30:52 - LMT 1884 +-3:30:52 j N%sT 1918 +-3:30:52 C N%sT 1919 +-3:30:52 j N%sT 1935 Mar 30 +-3:30 j N%sT 1942 May 11 +-3:30 C N%sT 1946 +-3:30 j N%sT 2011 N +-3:30 C N%sT +Z America/Swift_Current -7:11:20 - LMT 1905 S +-7 C M%sT 1946 Ap lastSu 2 +-7 r M%sT 1950 +-7 Sw M%sT 1972 Ap lastSu 2 +-6 - CST +Z America/Tegucigalpa -5:48:52 - LMT 1921 Ap +-6 HN C%sT +Z America/Thule -4:35:8 - LMT 1916 Jul 28 +-4 Th A%sT +Z America/Tijuana -7:48:4 - LMT 1922 Ja 1 7u +-7 - MST 1924 +-8 - PST 1927 Jun 10 +-7 - MST 1930 N 15 +-8 - PST 1931 Ap +-8 1 PDT 1931 S 30 +-8 - PST 1942 Ap 24 +-8 1 PWT 1945 Au 14 23u +-8 1 PPT 1945 N 15 +-8 - PST 1948 Ap 5 +-8 1 PDT 1949 Ja 14 +-8 - PST 1950 May +-8 1 PDT 1950 S 24 +-8 - PST 1951 Ap 29 2 +-8 1 PDT 1951 S 30 2 +-8 - PST 1952 Ap 27 2 +-8 1 PDT 1952 S 28 2 +-8 CA P%sT 1967 +-8 u P%sT 1996 +-8 m P%sT 2001 +-8 u P%sT 2002 F 20 +-8 m P%sT 2010 +-8 u P%sT +Z America/Toronto -5:17:32 - LMT 1895 +-5 C E%sT 1919 +-5 t E%sT 1942 F 9 2s +-5 C E%sT 1946 +-5 t E%sT 1974 +-5 C E%sT +Z America/Vancouver -8:12:28 - LMT 1884 +-8 Va P%sT 1987 +-8 C P%sT +Z America/Whitehorse -9:0:12 - LMT 1900 Au 20 +-9 Y Y%sT 1965 +-9 Yu Y%sT 1966 F 27 +-8 - PST 1980 +-8 C P%sT 2020 N +-7 - MST +Z America/Winnipeg -6:28:36 - LMT 1887 Jul 16 +-6 W C%sT 2006 +-6 C C%sT +Z America/Yakutat 14:41:5 - LMT 1867 O 19 15:12:18 +-9:18:55 - LMT 1900 Au 20 12 +-9 - YST 1942 +-9 u Y%sT 1946 +-9 - YST 1969 +-9 u Y%sT 1983 N 30 +-9 u AK%sT +Z Antarctica/Casey 0 - -00 1969 +8 - %z 2009 O 18 2 +11 - %z 2010 Mar 5 2 +8 - %z 2011 O 28 2 +11 - %z 2012 F 21 17u +8 - %z 2016 O 22 +11 - %z 2018 Mar 11 4 +8 - %z 2018 O 7 4 +11 - %z 2019 Mar 17 3 +8 - %z 2019 O 4 3 +11 - %z 2020 Mar 8 3 +8 - %z 2020 O 4 0:1 +11 - %z 2021 Mar 14 +8 - %z 2021 O 3 0:1 +11 - %z 2022 Mar 13 +8 - %z 2022 O 2 0:1 +11 - %z 2023 Mar 9 3 +8 - %z +Z Antarctica/Davis 0 - -00 1957 Ja 13 +7 - %z 1964 N +0 - -00 1969 F +7 - %z 2009 O 18 2 +5 - %z 2010 Mar 10 20u +7 - %z 2011 O 28 2 +5 - %z 2012 F 21 20u +7 - %z +Z Antarctica/Macquarie 0 - -00 1899 N +10 - AEST 1916 O 1 2 +10 1 AEDT 1917 F +10 AU AE%sT 1919 Ap 1 0s +0 - -00 1948 Mar 25 +10 AU AE%sT 1967 +10 AT AE%sT 2010 +10 1 AEDT 2011 +10 AT AE%sT +Z Antarctica/Mawson 0 - -00 1954 F 13 +6 - %z 2009 O 18 2 +5 - %z +Z Antarctica/Palmer 0 - -00 1965 +-4 A %z 1969 O 5 +-3 A %z 1982 May +-4 x %z 2016 D 4 +-3 - %z +Z Antarctica/Rothera 0 - -00 1976 D +-3 - %z +Z Antarctica/Troll 0 - -00 2005 F 12 +0 Tr %s +Z Antarctica/Vostok 0 - -00 1957 D 16 +7 - %z 1994 F +0 - -00 1994 N +7 - %z 2023 D 18 2 +5 - %z +Z Asia/Almaty 5:7:48 - LMT 1924 May 2 +5 - %z 1930 Jun 21 +6 R %z 1991 Mar 31 2s +5 R %z 1992 Ja 19 2s +6 R %z 2004 O 31 2s +6 - %z 2024 Mar +5 - %z +Z Asia/Amman 2:23:44 - LMT 1931 +2 J EE%sT 2022 O 28 0s +3 - %z +Z Asia/Anadyr 11:49:56 - LMT 1924 May 2 +12 - %z 1930 Jun 21 +13 R %z 1982 Ap 1 0s +12 R %z 1991 Mar 31 2s +11 R %z 1992 Ja 19 2s +12 R %z 2010 Mar 28 2s +11 R %z 2011 Mar 27 2s +12 - %z +Z Asia/Aqtau 3:21:4 - LMT 1924 May 2 +4 - %z 1930 Jun 21 +5 - %z 1981 O +6 - %z 1982 Ap +5 R %z 1991 Mar 31 2s +4 R %z 1992 Ja 19 2s +5 R %z 1994 S 25 2s +4 R %z 2004 O 31 2s +5 - %z +Z Asia/Aqtobe 3:48:40 - LMT 1924 May 2 +4 - %z 1930 Jun 21 +5 - %z 1981 Ap +5 1 %z 1981 O +6 - %z 1982 Ap +5 R %z 1991 Mar 31 2s +4 R %z 1992 Ja 19 2s +5 R %z 2004 O 31 2s +5 - %z +Z Asia/Ashgabat 3:53:32 - LMT 1924 May 2 +4 - %z 1930 Jun 21 +5 R %z 1991 Mar 31 2 +4 R %z 1992 Ja 19 2 +5 - %z +Z Asia/Atyrau 3:27:44 - LMT 1924 May 2 +3 - %z 1930 Jun 21 +5 - %z 1981 O +6 - %z 1982 Ap +5 R %z 1991 Mar 31 2s +4 R %z 1992 Ja 19 2s +5 R %z 1999 Mar 28 2s +4 R %z 2004 O 31 2s +5 - %z +Z Asia/Baghdad 2:57:40 - LMT 1890 +2:57:36 - BMT 1918 +3 - %z 1982 May +3 IQ %z +Z Asia/Baku 3:19:24 - LMT 1924 May 2 +3 - %z 1957 Mar +4 R %z 1991 Mar 31 2s +3 R %z 1992 S lastSu 2s +4 - %z 1996 +4 E %z 1997 +4 AZ %z +Z Asia/Bangkok 6:42:4 - LMT 1880 +6:42:4 - BMT 1920 Ap +7 - %z +Z Asia/Barnaul 5:35 - LMT 1919 D 10 +6 - %z 1930 Jun 21 +7 R %z 1991 Mar 31 2s +6 R %z 1992 Ja 19 2s +7 R %z 1995 May 28 +6 R %z 2011 Mar 27 2s +7 - %z 2014 O 26 2s +6 - %z 2016 Mar 27 2s +7 - %z +Z Asia/Beirut 2:22 - LMT 1880 +2 l EE%sT +Z Asia/Bishkek 4:58:24 - LMT 1924 May 2 +5 - %z 1930 Jun 21 +6 R %z 1991 Mar 31 2s +5 R %z 1991 Au 31 2 +5 KG %z 2005 Au 12 +6 - %z +Z Asia/Chita 7:33:52 - LMT 1919 D 15 +8 - %z 1930 Jun 21 +9 R %z 1991 Mar 31 2s +8 R %z 1992 Ja 19 2s +9 R %z 2011 Mar 27 2s +10 - %z 2014 O 26 2s +8 - %z 2016 Mar 27 2 +9 - %z +Z Asia/Colombo 5:19:24 - LMT 1880 +5:19:32 - MMT 1906 +5:30 - %z 1942 Ja 5 +5:30 0:30 %z 1942 S +5:30 1 %z 1945 O 16 2 +5:30 - %z 1996 May 25 +6:30 - %z 1996 O 26 0:30 +6 - %z 2006 Ap 15 0:30 +5:30 - %z +Z Asia/Damascus 2:25:12 - LMT 1920 +2 S EE%sT 2022 O 28 +3 - %z +Z Asia/Dhaka 6:1:40 - LMT 1890 +5:53:20 - HMT 1941 O +6:30 - %z 1942 May 15 +5:30 - %z 1942 S +6:30 - %z 1951 S 30 +6 - %z 2009 +6 BD %z +Z Asia/Dili 8:22:20 - LMT 1911 D 31 16u +8 - %z 1942 F 21 23 +9 - %z 1976 May 3 +8 - %z 2000 S 17 +9 - %z +Z Asia/Dubai 3:41:12 - LMT 1920 +4 - %z +Z Asia/Dushanbe 4:35:12 - LMT 1924 May 2 +5 - %z 1930 Jun 21 +6 R %z 1991 Mar 31 2s +5 1 %z 1991 S 9 2s +5 - %z +Z Asia/Famagusta 2:15:48 - LMT 1921 N 14 +2 CY EE%sT 1998 S +2 E EE%sT 2016 S 8 +3 - %z 2017 O 29 1u +2 E EE%sT +Z Asia/Gaza 2:17:52 - LMT 1900 O +2 Z EET/EEST 1948 May 15 +2 K EE%sT 1967 Jun 5 +2 Z I%sT 1996 +2 J EE%sT 1999 +2 P EE%sT 2008 Au 29 +2 - EET 2008 S +2 P EE%sT 2010 +2 - EET 2010 Mar 27 0:1 +2 P EE%sT 2011 Au +2 - EET 2012 +2 P EE%sT +Z Asia/Hebron 2:20:23 - LMT 1900 O +2 Z EET/EEST 1948 May 15 +2 K EE%sT 1967 Jun 5 +2 Z I%sT 1996 +2 J EE%sT 1999 +2 P EE%sT +Z Asia/Ho_Chi_Minh 7:6:30 - LMT 1906 Jul +7:6:30 - PLMT 1911 May +7 - %z 1942 D 31 23 +8 - %z 1945 Mar 14 23 +9 - %z 1945 S 1 24 +7 - %z 1947 Ap +8 - %z 1955 Jul 1 1 +7 - %z 1959 D 31 23 +8 - %z 1975 Jun 13 +7 - %z +Z Asia/Hong_Kong 7:36:42 - LMT 1904 O 29 17u +8 - HKT 1941 Jun 15 3 +8 1 HKST 1941 O 1 4 +8 0:30 HKWT 1941 D 25 +9 - JST 1945 N 18 2 +8 HK HK%sT +Z Asia/Hovd 6:6:36 - LMT 1905 Au +6 - %z 1978 +7 X %z +Z Asia/Irkutsk 6:57:5 - LMT 1880 +6:57:5 - IMT 1920 Ja 25 +7 - %z 1930 Jun 21 +8 R %z 1991 Mar 31 2s +7 R %z 1992 Ja 19 2s +8 R %z 2011 Mar 27 2s +9 - %z 2014 O 26 2s +8 - %z +Z Asia/Jakarta 7:7:12 - LMT 1867 Au 10 +7:7:12 - BMT 1923 D 31 16:40u +7:20 - %z 1932 N +7:30 - %z 1942 Mar 23 +9 - %z 1945 S 23 +7:30 - %z 1948 May +8 - %z 1950 May +7:30 - %z 1964 +7 - WIB +Z Asia/Jayapura 9:22:48 - LMT 1932 N +9 - %z 1944 S +9:30 - %z 1964 +9 - WIT +Z Asia/Jerusalem 2:20:54 - LMT 1880 +2:20:40 - JMT 1918 +2 Z I%sT +Z Asia/Kabul 4:36:48 - LMT 1890 +4 - %z 1945 +4:30 - %z +Z Asia/Kamchatka 10:34:36 - LMT 1922 N 10 +11 - %z 1930 Jun 21 +12 R %z 1991 Mar 31 2s +11 R %z 1992 Ja 19 2s +12 R %z 2010 Mar 28 2s +11 R %z 2011 Mar 27 2s +12 - %z +Z Asia/Karachi 4:28:12 - LMT 1907 +5:30 - %z 1942 S +5:30 1 %z 1945 O 15 +5:30 - %z 1951 S 30 +5 - %z 1971 Mar 26 +5 PK PK%sT +Z Asia/Kathmandu 5:41:16 - LMT 1920 +5:30 - %z 1986 +5:45 - %z +Z Asia/Khandyga 9:2:13 - LMT 1919 D 15 +8 - %z 1930 Jun 21 +9 R %z 1991 Mar 31 2s +8 R %z 1992 Ja 19 2s +9 R %z 2004 +10 R %z 2011 Mar 27 2s +11 - %z 2011 S 13 0s +10 - %z 2014 O 26 2s +9 - %z +Z Asia/Kolkata 5:53:28 - LMT 1854 Jun 28 +5:53:20 - HMT 1870 +5:21:10 - MMT 1906 +5:30 - IST 1941 O +5:30 1 %z 1942 May 15 +5:30 - IST 1942 S +5:30 1 %z 1945 O 15 +5:30 - IST +Z Asia/Krasnoyarsk 6:11:26 - LMT 1920 Ja 6 +6 - %z 1930 Jun 21 +7 R %z 1991 Mar 31 2s +6 R %z 1992 Ja 19 2s +7 R %z 2011 Mar 27 2s +8 - %z 2014 O 26 2s +7 - %z +Z Asia/Kuching 7:21:20 - LMT 1926 Mar +7:30 - %z 1933 +8 NB %z 1942 F 16 +9 - %z 1945 S 12 +8 - %z +Z Asia/Macau 7:34:10 - LMT 1904 O 30 +8 - CST 1941 D 21 23 +9 _ %z 1945 S 30 24 +8 _ C%sT +Z Asia/Magadan 10:3:12 - LMT 1924 May 2 +10 - %z 1930 Jun 21 +11 R %z 1991 Mar 31 2s +10 R %z 1992 Ja 19 2s +11 R %z 2011 Mar 27 2s +12 - %z 2014 O 26 2s +10 - %z 2016 Ap 24 2s +11 - %z +Z Asia/Makassar 7:57:36 - LMT 1920 +7:57:36 - MMT 1932 N +8 - %z 1942 F 9 +9 - %z 1945 S 23 +8 - WITA +Z Asia/Manila -15:56:8 - LMT 1844 D 31 +8:3:52 - LMT 1899 S 6 4u +8 PH P%sT 1942 F 11 24 +9 - JST 1945 Mar 4 +8 PH P%sT +Z Asia/Nicosia 2:13:28 - LMT 1921 N 14 +2 CY EE%sT 1998 S +2 E EE%sT +Z Asia/Novokuznetsk 5:48:48 - LMT 1924 May +6 - %z 1930 Jun 21 +7 R %z 1991 Mar 31 2s +6 R %z 1992 Ja 19 2s +7 R %z 2010 Mar 28 2s +6 R %z 2011 Mar 27 2s +7 - %z +Z Asia/Novosibirsk 5:31:40 - LMT 1919 D 14 6 +6 - %z 1930 Jun 21 +7 R %z 1991 Mar 31 2s +6 R %z 1992 Ja 19 2s +7 R %z 1993 May 23 +6 R %z 2011 Mar 27 2s +7 - %z 2014 O 26 2s +6 - %z 2016 Jul 24 2s +7 - %z +Z Asia/Omsk 4:53:30 - LMT 1919 N 14 +5 - %z 1930 Jun 21 +6 R %z 1991 Mar 31 2s +5 R %z 1992 Ja 19 2s +6 R %z 2011 Mar 27 2s +7 - %z 2014 O 26 2s +6 - %z +Z Asia/Oral 3:25:24 - LMT 1924 May 2 +3 - %z 1930 Jun 21 +5 - %z 1981 Ap +5 1 %z 1981 O +6 - %z 1982 Ap +5 R %z 1989 Mar 26 2s +4 R %z 1992 Ja 19 2s +5 R %z 1992 Mar 29 2s +4 R %z 2004 O 31 2s +5 - %z +Z Asia/Pontianak 7:17:20 - LMT 1908 May +7:17:20 - PMT 1932 N +7:30 - %z 1942 Ja 29 +9 - %z 1945 S 23 +7:30 - %z 1948 May +8 - %z 1950 May +7:30 - %z 1964 +8 - WITA 1988 +7 - WIB +Z Asia/Pyongyang 8:23 - LMT 1908 Ap +8:30 - KST 1912 +9 - JST 1945 Au 24 +9 - KST 2015 Au 15 +8:30 - KST 2018 May 4 23:30 +9 - KST +Z Asia/Qatar 3:26:8 - LMT 1920 +4 - %z 1972 Jun +3 - %z +Z Asia/Qostanay 4:14:28 - LMT 1924 May 2 +4 - %z 1930 Jun 21 +5 - %z 1981 Ap +5 1 %z 1981 O +6 - %z 1982 Ap +5 R %z 1991 Mar 31 2s +4 R %z 1992 Ja 19 2s +5 R %z 2004 O 31 2s +6 - %z 2024 Mar +5 - %z +Z Asia/Qyzylorda 4:21:52 - LMT 1924 May 2 +4 - %z 1930 Jun 21 +5 - %z 1981 Ap +5 1 %z 1981 O +6 - %z 1982 Ap +5 R %z 1991 Mar 31 2s +4 R %z 1991 S 29 2s +5 R %z 1992 Ja 19 2s +6 R %z 1992 Mar 29 2s +5 R %z 2004 O 31 2s +6 - %z 2018 D 21 +5 - %z +Z Asia/Riyadh 3:6:52 - LMT 1947 Mar 14 +3 - %z +Z Asia/Sakhalin 9:30:48 - LMT 1905 Au 23 +9 - %z 1945 Au 25 +11 R %z 1991 Mar 31 2s +10 R %z 1992 Ja 19 2s +11 R %z 1997 Mar lastSu 2s +10 R %z 2011 Mar 27 2s +11 - %z 2014 O 26 2s +10 - %z 2016 Mar 27 2s +11 - %z +Z Asia/Samarkand 4:27:53 - LMT 1924 May 2 +4 - %z 1930 Jun 21 +5 - %z 1981 Ap +5 1 %z 1981 O +6 - %z 1982 Ap +5 R %z 1992 +5 - %z +Z Asia/Seoul 8:27:52 - LMT 1908 Ap +8:30 - KST 1912 +9 - JST 1945 S 8 +9 KR K%sT 1954 Mar 21 +8:30 KR K%sT 1961 Au 10 +9 KR K%sT +Z Asia/Shanghai 8:5:43 - LMT 1901 +8 Sh C%sT 1949 May 28 +8 CN C%sT +Z Asia/Singapore 6:55:25 - LMT 1901 +6:55:25 - SMT 1905 Jun +7 - %z 1933 +7 0:20 %z 1936 +7:20 - %z 1941 S +7:30 - %z 1942 F 16 +9 - %z 1945 S 12 +7:30 - %z 1981 D 31 16u +8 - %z +Z Asia/Srednekolymsk 10:14:52 - LMT 1924 May 2 +10 - %z 1930 Jun 21 +11 R %z 1991 Mar 31 2s +10 R %z 1992 Ja 19 2s +11 R %z 2011 Mar 27 2s +12 - %z 2014 O 26 2s +11 - %z +Z Asia/Taipei 8:6 - LMT 1896 +8 - CST 1937 O +9 - JST 1945 S 21 1 +8 f C%sT +Z Asia/Tashkent 4:37:11 - LMT 1924 May 2 +5 - %z 1930 Jun 21 +6 R %z 1991 Mar 31 2 +5 R %z 1992 +5 - %z +Z Asia/Tbilisi 2:59:11 - LMT 1880 +2:59:11 - TBMT 1924 May 2 +3 - %z 1957 Mar +4 R %z 1991 Mar 31 2s +3 R %z 1992 +3 e %z 1994 S lastSu +4 e %z 1996 O lastSu +4 1 %z 1997 Mar lastSu +4 e %z 2004 Jun 27 +3 R %z 2005 Mar lastSu 2 +4 - %z +Z Asia/Tehran 3:25:44 - LMT 1916 +3:25:44 - TMT 1935 Jun 13 +3:30 i %z 1977 O 20 24 +4 i %z 1978 N 10 24 +3:30 i %z +Z Asia/Thimphu 5:58:36 - LMT 1947 Au 15 +5:30 - %z 1987 O +6 - %z +Z Asia/Tokyo 9:18:59 - LMT 1887 D 31 15u +9 JP J%sT +Z Asia/Tomsk 5:39:51 - LMT 1919 D 22 +6 - %z 1930 Jun 21 +7 R %z 1991 Mar 31 2s +6 R %z 1992 Ja 19 2s +7 R %z 2002 May 1 3 +6 R %z 2011 Mar 27 2s +7 - %z 2014 O 26 2s +6 - %z 2016 May 29 2s +7 - %z +Z Asia/Ulaanbaatar 7:7:32 - LMT 1905 Au +7 - %z 1978 +8 X %z +Z Asia/Urumqi 5:50:20 - LMT 1928 +6 - %z +Z Asia/Ust-Nera 9:32:54 - LMT 1919 D 15 +8 - %z 1930 Jun 21 +9 R %z 1981 Ap +11 R %z 1991 Mar 31 2s +10 R %z 1992 Ja 19 2s +11 R %z 2011 Mar 27 2s +12 - %z 2011 S 13 0s +11 - %z 2014 O 26 2s +10 - %z +Z Asia/Vladivostok 8:47:31 - LMT 1922 N 15 +9 - %z 1930 Jun 21 +10 R %z 1991 Mar 31 2s +9 R %z 1992 Ja 19 2s +10 R %z 2011 Mar 27 2s +11 - %z 2014 O 26 2s +10 - %z +Z Asia/Yakutsk 8:38:58 - LMT 1919 D 15 +8 - %z 1930 Jun 21 +9 R %z 1991 Mar 31 2s +8 R %z 1992 Ja 19 2s +9 R %z 2011 Mar 27 2s +10 - %z 2014 O 26 2s +9 - %z +Z Asia/Yangon 6:24:47 - LMT 1880 +6:24:47 - RMT 1920 +6:30 - %z 1942 May +9 - %z 1945 May 3 +6:30 - %z +Z Asia/Yekaterinburg 4:2:33 - LMT 1916 Jul 3 +3:45:5 - PMT 1919 Jul 15 4 +4 - %z 1930 Jun 21 +5 R %z 1991 Mar 31 2s +4 R %z 1992 Ja 19 2s +5 R %z 2011 Mar 27 2s +6 - %z 2014 O 26 2s +5 - %z +Z Asia/Yerevan 2:58 - LMT 1924 May 2 +3 - %z 1957 Mar +4 R %z 1991 Mar 31 2s +3 R %z 1995 S 24 2s +4 - %z 1997 +4 R %z 2011 +4 AM %z +Z Atlantic/Azores -1:42:40 - LMT 1884 +-1:54:32 - HMT 1912 Ja 1 2u +-2 p %z 1966 O 2 2s +-1 - %z 1982 Mar 28 0s +-1 p %z 1986 +-1 E %z 1992 D 27 1s +0 E WE%sT 1993 Jun 17 1u +-1 E %z +Z Atlantic/Bermuda -4:19:18 - LMT 1890 +-4:19:18 Be BMT/BST 1930 Ja 1 2 +-4 Be A%sT 1974 Ap 28 2 +-4 C A%sT 1976 +-4 u A%sT +Z Atlantic/Canary -1:1:36 - LMT 1922 Mar +-1 - %z 1946 S 30 1 +0 - WET 1980 Ap 6 0s +0 1 WEST 1980 S 28 1u +0 E WE%sT +Z Atlantic/Cape_Verde -1:34:4 - LMT 1912 Ja 1 2u +-2 - %z 1942 S +-2 1 %z 1945 O 15 +-2 - %z 1975 N 25 2 +-1 - %z +Z Atlantic/Faroe -0:27:4 - LMT 1908 Ja 11 +0 - WET 1981 +0 E WE%sT +Z Atlantic/Madeira -1:7:36 - LMT 1884 +-1:7:36 - FMT 1912 Ja 1 1u +-1 p %z 1966 O 2 2s +0 - WET 1982 Ap 4 +0 p WE%sT 1986 Jul 31 +0 E WE%sT +Z Atlantic/South_Georgia -2:26:8 - LMT 1890 +-2 - %z +Z Atlantic/Stanley -3:51:24 - LMT 1890 +-3:51:24 - SMT 1912 Mar 12 +-4 FK %z 1983 May +-3 FK %z 1985 S 15 +-4 FK %z 2010 S 5 2 +-3 - %z +Z Australia/Adelaide 9:14:20 - LMT 1895 F +9 - ACST 1899 May +9:30 AU AC%sT 1971 +9:30 AS AC%sT +Z Australia/Brisbane 10:12:8 - LMT 1895 +10 AU AE%sT 1971 +10 AQ AE%sT +Z Australia/Broken_Hill 9:25:48 - LMT 1895 F +10 - AEST 1896 Au 23 +9 - ACST 1899 May +9:30 AU AC%sT 1971 +9:30 AN AC%sT 2000 +9:30 AS AC%sT +Z Australia/Darwin 8:43:20 - LMT 1895 F +9 - ACST 1899 May +9:30 AU AC%sT +Z Australia/Eucla 8:35:28 - LMT 1895 D +8:45 AU %z 1943 Jul +8:45 AW %z +Z Australia/Hobart 9:49:16 - LMT 1895 S +10 AT AE%sT 1919 O 24 +10 AU AE%sT 1967 +10 AT AE%sT +Z Australia/Lindeman 9:55:56 - LMT 1895 +10 AU AE%sT 1971 +10 AQ AE%sT 1992 Jul +10 Ho AE%sT +Z Australia/Lord_Howe 10:36:20 - LMT 1895 F +10 - AEST 1981 Mar +10:30 LH %z 1985 Jul +10:30 LH %z +Z Australia/Melbourne 9:39:52 - LMT 1895 F +10 AU AE%sT 1971 +10 AV AE%sT +Z Australia/Perth 7:43:24 - LMT 1895 D +8 AU AW%sT 1943 Jul +8 AW AW%sT +Z Australia/Sydney 10:4:52 - LMT 1895 F +10 AU AE%sT 1971 +10 AN AE%sT +Z Etc/GMT 0 - GMT +Z Etc/GMT+1 -1 - %z +Z Etc/GMT+10 -10 - %z +Z Etc/GMT+11 -11 - %z +Z Etc/GMT+12 -12 - %z +Z Etc/GMT+2 -2 - %z +Z Etc/GMT+3 -3 - %z +Z Etc/GMT+4 -4 - %z +Z Etc/GMT+5 -5 - %z +Z Etc/GMT+6 -6 - %z +Z Etc/GMT+7 -7 - %z +Z Etc/GMT+8 -8 - %z +Z Etc/GMT+9 -9 - %z +Z Etc/GMT-1 1 - %z +Z Etc/GMT-10 10 - %z +Z Etc/GMT-11 11 - %z +Z Etc/GMT-12 12 - %z +Z Etc/GMT-13 13 - %z +Z Etc/GMT-14 14 - %z +Z Etc/GMT-2 2 - %z +Z Etc/GMT-3 3 - %z +Z Etc/GMT-4 4 - %z +Z Etc/GMT-5 5 - %z +Z Etc/GMT-6 6 - %z +Z Etc/GMT-7 7 - %z +Z Etc/GMT-8 8 - %z +Z Etc/GMT-9 9 - %z +Z Etc/UTC 0 - UTC +Z Europe/Andorra 0:6:4 - LMT 1901 +0 - WET 1946 S 30 +1 - CET 1985 Mar 31 2 +1 E CE%sT +Z Europe/Astrakhan 3:12:12 - LMT 1924 May +3 - %z 1930 Jun 21 +4 R %z 1989 Mar 26 2s +3 R %z 1991 Mar 31 2s +4 - %z 1992 Mar 29 2s +3 R %z 2011 Mar 27 2s +4 - %z 2014 O 26 2s +3 - %z 2016 Mar 27 2s +4 - %z +Z Europe/Athens 1:34:52 - LMT 1895 S 14 +1:34:52 - AMT 1916 Jul 28 0:1 +2 g EE%sT 1941 Ap 30 +1 g CE%sT 1944 Ap 4 +2 g EE%sT 1981 +2 E EE%sT +Z Europe/Belgrade 1:22 - LMT 1884 +1 - CET 1941 Ap 18 23 +1 c CE%sT 1945 +1 - CET 1945 May 8 2s +1 1 CEST 1945 S 16 2s +1 - CET 1982 N 27 +1 E CE%sT +Z Europe/Berlin 0:53:28 - LMT 1893 Ap +1 c CE%sT 1945 May 24 2 +1 So CE%sT 1946 +1 DE CE%sT 1980 +1 E CE%sT +Z Europe/Brussels 0:17:30 - LMT 1880 +0:17:30 - BMT 1892 May 1 0:17:30 +0 - WET 1914 N 8 +1 - CET 1916 May +1 c CE%sT 1918 N 11 11u +0 b WE%sT 1940 May 20 2s +1 c CE%sT 1944 S 3 +1 b CE%sT 1977 +1 E CE%sT +Z Europe/Bucharest 1:44:24 - LMT 1891 O +1:44:24 - BMT 1931 Jul 24 +2 z EE%sT 1981 Mar 29 2s +2 c EE%sT 1991 +2 z EE%sT 1994 +2 e EE%sT 1997 +2 E EE%sT +Z Europe/Budapest 1:16:20 - LMT 1890 N +1 c CE%sT 1918 +1 h CE%sT 1941 Ap 7 23 +1 c CE%sT 1945 +1 h CE%sT 1984 +1 E CE%sT +Z Europe/Chisinau 1:55:20 - LMT 1880 +1:55 - CMT 1918 F 15 +1:44:24 - BMT 1931 Jul 24 +2 z EE%sT 1940 Au 15 +2 1 EEST 1941 Jul 17 +1 c CE%sT 1944 Au 24 +3 R MSK/MSD 1990 May 6 2 +2 R EE%sT 1992 +2 e EE%sT 1997 +2 MD EE%sT 2022 +2 E EE%sT +Z Europe/Dublin -0:25:21 - LMT 1880 Au 2 +-0:25:21 - DMT 1916 May 21 2s +-0:25:21 1 IST 1916 O 1 2s +0 G %s 1921 D 6 +0 G GMT/IST 1940 F 25 2s +0 1 IST 1946 O 6 2s +0 - GMT 1947 Mar 16 2s +0 1 IST 1947 N 2 2s +0 - GMT 1948 Ap 18 2s +0 G GMT/IST 1968 O 27 +1 IE IST/GMT +Z Europe/Gibraltar -0:21:24 - LMT 1880 Au 2 +0 G %s 1957 Ap 14 2 +1 - CET 1982 +1 E CE%sT +Z Europe/Helsinki 1:39:49 - LMT 1878 May 31 +1:39:49 - HMT 1921 May +2 FI EE%sT 1983 +2 E EE%sT +Z Europe/Istanbul 1:55:52 - LMT 1880 +1:56:56 - IMT 1910 O +2 T EE%sT 1978 Jun 29 +3 T %z 1984 N 1 2 +2 T EE%sT 2007 +2 E EE%sT 2011 Mar 27 1u +2 - EET 2011 Mar 28 1u +2 E EE%sT 2014 Mar 30 1u +2 - EET 2014 Mar 31 1u +2 E EE%sT 2015 O 25 1u +2 1 EEST 2015 N 8 1u +2 E EE%sT 2016 S 7 +3 - %z +Z Europe/Kaliningrad 1:22 - LMT 1893 Ap +1 c CE%sT 1945 Ap 10 +2 O EE%sT 1946 Ap 7 +3 R MSK/MSD 1989 Mar 26 2s +2 R EE%sT 2011 Mar 27 2s +3 - %z 2014 O 26 2s +2 - EET +Z Europe/Kirov 3:18:48 - LMT 1919 Jul 1 0u +3 - %z 1930 Jun 21 +4 R %z 1989 Mar 26 2s +3 R MSK/MSD 1991 Mar 31 2s +4 - %z 1992 Mar 29 2s +3 R MSK/MSD 2011 Mar 27 2s +4 - MSK 2014 O 26 2s +3 - MSK +Z Europe/Kyiv 2:2:4 - LMT 1880 +2:2:4 - KMT 1924 May 2 +2 - EET 1930 Jun 21 +3 - MSK 1941 S 20 +1 c CE%sT 1943 N 6 +3 R MSK/MSD 1990 Jul 1 2 +2 1 EEST 1991 S 29 3 +2 c EE%sT 1996 May 13 +2 E EE%sT +Z Europe/Lisbon -0:36:45 - LMT 1884 +-0:36:45 - LMT 1912 Ja 1 0u +0 p WE%sT 1966 O 2 2s +1 - CET 1976 S 26 1 +0 p WE%sT 1986 +0 E WE%sT 1992 S 27 1u +1 E CE%sT 1996 Mar 31 1u +0 E WE%sT +Z Europe/London -0:1:15 - LMT 1847 D +0 G %s 1968 O 27 +1 - BST 1971 O 31 2u +0 G %s 1996 +0 E GMT/BST +Z Europe/Madrid -0:14:44 - LMT 1901 Ja 1 0u +0 s WE%sT 1940 Mar 16 23 +1 s CE%sT 1979 +1 E CE%sT +Z Europe/Malta 0:58:4 - LMT 1893 N 2 +1 I CE%sT 1973 Mar 31 +1 MT CE%sT 1981 +1 E CE%sT +Z Europe/Minsk 1:50:16 - LMT 1880 +1:50 - MMT 1924 May 2 +2 - EET 1930 Jun 21 +3 - MSK 1941 Jun 28 +1 c CE%sT 1944 Jul 3 +3 R MSK/MSD 1990 +3 - MSK 1991 Mar 31 2s +2 R EE%sT 2011 Mar 27 2s +3 - %z +Z Europe/Moscow 2:30:17 - LMT 1880 +2:30:17 - MMT 1916 Jul 3 +2:31:19 R %s 1919 Jul 1 0u +3 R %s 1921 O +3 R MSK/MSD 1922 O +2 - EET 1930 Jun 21 +3 R MSK/MSD 1991 Mar 31 2s +2 R EE%sT 1992 Ja 19 2s +3 R MSK/MSD 2011 Mar 27 2s +4 - MSK 2014 O 26 2s +3 - MSK +Z Europe/Paris 0:9:21 - LMT 1891 Mar 16 +0:9:21 - PMT 1911 Mar 11 +0 F WE%sT 1940 Jun 14 23 +1 c CE%sT 1944 Au 25 +0 F WE%sT 1945 S 16 3 +1 F CE%sT 1977 +1 E CE%sT +Z Europe/Prague 0:57:44 - LMT 1850 +0:57:44 - PMT 1891 O +1 c CE%sT 1945 May 9 +1 CZ CE%sT 1946 D 1 3 +1 -1 GMT 1947 F 23 2 +1 CZ CE%sT 1979 +1 E CE%sT +Z Europe/Riga 1:36:34 - LMT 1880 +1:36:34 - RMT 1918 Ap 15 2 +1:36:34 1 LST 1918 S 16 3 +1:36:34 - RMT 1919 Ap 1 2 +1:36:34 1 LST 1919 May 22 3 +1:36:34 - RMT 1926 May 11 +2 - EET 1940 Au 5 +3 - MSK 1941 Jul +1 c CE%sT 1944 O 13 +3 R MSK/MSD 1989 Mar lastSu 2s +2 1 EEST 1989 S lastSu 2s +2 LV EE%sT 1997 Ja 21 +2 E EE%sT 2000 F 29 +2 - EET 2001 Ja 2 +2 E EE%sT +Z Europe/Rome 0:49:56 - LMT 1866 D 12 +0:49:56 - RMT 1893 O 31 23u +1 I CE%sT 1943 S 10 +1 c CE%sT 1944 Jun 4 +1 I CE%sT 1980 +1 E CE%sT +Z Europe/Samara 3:20:20 - LMT 1919 Jul 1 0u +3 - %z 1930 Jun 21 +4 - %z 1935 Ja 27 +4 R %z 1989 Mar 26 2s +3 R %z 1991 Mar 31 2s +2 R %z 1991 S 29 2s +3 - %z 1991 O 20 3 +4 R %z 2010 Mar 28 2s +3 R %z 2011 Mar 27 2s +4 - %z +Z Europe/Saratov 3:4:18 - LMT 1919 Jul 1 0u +3 - %z 1930 Jun 21 +4 R %z 1988 Mar 27 2s +3 R %z 1991 Mar 31 2s +4 - %z 1992 Mar 29 2s +3 R %z 2011 Mar 27 2s +4 - %z 2014 O 26 2s +3 - %z 2016 D 4 2s +4 - %z +Z Europe/Simferopol 2:16:24 - LMT 1880 +2:16 - SMT 1924 May 2 +2 - EET 1930 Jun 21 +3 - MSK 1941 N +1 c CE%sT 1944 Ap 13 +3 R MSK/MSD 1990 +3 - MSK 1990 Jul 1 2 +2 - EET 1992 Mar 20 +2 c EE%sT 1994 May +3 c MSK/MSD 1996 Mar 31 0s +3 1 MSD 1996 O 27 3s +3 - MSK 1997 Mar lastSu 1u +2 E EE%sT 2014 Mar 30 2 +4 - MSK 2014 O 26 2s +3 - MSK +Z Europe/Sofia 1:33:16 - LMT 1880 +1:56:56 - IMT 1894 N 30 +2 - EET 1942 N 2 3 +1 c CE%sT 1945 +1 - CET 1945 Ap 2 3 +2 - EET 1979 Mar 31 23 +2 BG EE%sT 1982 S 26 3 +2 c EE%sT 1991 +2 e EE%sT 1997 +2 E EE%sT +Z Europe/Tallinn 1:39 - LMT 1880 +1:39 - TMT 1918 F +1 c CE%sT 1919 Jul +1:39 - TMT 1921 May +2 - EET 1940 Au 6 +3 - MSK 1941 S 15 +1 c CE%sT 1944 S 22 +3 R MSK/MSD 1989 Mar 26 2s +2 1 EEST 1989 S 24 2s +2 c EE%sT 1998 S 22 +2 E EE%sT 1999 O 31 4 +2 - EET 2002 F 21 +2 E EE%sT +Z Europe/Tirane 1:19:20 - LMT 1914 +1 - CET 1940 Jun 16 +1 q CE%sT 1984 Jul +1 E CE%sT +Z Europe/Ulyanovsk 3:13:36 - LMT 1919 Jul 1 0u +3 - %z 1930 Jun 21 +4 R %z 1989 Mar 26 2s +3 R %z 1991 Mar 31 2s +2 R %z 1992 Ja 19 2s +3 R %z 2011 Mar 27 2s +4 - %z 2014 O 26 2s +3 - %z 2016 Mar 27 2s +4 - %z +Z Europe/Vienna 1:5:21 - LMT 1893 Ap +1 c CE%sT 1920 +1 a CE%sT 1940 Ap 1 2s +1 c CE%sT 1945 Ap 2 2s +1 1 CEST 1945 Ap 12 2s +1 - CET 1946 +1 a CE%sT 1981 +1 E CE%sT +Z Europe/Vilnius 1:41:16 - LMT 1880 +1:24 - WMT 1917 +1:35:36 - KMT 1919 O 10 +1 - CET 1920 Jul 12 +2 - EET 1920 O 9 +1 - CET 1940 Au 3 +3 - MSK 1941 Jun 24 +1 c CE%sT 1944 Au +3 R MSK/MSD 1989 Mar 26 2s +2 R EE%sT 1991 S 29 2s +2 c EE%sT 1998 +2 - EET 1998 Mar 29 1u +1 E CE%sT 1999 O 31 1u +2 - EET 2003 +2 E EE%sT +Z Europe/Volgograd 2:57:40 - LMT 1920 Ja 3 +3 - %z 1930 Jun 21 +4 - %z 1961 N 11 +4 R %z 1988 Mar 27 2s +3 R MSK/MSD 1991 Mar 31 2s +4 - %z 1992 Mar 29 2s +3 R MSK/MSD 2011 Mar 27 2s +4 - MSK 2014 O 26 2s +3 - MSK 2018 O 28 2s +4 - %z 2020 D 27 2s +3 - MSK +Z Europe/Warsaw 1:24 - LMT 1880 +1:24 - WMT 1915 Au 5 +1 c CE%sT 1918 S 16 3 +2 O EE%sT 1922 Jun +1 O CE%sT 1940 Jun 23 2 +1 c CE%sT 1944 O +1 O CE%sT 1977 +1 W- CE%sT 1988 +1 E CE%sT +Z Europe/Zurich 0:34:8 - LMT 1853 Jul 16 +0:29:46 - BMT 1894 Jun +1 CH CE%sT 1981 +1 E CE%sT +Z Factory 0 - -00 +Z Indian/Chagos 4:49:40 - LMT 1907 +5 - %z 1996 +6 - %z +Z Indian/Maldives 4:54 - LMT 1880 +4:54 - MMT 1960 +5 - %z +Z Indian/Mauritius 3:50 - LMT 1907 +4 MU %z +Z Pacific/Apia 12:33:4 - LMT 1892 Jul 5 +-11:26:56 - LMT 1911 +-11:30 - %z 1950 +-11 WS %z 2011 D 29 24 +13 WS %z +Z Pacific/Auckland 11:39:4 - LMT 1868 N 2 +11:30 NZ NZ%sT 1946 +12 NZ NZ%sT +Z Pacific/Bougainville 10:22:16 - LMT 1880 +9:48:32 - PMMT 1895 +10 - %z 1942 Jul +9 - %z 1945 Au 21 +10 - %z 2014 D 28 2 +11 - %z +Z Pacific/Chatham 12:13:48 - LMT 1868 N 2 +12:15 - %z 1946 +12:45 k %z +Z Pacific/Easter -7:17:28 - LMT 1890 +-7:17:28 - EMT 1932 S +-7 x %z 1982 Mar 14 3u +-6 x %z +Z Pacific/Efate 11:13:16 - LMT 1912 Ja 13 +11 VU %z +Z Pacific/Fakaofo -11:24:56 - LMT 1901 +-11 - %z 2011 D 30 +13 - %z +Z Pacific/Fiji 11:55:44 - LMT 1915 O 26 +12 FJ %z +Z Pacific/Galapagos -5:58:24 - LMT 1931 +-5 - %z 1986 +-6 EC %z +Z Pacific/Gambier -8:59:48 - LMT 1912 O +-9 - %z +Z Pacific/Guadalcanal 10:39:48 - LMT 1912 O +11 - %z +Z Pacific/Guam -14:21 - LMT 1844 D 31 +9:39 - LMT 1901 +10 - GST 1941 D 10 +9 - %z 1944 Jul 31 +10 Gu G%sT 2000 D 23 +10 - ChST +Z Pacific/Honolulu -10:31:26 - LMT 1896 Ja 13 12 +-10:30 - HST 1933 Ap 30 2 +-10:30 1 HDT 1933 May 21 12 +-10:30 u H%sT 1947 Jun 8 2 +-10 - HST +Z Pacific/Kanton 0 - -00 1937 Au 31 +-12 - %z 1979 O +-11 - %z 1994 D 31 +13 - %z +Z Pacific/Kiritimati -10:29:20 - LMT 1901 +-10:40 - %z 1979 O +-10 - %z 1994 D 31 +14 - %z +Z Pacific/Kosrae -13:8:4 - LMT 1844 D 31 +10:51:56 - LMT 1901 +11 - %z 1914 O +9 - %z 1919 F +11 - %z 1937 +10 - %z 1941 Ap +9 - %z 1945 Au +11 - %z 1969 O +12 - %z 1999 +11 - %z +Z Pacific/Kwajalein 11:9:20 - LMT 1901 +11 - %z 1937 +10 - %z 1941 Ap +9 - %z 1944 F 6 +11 - %z 1969 O +-12 - %z 1993 Au 20 24 +12 - %z +Z Pacific/Marquesas -9:18 - LMT 1912 O +-9:30 - %z +Z Pacific/Nauru 11:7:40 - LMT 1921 Ja 15 +11:30 - %z 1942 Au 29 +9 - %z 1945 S 8 +11:30 - %z 1979 F 10 2 +12 - %z +Z Pacific/Niue -11:19:40 - LMT 1952 O 16 +-11:20 - %z 1964 Jul +-11 - %z +Z Pacific/Norfolk 11:11:52 - LMT 1901 +11:12 - %z 1951 +11:30 - %z 1974 O 27 2s +11:30 1 %z 1975 Mar 2 2s +11:30 - %z 2015 O 4 2s +11 - %z 2019 Jul +11 AN %z +Z Pacific/Noumea 11:5:48 - LMT 1912 Ja 13 +11 NC %z +Z Pacific/Pago_Pago 12:37:12 - LMT 1892 Jul 5 +-11:22:48 - LMT 1911 +-11 - SST +Z Pacific/Palau -15:2:4 - LMT 1844 D 31 +8:57:56 - LMT 1901 +9 - %z +Z Pacific/Pitcairn -8:40:20 - LMT 1901 +-8:30 - %z 1998 Ap 27 +-8 - %z +Z Pacific/Port_Moresby 9:48:40 - LMT 1880 +9:48:32 - PMMT 1895 +10 - %z +Z Pacific/Rarotonga 13:20:56 - LMT 1899 D 26 +-10:39:4 - LMT 1952 O 16 +-10:30 - %z 1978 N 12 +-10 CK %z +Z Pacific/Tahiti -9:58:16 - LMT 1912 O +-10 - %z +Z Pacific/Tarawa 11:32:4 - LMT 1901 +12 - %z +Z Pacific/Tongatapu 12:19:12 - LMT 1945 S 10 +12:20 - %z 1961 +13 - %z 1999 +13 TO %z +L Etc/GMT GMT +L Australia/Sydney Australia/ACT +L 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+L America/Puerto_Rico America/Antigua +L America/Puerto_Rico America/Aruba +L America/Panama America/Atikokan +L America/Puerto_Rico America/Blanc-Sablon +L America/Panama America/Cayman +L America/Phoenix America/Creston +L America/Puerto_Rico America/Curacao +L America/Puerto_Rico America/Dominica +L America/Puerto_Rico America/Grenada +L America/Puerto_Rico America/Guadeloupe +L America/Puerto_Rico America/Kralendijk +L America/Puerto_Rico America/Lower_Princes +L America/Puerto_Rico America/Marigot +L America/Puerto_Rico America/Montserrat +L America/Toronto America/Nassau +L America/Puerto_Rico America/Port_of_Spain +L America/Puerto_Rico America/St_Barthelemy +L America/Puerto_Rico America/St_Kitts +L America/Puerto_Rico America/St_Lucia +L America/Puerto_Rico America/St_Thomas +L America/Puerto_Rico America/St_Vincent +L America/Puerto_Rico America/Tortola +L Pacific/Port_Moresby Antarctica/DumontDUrville +L Pacific/Auckland Antarctica/McMurdo +L Asia/Riyadh Antarctica/Syowa +L Europe/Berlin Arctic/Longyearbyen +L Asia/Riyadh Asia/Aden +L Asia/Qatar Asia/Bahrain +L Asia/Kuching Asia/Brunei +L Asia/Singapore Asia/Kuala_Lumpur +L Asia/Riyadh Asia/Kuwait +L Asia/Dubai Asia/Muscat +L Asia/Bangkok Asia/Phnom_Penh +L Asia/Bangkok Asia/Vientiane +L Africa/Abidjan Atlantic/Reykjavik +L Africa/Abidjan Atlantic/St_Helena +L Europe/Brussels Europe/Amsterdam +L Europe/Prague Europe/Bratislava +L Europe/Zurich Europe/Busingen +L Europe/Berlin Europe/Copenhagen +L Europe/London Europe/Guernsey +L Europe/London Europe/Isle_of_Man +L Europe/London Europe/Jersey +L Europe/Belgrade Europe/Ljubljana +L Europe/Brussels Europe/Luxembourg +L Europe/Helsinki Europe/Mariehamn +L Europe/Paris Europe/Monaco +L Europe/Berlin Europe/Oslo +L Europe/Belgrade Europe/Podgorica +L Europe/Rome Europe/San_Marino +L Europe/Belgrade Europe/Sarajevo +L Europe/Belgrade Europe/Skopje +L Europe/Berlin Europe/Stockholm +L Europe/Zurich Europe/Vaduz +L Europe/Rome Europe/Vatican +L Europe/Belgrade Europe/Zagreb +L Africa/Nairobi Indian/Antananarivo +L Asia/Bangkok Indian/Christmas +L Asia/Yangon Indian/Cocos +L Africa/Nairobi Indian/Comoro +L Indian/Maldives Indian/Kerguelen +L Asia/Dubai Indian/Mahe +L Africa/Nairobi Indian/Mayotte +L Asia/Dubai Indian/Reunion +L Pacific/Port_Moresby Pacific/Chuuk +L Pacific/Tarawa Pacific/Funafuti +L Pacific/Tarawa Pacific/Majuro +L Pacific/Pago_Pago Pacific/Midway +L Pacific/Guadalcanal Pacific/Pohnpei +L Pacific/Guam Pacific/Saipan +L Pacific/Tarawa Pacific/Wake +L Pacific/Tarawa Pacific/Wallis +L Africa/Abidjan Africa/Timbuktu +L America/Argentina/Catamarca America/Argentina/ComodRivadavia +L America/Adak America/Atka +L America/Panama America/Coral_Harbour +L America/Tijuana America/Ensenada +L America/Indiana/Indianapolis America/Fort_Wayne +L America/Toronto America/Montreal +L America/Toronto America/Nipigon +L America/Iqaluit America/Pangnirtung +L America/Rio_Branco America/Porto_Acre +L America/Winnipeg America/Rainy_River +L America/Argentina/Cordoba America/Rosario +L America/Tijuana America/Santa_Isabel +L America/Denver America/Shiprock +L America/Toronto America/Thunder_Bay +L America/Edmonton America/Yellowknife +L Pacific/Auckland Antarctica/South_Pole +L Asia/Ulaanbaatar Asia/Choibalsan +L Asia/Shanghai Asia/Chongqing +L Asia/Shanghai Asia/Harbin +L Asia/Urumqi Asia/Kashgar +L Asia/Jerusalem Asia/Tel_Aviv +L Europe/Berlin Atlantic/Jan_Mayen +L Australia/Sydney Australia/Canberra +L Australia/Hobart Australia/Currie +L Europe/London Europe/Belfast +L Europe/Chisinau Europe/Tiraspol +L Europe/Kyiv Europe/Uzhgorod +L Europe/Kyiv Europe/Zaporozhye +L Pacific/Kanton Pacific/Enderbury +L Pacific/Honolulu Pacific/Johnston +L Pacific/Port_Moresby Pacific/Yap +L Europe/Lisbon WET +L Africa/Nairobi Africa/Asmera +L America/Nuuk America/Godthab +L Asia/Ashgabat Asia/Ashkhabad +L Asia/Kolkata Asia/Calcutta +L Asia/Shanghai Asia/Chungking +L Asia/Dhaka Asia/Dacca +L Europe/Istanbul Asia/Istanbul +L Asia/Kathmandu Asia/Katmandu +L Asia/Macau Asia/Macao +L Asia/Yangon Asia/Rangoon +L Asia/Ho_Chi_Minh Asia/Saigon +L Asia/Thimphu Asia/Thimbu +L Asia/Makassar Asia/Ujung_Pandang +L Asia/Ulaanbaatar Asia/Ulan_Bator +L Atlantic/Faroe Atlantic/Faeroe +L Europe/Kyiv Europe/Kiev +L Asia/Nicosia Europe/Nicosia +L Pacific/Honolulu HST +L America/Los_Angeles PST8PDT +L Pacific/Guadalcanal Pacific/Ponape +L Pacific/Port_Moresby Pacific/Truk diff --git a/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/zone.tab b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/zone.tab new file mode 100644 index 0000000000000000000000000000000000000000..2626b0550341a0605087f33cac6952d5fbb24e67 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/zone.tab @@ -0,0 +1,448 @@ +# tzdb timezone descriptions (deprecated version) +# +# This file is in the public domain, so clarified as of +# 2009-05-17 by Arthur David Olson. +# +# From Paul Eggert (2021-09-20): +# This file is intended as a backward-compatibility aid for older programs. +# New programs should use zone1970.tab. This file is like zone1970.tab (see +# zone1970.tab's comments), but with the following additional restrictions: +# +# 1. This file contains only ASCII characters. +# 2. The first data column contains exactly one country code. +# +# Because of (2), each row stands for an area that is the intersection +# of a region identified by a country code and of a timezone where civil +# clocks have agreed since 1970; this is a narrower definition than +# that of zone1970.tab. +# +# Unlike zone1970.tab, a row's third column can be a Link from +# 'backward' instead of a Zone. +# +# This table is intended as an aid for users, to help them select timezones +# appropriate for their practical needs. It is not intended to take or +# endorse any position on legal or territorial claims. +# +#country- +#code coordinates TZ comments +AD +4230+00131 Europe/Andorra +AE +2518+05518 Asia/Dubai +AF +3431+06912 Asia/Kabul +AG +1703-06148 America/Antigua +AI +1812-06304 America/Anguilla +AL +4120+01950 Europe/Tirane +AM +4011+04430 Asia/Yerevan +AO -0848+01314 Africa/Luanda +AQ -7750+16636 Antarctica/McMurdo New Zealand time - McMurdo, South Pole +AQ -6617+11031 Antarctica/Casey Casey +AQ -6835+07758 Antarctica/Davis Davis +AQ -6640+14001 Antarctica/DumontDUrville Dumont-d'Urville +AQ -6736+06253 Antarctica/Mawson Mawson +AQ -6448-06406 Antarctica/Palmer Palmer +AQ -6734-06808 Antarctica/Rothera Rothera +AQ -690022+0393524 Antarctica/Syowa Syowa +AQ -720041+0023206 Antarctica/Troll Troll +AQ -7824+10654 Antarctica/Vostok Vostok +AR -3436-05827 America/Argentina/Buenos_Aires Buenos Aires (BA, CF) +AR -3124-06411 America/Argentina/Cordoba Argentina (most areas: CB, CC, CN, ER, FM, MN, SE, SF) +AR -2447-06525 America/Argentina/Salta Salta (SA, LP, NQ, RN) +AR -2411-06518 America/Argentina/Jujuy Jujuy (JY) +AR -2649-06513 America/Argentina/Tucuman Tucuman (TM) +AR -2828-06547 America/Argentina/Catamarca Catamarca (CT), Chubut (CH) +AR -2926-06651 America/Argentina/La_Rioja La Rioja (LR) +AR -3132-06831 America/Argentina/San_Juan San Juan (SJ) +AR -3253-06849 America/Argentina/Mendoza Mendoza (MZ) +AR -3319-06621 America/Argentina/San_Luis San Luis (SL) +AR -5138-06913 America/Argentina/Rio_Gallegos Santa Cruz (SC) +AR -5448-06818 America/Argentina/Ushuaia Tierra del Fuego (TF) +AS -1416-17042 Pacific/Pago_Pago +AT +4813+01620 Europe/Vienna +AU -3133+15905 Australia/Lord_Howe Lord Howe Island +AU -5430+15857 Antarctica/Macquarie Macquarie Island +AU -4253+14719 Australia/Hobart Tasmania +AU -3749+14458 Australia/Melbourne Victoria +AU -3352+15113 Australia/Sydney New South Wales (most areas) +AU -3157+14127 Australia/Broken_Hill New South Wales (Yancowinna) +AU -2728+15302 Australia/Brisbane Queensland (most areas) +AU -2016+14900 Australia/Lindeman Queensland (Whitsunday Islands) +AU -3455+13835 Australia/Adelaide South Australia +AU -1228+13050 Australia/Darwin Northern Territory +AU -3157+11551 Australia/Perth Western Australia (most areas) +AU -3143+12852 Australia/Eucla Western Australia (Eucla) +AW +1230-06958 America/Aruba +AX +6006+01957 Europe/Mariehamn +AZ +4023+04951 Asia/Baku +BA +4352+01825 Europe/Sarajevo +BB +1306-05937 America/Barbados +BD +2343+09025 Asia/Dhaka +BE +5050+00420 Europe/Brussels +BF +1222-00131 Africa/Ouagadougou +BG +4241+02319 Europe/Sofia +BH +2623+05035 Asia/Bahrain +BI -0323+02922 Africa/Bujumbura +BJ +0629+00237 Africa/Porto-Novo +BL +1753-06251 America/St_Barthelemy +BM +3217-06446 Atlantic/Bermuda +BN +0456+11455 Asia/Brunei +BO -1630-06809 America/La_Paz +BQ +120903-0681636 America/Kralendijk +BR -0351-03225 America/Noronha Atlantic islands +BR -0127-04829 America/Belem Para (east), Amapa +BR -0343-03830 America/Fortaleza Brazil (northeast: MA, PI, CE, RN, PB) +BR -0803-03454 America/Recife Pernambuco +BR -0712-04812 America/Araguaina Tocantins +BR -0940-03543 America/Maceio Alagoas, Sergipe +BR -1259-03831 America/Bahia Bahia +BR -2332-04637 America/Sao_Paulo Brazil (southeast: GO, DF, MG, ES, RJ, SP, PR, SC, RS) +BR -2027-05437 America/Campo_Grande Mato Grosso do Sul +BR -1535-05605 America/Cuiaba Mato Grosso +BR -0226-05452 America/Santarem Para (west) +BR -0846-06354 America/Porto_Velho Rondonia +BR +0249-06040 America/Boa_Vista Roraima +BR -0308-06001 America/Manaus Amazonas (east) +BR -0640-06952 America/Eirunepe Amazonas (west) +BR -0958-06748 America/Rio_Branco Acre +BS +2505-07721 America/Nassau +BT +2728+08939 Asia/Thimphu +BW -2439+02555 Africa/Gaborone +BY +5354+02734 Europe/Minsk +BZ +1730-08812 America/Belize +CA +4734-05243 America/St_Johns Newfoundland, Labrador (SE) +CA +4439-06336 America/Halifax Atlantic - NS (most areas), PE +CA +4612-05957 America/Glace_Bay Atlantic - NS (Cape Breton) +CA +4606-06447 America/Moncton Atlantic - New Brunswick +CA +5320-06025 America/Goose_Bay Atlantic - Labrador (most areas) +CA +5125-05707 America/Blanc-Sablon AST - QC (Lower North Shore) +CA +4339-07923 America/Toronto Eastern - ON & QC (most areas) +CA +6344-06828 America/Iqaluit Eastern - NU (most areas) +CA +484531-0913718 America/Atikokan EST - ON (Atikokan), NU (Coral H) +CA +4953-09709 America/Winnipeg Central - ON (west), Manitoba +CA +744144-0944945 America/Resolute Central - NU (Resolute) +CA +624900-0920459 America/Rankin_Inlet Central - NU (central) +CA +5024-10439 America/Regina CST - SK (most areas) +CA +5017-10750 America/Swift_Current CST - SK (midwest) +CA +5333-11328 America/Edmonton Mountain - AB, BC(E), NT(E), SK(W) +CA +690650-1050310 America/Cambridge_Bay Mountain - NU (west) +CA +682059-1334300 America/Inuvik Mountain - NT (west) +CA +4906-11631 America/Creston MST - BC (Creston) +CA +5546-12014 America/Dawson_Creek MST - BC (Dawson Cr, Ft St John) +CA +5848-12242 America/Fort_Nelson MST - BC (Ft Nelson) +CA +6043-13503 America/Whitehorse MST - Yukon (east) +CA +6404-13925 America/Dawson MST - Yukon (west) +CA +4916-12307 America/Vancouver Pacific - BC (most areas) +CC -1210+09655 Indian/Cocos +CD -0418+01518 Africa/Kinshasa Dem. Rep. of Congo (west) +CD -1140+02728 Africa/Lubumbashi Dem. Rep. of Congo (east) +CF +0422+01835 Africa/Bangui +CG -0416+01517 Africa/Brazzaville +CH +4723+00832 Europe/Zurich +CI +0519-00402 Africa/Abidjan +CK -2114-15946 Pacific/Rarotonga +CL -3327-07040 America/Santiago most of Chile +CL -4534-07204 America/Coyhaique Aysen Region +CL -5309-07055 America/Punta_Arenas Magallanes Region +CL -2709-10926 Pacific/Easter Easter Island +CM +0403+00942 Africa/Douala +CN +3114+12128 Asia/Shanghai Beijing Time +CN +4348+08735 Asia/Urumqi Xinjiang Time +CO +0436-07405 America/Bogota +CR +0956-08405 America/Costa_Rica +CU +2308-08222 America/Havana +CV +1455-02331 Atlantic/Cape_Verde +CW +1211-06900 America/Curacao +CX -1025+10543 Indian/Christmas +CY +3510+03322 Asia/Nicosia most of Cyprus +CY +3507+03357 Asia/Famagusta Northern Cyprus +CZ +5005+01426 Europe/Prague +DE +5230+01322 Europe/Berlin most of Germany +DE +4742+00841 Europe/Busingen Busingen +DJ +1136+04309 Africa/Djibouti +DK +5540+01235 Europe/Copenhagen +DM +1518-06124 America/Dominica +DO +1828-06954 America/Santo_Domingo +DZ +3647+00303 Africa/Algiers +EC -0210-07950 America/Guayaquil Ecuador (mainland) +EC -0054-08936 Pacific/Galapagos Galapagos Islands +EE +5925+02445 Europe/Tallinn +EG +3003+03115 Africa/Cairo +EH +2709-01312 Africa/El_Aaiun +ER +1520+03853 Africa/Asmara +ES +4024-00341 Europe/Madrid Spain (mainland) +ES +3553-00519 Africa/Ceuta Ceuta, Melilla +ES +2806-01524 Atlantic/Canary Canary Islands +ET +0902+03842 Africa/Addis_Ababa +FI +6010+02458 Europe/Helsinki +FJ -1808+17825 Pacific/Fiji +FK -5142-05751 Atlantic/Stanley +FM +0725+15147 Pacific/Chuuk Chuuk/Truk, Yap +FM +0658+15813 Pacific/Pohnpei Pohnpei/Ponape +FM +0519+16259 Pacific/Kosrae Kosrae +FO +6201-00646 Atlantic/Faroe +FR +4852+00220 Europe/Paris +GA +0023+00927 Africa/Libreville +GB +513030-0000731 Europe/London +GD +1203-06145 America/Grenada +GE +4143+04449 Asia/Tbilisi +GF +0456-05220 America/Cayenne +GG +492717-0023210 Europe/Guernsey +GH +0533-00013 Africa/Accra +GI +3608-00521 Europe/Gibraltar +GL +6411-05144 America/Nuuk most of Greenland +GL +7646-01840 America/Danmarkshavn National Park (east coast) +GL +7029-02158 America/Scoresbysund Scoresbysund/Ittoqqortoormiit +GL +7634-06847 America/Thule Thule/Pituffik +GM +1328-01639 Africa/Banjul +GN +0931-01343 Africa/Conakry +GP +1614-06132 America/Guadeloupe +GQ +0345+00847 Africa/Malabo +GR +3758+02343 Europe/Athens +GS -5416-03632 Atlantic/South_Georgia +GT +1438-09031 America/Guatemala +GU +1328+14445 Pacific/Guam +GW +1151-01535 Africa/Bissau +GY +0648-05810 America/Guyana +HK +2217+11409 Asia/Hong_Kong +HN +1406-08713 America/Tegucigalpa +HR +4548+01558 Europe/Zagreb +HT +1832-07220 America/Port-au-Prince +HU +4730+01905 Europe/Budapest +ID -0610+10648 Asia/Jakarta Java, Sumatra +ID -0002+10920 Asia/Pontianak Borneo (west, central) +ID -0507+11924 Asia/Makassar Borneo (east, south), Sulawesi/Celebes, Bali, Nusa Tengarra, Timor (west) +ID -0232+14042 Asia/Jayapura New Guinea (West Papua / Irian Jaya), Malukus/Moluccas +IE +5320-00615 Europe/Dublin +IL +314650+0351326 Asia/Jerusalem +IM +5409-00428 Europe/Isle_of_Man +IN +2232+08822 Asia/Kolkata +IO -0720+07225 Indian/Chagos +IQ +3321+04425 Asia/Baghdad +IR +3540+05126 Asia/Tehran +IS +6409-02151 Atlantic/Reykjavik +IT +4154+01229 Europe/Rome +JE +491101-0020624 Europe/Jersey +JM +175805-0764736 America/Jamaica +JO +3157+03556 Asia/Amman +JP +353916+1394441 Asia/Tokyo +KE -0117+03649 Africa/Nairobi +KG +4254+07436 Asia/Bishkek +KH +1133+10455 Asia/Phnom_Penh +KI +0125+17300 Pacific/Tarawa Gilbert Islands +KI -0247-17143 Pacific/Kanton Phoenix Islands +KI +0152-15720 Pacific/Kiritimati Line Islands +KM -1141+04316 Indian/Comoro +KN +1718-06243 America/St_Kitts +KP +3901+12545 Asia/Pyongyang +KR +3733+12658 Asia/Seoul +KW +2920+04759 Asia/Kuwait +KY +1918-08123 America/Cayman +KZ +4315+07657 Asia/Almaty most of Kazakhstan +KZ +4448+06528 Asia/Qyzylorda Qyzylorda/Kyzylorda/Kzyl-Orda +KZ +5312+06337 Asia/Qostanay Qostanay/Kostanay/Kustanay +KZ +5017+05710 Asia/Aqtobe Aqtobe/Aktobe +KZ +4431+05016 Asia/Aqtau Mangghystau/Mankistau +KZ +4707+05156 Asia/Atyrau Atyrau/Atirau/Gur'yev +KZ +5113+05121 Asia/Oral West Kazakhstan +LA +1758+10236 Asia/Vientiane +LB +3353+03530 Asia/Beirut +LC +1401-06100 America/St_Lucia +LI +4709+00931 Europe/Vaduz +LK +0656+07951 Asia/Colombo +LR +0618-01047 Africa/Monrovia +LS -2928+02730 Africa/Maseru +LT +5441+02519 Europe/Vilnius +LU +4936+00609 Europe/Luxembourg +LV +5657+02406 Europe/Riga +LY +3254+01311 Africa/Tripoli +MA +3339-00735 Africa/Casablanca +MC +4342+00723 Europe/Monaco +MD +4700+02850 Europe/Chisinau +ME +4226+01916 Europe/Podgorica +MF +1804-06305 America/Marigot +MG -1855+04731 Indian/Antananarivo +MH +0709+17112 Pacific/Majuro most of Marshall Islands +MH +0905+16720 Pacific/Kwajalein Kwajalein +MK +4159+02126 Europe/Skopje +ML +1239-00800 Africa/Bamako +MM +1647+09610 Asia/Yangon +MN +4755+10653 Asia/Ulaanbaatar most of Mongolia +MN +4801+09139 Asia/Hovd Bayan-Olgii, Hovd, Uvs +MO +221150+1133230 Asia/Macau +MP +1512+14545 Pacific/Saipan +MQ +1436-06105 America/Martinique +MR +1806-01557 Africa/Nouakchott +MS +1643-06213 America/Montserrat +MT +3554+01431 Europe/Malta +MU -2010+05730 Indian/Mauritius +MV +0410+07330 Indian/Maldives +MW -1547+03500 Africa/Blantyre +MX +1924-09909 America/Mexico_City Central Mexico +MX +2105-08646 America/Cancun Quintana Roo +MX +2058-08937 America/Merida Campeche, Yucatan +MX +2540-10019 America/Monterrey Durango; Coahuila, Nuevo Leon, Tamaulipas (most areas) +MX +2550-09730 America/Matamoros Coahuila, Nuevo Leon, Tamaulipas (US border) +MX +2838-10605 America/Chihuahua Chihuahua (most areas) +MX +3144-10629 America/Ciudad_Juarez Chihuahua (US border - west) +MX +2934-10425 America/Ojinaga Chihuahua (US border - east) +MX +2313-10625 America/Mazatlan Baja California Sur, Nayarit (most areas), Sinaloa +MX +2048-10515 America/Bahia_Banderas Bahia de Banderas +MX +2904-11058 America/Hermosillo Sonora +MX +3232-11701 America/Tijuana Baja California +MY +0310+10142 Asia/Kuala_Lumpur Malaysia (peninsula) +MY +0133+11020 Asia/Kuching Sabah, Sarawak +MZ -2558+03235 Africa/Maputo +NA -2234+01706 Africa/Windhoek +NC -2216+16627 Pacific/Noumea +NE +1331+00207 Africa/Niamey +NF -2903+16758 Pacific/Norfolk +NG +0627+00324 Africa/Lagos +NI +1209-08617 America/Managua +NL +5222+00454 Europe/Amsterdam +NO +5955+01045 Europe/Oslo +NP +2743+08519 Asia/Kathmandu +NR -0031+16655 Pacific/Nauru +NU -1901-16955 Pacific/Niue +NZ -3652+17446 Pacific/Auckland most of New Zealand +NZ -4357-17633 Pacific/Chatham Chatham Islands +OM +2336+05835 Asia/Muscat +PA +0858-07932 America/Panama +PE -1203-07703 America/Lima +PF -1732-14934 Pacific/Tahiti Society Islands +PF -0900-13930 Pacific/Marquesas Marquesas Islands +PF -2308-13457 Pacific/Gambier Gambier Islands +PG -0930+14710 Pacific/Port_Moresby most of Papua New Guinea +PG -0613+15534 Pacific/Bougainville Bougainville +PH +143512+1205804 Asia/Manila +PK +2452+06703 Asia/Karachi +PL +5215+02100 Europe/Warsaw +PM +4703-05620 America/Miquelon +PN -2504-13005 Pacific/Pitcairn +PR +182806-0660622 America/Puerto_Rico +PS +3130+03428 Asia/Gaza Gaza Strip +PS +313200+0350542 Asia/Hebron West Bank +PT +3843-00908 Europe/Lisbon Portugal (mainland) +PT +3238-01654 Atlantic/Madeira Madeira Islands +PT +3744-02540 Atlantic/Azores Azores +PW +0720+13429 Pacific/Palau +PY -2516-05740 America/Asuncion +QA +2517+05132 Asia/Qatar +RE -2052+05528 Indian/Reunion +RO +4426+02606 Europe/Bucharest +RS +4450+02030 Europe/Belgrade +RU +5443+02030 Europe/Kaliningrad MSK-01 - Kaliningrad +RU +554521+0373704 Europe/Moscow MSK+00 - Moscow area +# The obsolescent zone.tab format cannot represent Europe/Simferopol well. +# Put it in RU section and list as UA. See "territorial claims" above. +# Programs should use zone1970.tab instead; see above. +UA +4457+03406 Europe/Simferopol Crimea +RU +5836+04939 Europe/Kirov MSK+00 - Kirov +RU +4844+04425 Europe/Volgograd MSK+00 - Volgograd +RU +4621+04803 Europe/Astrakhan MSK+01 - Astrakhan +RU +5134+04602 Europe/Saratov MSK+01 - Saratov +RU +5420+04824 Europe/Ulyanovsk MSK+01 - Ulyanovsk +RU +5312+05009 Europe/Samara MSK+01 - Samara, Udmurtia +RU +5651+06036 Asia/Yekaterinburg MSK+02 - Urals +RU +5500+07324 Asia/Omsk MSK+03 - Omsk +RU +5502+08255 Asia/Novosibirsk MSK+04 - Novosibirsk +RU +5322+08345 Asia/Barnaul MSK+04 - Altai +RU +5630+08458 Asia/Tomsk MSK+04 - Tomsk +RU +5345+08707 Asia/Novokuznetsk MSK+04 - Kemerovo +RU +5601+09250 Asia/Krasnoyarsk MSK+04 - Krasnoyarsk area +RU +5216+10420 Asia/Irkutsk MSK+05 - Irkutsk, Buryatia +RU +5203+11328 Asia/Chita MSK+06 - Zabaykalsky +RU +6200+12940 Asia/Yakutsk MSK+06 - Lena River +RU +623923+1353314 Asia/Khandyga MSK+06 - Tomponsky, Ust-Maysky +RU +4310+13156 Asia/Vladivostok MSK+07 - Amur River +RU +643337+1431336 Asia/Ust-Nera MSK+07 - Oymyakonsky +RU +5934+15048 Asia/Magadan MSK+08 - Magadan +RU +4658+14242 Asia/Sakhalin MSK+08 - Sakhalin Island +RU +6728+15343 Asia/Srednekolymsk MSK+08 - Sakha (E), N Kuril Is +RU +5301+15839 Asia/Kamchatka MSK+09 - Kamchatka +RU +6445+17729 Asia/Anadyr MSK+09 - Bering Sea +RW -0157+03004 Africa/Kigali +SA +2438+04643 Asia/Riyadh +SB -0932+16012 Pacific/Guadalcanal +SC -0440+05528 Indian/Mahe +SD +1536+03232 Africa/Khartoum +SE +5920+01803 Europe/Stockholm +SG +0117+10351 Asia/Singapore +SH -1555-00542 Atlantic/St_Helena +SI +4603+01431 Europe/Ljubljana +SJ +7800+01600 Arctic/Longyearbyen +SK +4809+01707 Europe/Bratislava +SL +0830-01315 Africa/Freetown +SM +4355+01228 Europe/San_Marino +SN +1440-01726 Africa/Dakar +SO +0204+04522 Africa/Mogadishu +SR +0550-05510 America/Paramaribo +SS +0451+03137 Africa/Juba +ST +0020+00644 Africa/Sao_Tome +SV +1342-08912 America/El_Salvador +SX +180305-0630250 America/Lower_Princes +SY +3330+03618 Asia/Damascus +SZ -2618+03106 Africa/Mbabane +TC +2128-07108 America/Grand_Turk +TD +1207+01503 Africa/Ndjamena +TF -492110+0701303 Indian/Kerguelen +TG +0608+00113 Africa/Lome +TH +1345+10031 Asia/Bangkok +TJ +3835+06848 Asia/Dushanbe +TK -0922-17114 Pacific/Fakaofo +TL -0833+12535 Asia/Dili +TM +3757+05823 Asia/Ashgabat +TN +3648+01011 Africa/Tunis +TO -210800-1751200 Pacific/Tongatapu +TR +4101+02858 Europe/Istanbul +TT +1039-06131 America/Port_of_Spain +TV -0831+17913 Pacific/Funafuti +TW +2503+12130 Asia/Taipei +TZ -0648+03917 Africa/Dar_es_Salaam +UA +5026+03031 Europe/Kyiv most of Ukraine +UG +0019+03225 Africa/Kampala +UM +2813-17722 Pacific/Midway Midway Islands +UM +1917+16637 Pacific/Wake Wake Island +US +404251-0740023 America/New_York Eastern (most areas) +US +421953-0830245 America/Detroit Eastern - MI (most areas) +US +381515-0854534 America/Kentucky/Louisville Eastern - KY (Louisville area) +US +364947-0845057 America/Kentucky/Monticello Eastern - KY (Wayne) +US +394606-0860929 America/Indiana/Indianapolis Eastern - IN (most areas) +US +384038-0873143 America/Indiana/Vincennes Eastern - IN (Da, Du, K, Mn) +US +410305-0863611 America/Indiana/Winamac Eastern - IN (Pulaski) +US +382232-0862041 America/Indiana/Marengo Eastern - IN (Crawford) +US +382931-0871643 America/Indiana/Petersburg Eastern - IN (Pike) +US +384452-0850402 America/Indiana/Vevay Eastern - IN (Switzerland) +US +415100-0873900 America/Chicago Central (most areas) +US +375711-0864541 America/Indiana/Tell_City Central - IN (Perry) +US +411745-0863730 America/Indiana/Knox Central - IN (Starke) +US +450628-0873651 America/Menominee Central - MI (Wisconsin border) +US +470659-1011757 America/North_Dakota/Center Central - ND (Oliver) +US +465042-1012439 America/North_Dakota/New_Salem Central - ND (Morton rural) +US +471551-1014640 America/North_Dakota/Beulah Central - ND (Mercer) +US +394421-1045903 America/Denver Mountain (most areas) +US +433649-1161209 America/Boise Mountain - ID (south), OR (east) +US +332654-1120424 America/Phoenix MST - AZ (except Navajo) +US +340308-1181434 America/Los_Angeles Pacific +US +611305-1495401 America/Anchorage Alaska (most areas) +US +581807-1342511 America/Juneau Alaska - Juneau area +US +571035-1351807 America/Sitka Alaska - Sitka area +US +550737-1313435 America/Metlakatla Alaska - Annette Island +US +593249-1394338 America/Yakutat Alaska - Yakutat +US +643004-1652423 America/Nome Alaska (west) +US +515248-1763929 America/Adak Alaska - western Aleutians +US +211825-1575130 Pacific/Honolulu Hawaii +UY -345433-0561245 America/Montevideo +UZ +3940+06648 Asia/Samarkand Uzbekistan (west) +UZ +4120+06918 Asia/Tashkent Uzbekistan (east) +VA +415408+0122711 Europe/Vatican +VC +1309-06114 America/St_Vincent +VE +1030-06656 America/Caracas +VG +1827-06437 America/Tortola +VI +1821-06456 America/St_Thomas +VN +1045+10640 Asia/Ho_Chi_Minh +VU -1740+16825 Pacific/Efate +WF -1318-17610 Pacific/Wallis +WS -1350-17144 Pacific/Apia +YE +1245+04512 Asia/Aden +YT -1247+04514 Indian/Mayotte +ZA -2615+02800 Africa/Johannesburg +ZM -1525+02817 Africa/Lusaka +ZW -1750+03103 Africa/Harare diff --git a/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/zone1970.tab b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/zone1970.tab new file mode 100644 index 0000000000000000000000000000000000000000..cd43e3d2e0d8a4550ea6ae52d0516a4f2e987a0b --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/zone1970.tab @@ -0,0 +1,375 @@ +# tzdb timezone descriptions +# +# This file is in the public domain. +# +# From Paul Eggert (2025-05-15): +# This file contains a table where each row stands for a timezone where +# civil timestamps have agreed since 1970. Columns are separated by +# a single tab. Lines beginning with ‘#’ are comments. All text uses +# UTF-8 encoding. The columns of the table are as follows: +# +# 1. The countries that overlap the timezone, as a comma-separated list +# of ISO 3166 2-character country codes. +# 2. Latitude and longitude of the timezone’s principal location +# in ISO 6709 sign-degrees-minutes-seconds format, +# either ±DDMM±DDDMM or ±DDMMSS±DDDMMSS, +# first latitude (+ is north), then longitude (+ is east). +# 3. Timezone name used in value of TZ environment variable. +# Please see the theory.html file for how these names are chosen. +# If multiple timezones overlap a country, each has a row in the +# table, with each column 1 containing the country code. +# 4. Comments; present if and only if countries have multiple timezones, +# and useful only for those countries. For example, the comments +# for the row with countries CH,DE,LI and name Europe/Zurich +# are useful only for DE, since CH and LI have no other timezones. +# +# If a timezone covers multiple countries, the most-populous city is used, +# and that country is listed first in column 1; any other countries +# are listed alphabetically by country code. The table is sorted +# first by country code, then (if possible) by an order within the +# country that (1) makes some geographical sense, and (2) puts the +# most populous timezones first, where that does not contradict (1). +# +# This table is intended as an aid for users, to help them select timezones +# appropriate for their practical needs. It is not intended to take or +# endorse any position on legal or territorial claims. +# +#country- +#codes coordinates TZ comments +AD +4230+00131 Europe/Andorra +AE,OM,RE,SC,TF +2518+05518 Asia/Dubai Crozet +AF +3431+06912 Asia/Kabul +AL +4120+01950 Europe/Tirane +AM +4011+04430 Asia/Yerevan +AQ -6617+11031 Antarctica/Casey Casey +AQ -6835+07758 Antarctica/Davis Davis +AQ -6736+06253 Antarctica/Mawson Mawson +AQ -6448-06406 Antarctica/Palmer Palmer +AQ -6734-06808 Antarctica/Rothera Rothera +AQ -720041+0023206 Antarctica/Troll Troll +AQ -7824+10654 Antarctica/Vostok Vostok +AR -3436-05827 America/Argentina/Buenos_Aires Buenos Aires (BA, CF) +AR -3124-06411 America/Argentina/Cordoba most areas: CB, CC, CN, ER, FM, MN, SE, SF +AR -2447-06525 America/Argentina/Salta Salta (SA, LP, NQ, RN) +AR -2411-06518 America/Argentina/Jujuy Jujuy (JY) +AR -2649-06513 America/Argentina/Tucuman Tucumán (TM) +AR -2828-06547 America/Argentina/Catamarca Catamarca (CT), Chubut (CH) +AR -2926-06651 America/Argentina/La_Rioja La Rioja (LR) +AR -3132-06831 America/Argentina/San_Juan San Juan (SJ) +AR -3253-06849 America/Argentina/Mendoza Mendoza (MZ) +AR -3319-06621 America/Argentina/San_Luis San Luis (SL) +AR -5138-06913 America/Argentina/Rio_Gallegos Santa Cruz (SC) +AR -5448-06818 America/Argentina/Ushuaia Tierra del Fuego (TF) +AS,UM -1416-17042 Pacific/Pago_Pago Midway +AT +4813+01620 Europe/Vienna +AU -3133+15905 Australia/Lord_Howe Lord Howe Island +AU -5430+15857 Antarctica/Macquarie Macquarie Island +AU -4253+14719 Australia/Hobart Tasmania +AU -3749+14458 Australia/Melbourne Victoria +AU -3352+15113 Australia/Sydney New South Wales (most areas) +AU -3157+14127 Australia/Broken_Hill New South Wales (Yancowinna) +AU -2728+15302 Australia/Brisbane Queensland (most areas) +AU -2016+14900 Australia/Lindeman Queensland (Whitsunday Islands) +AU -3455+13835 Australia/Adelaide South Australia +AU -1228+13050 Australia/Darwin Northern Territory +AU -3157+11551 Australia/Perth Western Australia (most areas) +AU -3143+12852 Australia/Eucla Western Australia (Eucla) +AZ +4023+04951 Asia/Baku +BB +1306-05937 America/Barbados +BD +2343+09025 Asia/Dhaka +BE,LU,NL +5050+00420 Europe/Brussels +BG +4241+02319 Europe/Sofia +BM +3217-06446 Atlantic/Bermuda +BO -1630-06809 America/La_Paz +BR -0351-03225 America/Noronha Atlantic islands +BR -0127-04829 America/Belem Pará (east), Amapá +BR -0343-03830 America/Fortaleza Brazil (northeast: MA, PI, CE, RN, PB) +BR -0803-03454 America/Recife Pernambuco +BR -0712-04812 America/Araguaina Tocantins +BR -0940-03543 America/Maceio Alagoas, Sergipe +BR -1259-03831 America/Bahia Bahia +BR -2332-04637 America/Sao_Paulo Brazil (southeast: GO, DF, MG, ES, RJ, SP, PR, SC, RS) +BR -2027-05437 America/Campo_Grande Mato Grosso do Sul +BR -1535-05605 America/Cuiaba Mato Grosso +BR -0226-05452 America/Santarem Pará (west) +BR -0846-06354 America/Porto_Velho Rondônia +BR +0249-06040 America/Boa_Vista Roraima +BR -0308-06001 America/Manaus Amazonas (east) +BR -0640-06952 America/Eirunepe Amazonas (west) +BR -0958-06748 America/Rio_Branco Acre +BT +2728+08939 Asia/Thimphu +BY +5354+02734 Europe/Minsk +BZ +1730-08812 America/Belize +CA +4734-05243 America/St_Johns Newfoundland, Labrador (SE) +CA +4439-06336 America/Halifax Atlantic - NS (most areas), PE +CA +4612-05957 America/Glace_Bay Atlantic - NS (Cape Breton) +CA +4606-06447 America/Moncton Atlantic - New Brunswick +CA +5320-06025 America/Goose_Bay Atlantic - Labrador (most areas) +CA,BS +4339-07923 America/Toronto Eastern - ON & QC (most areas) +CA +6344-06828 America/Iqaluit Eastern - NU (most areas) +CA +4953-09709 America/Winnipeg Central - ON (west), Manitoba +CA +744144-0944945 America/Resolute Central - NU (Resolute) +CA +624900-0920459 America/Rankin_Inlet Central - NU (central) +CA +5024-10439 America/Regina CST - SK (most areas) +CA +5017-10750 America/Swift_Current CST - SK (midwest) +CA +5333-11328 America/Edmonton Mountain - AB, BC(E), NT(E), SK(W) +CA +690650-1050310 America/Cambridge_Bay Mountain - NU (west) +CA +682059-1334300 America/Inuvik Mountain - NT (west) +CA +5546-12014 America/Dawson_Creek MST - BC (Dawson Cr, Ft St John) +CA +5848-12242 America/Fort_Nelson MST - BC (Ft Nelson) +CA +6043-13503 America/Whitehorse MST - Yukon (east) +CA +6404-13925 America/Dawson MST - Yukon (west) +CA +4916-12307 America/Vancouver Pacific - BC (most areas) +CH,DE,LI +4723+00832 Europe/Zurich Büsingen +CI,BF,GH,GM,GN,IS,ML,MR,SH,SL,SN,TG +0519-00402 Africa/Abidjan +CK -2114-15946 Pacific/Rarotonga +CL -3327-07040 America/Santiago most of Chile +CL -4534-07204 America/Coyhaique Aysén Region +CL -5309-07055 America/Punta_Arenas Magallanes Region +CL -2709-10926 Pacific/Easter Easter Island +CN +3114+12128 Asia/Shanghai Beijing Time +CN +4348+08735 Asia/Urumqi Xinjiang Time +CO +0436-07405 America/Bogota +CR +0956-08405 America/Costa_Rica +CU +2308-08222 America/Havana +CV +1455-02331 Atlantic/Cape_Verde +CY +3510+03322 Asia/Nicosia most of Cyprus +CY +3507+03357 Asia/Famagusta Northern Cyprus +CZ,SK +5005+01426 Europe/Prague +DE,DK,NO,SE,SJ +5230+01322 Europe/Berlin most of Germany +DO +1828-06954 America/Santo_Domingo +DZ +3647+00303 Africa/Algiers +EC -0210-07950 America/Guayaquil Ecuador (mainland) +EC -0054-08936 Pacific/Galapagos Galápagos Islands +EE +5925+02445 Europe/Tallinn +EG +3003+03115 Africa/Cairo +EH +2709-01312 Africa/El_Aaiun +ES +4024-00341 Europe/Madrid Spain (mainland) +ES +3553-00519 Africa/Ceuta Ceuta, Melilla +ES +2806-01524 Atlantic/Canary Canary Islands +FI,AX +6010+02458 Europe/Helsinki +FJ -1808+17825 Pacific/Fiji +FK -5142-05751 Atlantic/Stanley +FM +0519+16259 Pacific/Kosrae Kosrae +FO +6201-00646 Atlantic/Faroe +FR,MC +4852+00220 Europe/Paris +GB,GG,IM,JE +513030-0000731 Europe/London +GE +4143+04449 Asia/Tbilisi +GF +0456-05220 America/Cayenne +GI +3608-00521 Europe/Gibraltar +GL +6411-05144 America/Nuuk most of Greenland +GL +7646-01840 America/Danmarkshavn National Park (east coast) +GL +7029-02158 America/Scoresbysund Scoresbysund/Ittoqqortoormiit +GL +7634-06847 America/Thule Thule/Pituffik +GR +3758+02343 Europe/Athens +GS -5416-03632 Atlantic/South_Georgia +GT +1438-09031 America/Guatemala +GU,MP +1328+14445 Pacific/Guam +GW +1151-01535 Africa/Bissau +GY +0648-05810 America/Guyana +HK +2217+11409 Asia/Hong_Kong +HN +1406-08713 America/Tegucigalpa +HT +1832-07220 America/Port-au-Prince +HU +4730+01905 Europe/Budapest +ID -0610+10648 Asia/Jakarta Java, Sumatra +ID -0002+10920 Asia/Pontianak Borneo (west, central) +ID -0507+11924 Asia/Makassar Borneo (east, south), Sulawesi/Celebes, Bali, Nusa Tengarra, Timor (west) +ID -0232+14042 Asia/Jayapura New Guinea (West Papua / Irian Jaya), Malukus/Moluccas +IE +5320-00615 Europe/Dublin +IL +314650+0351326 Asia/Jerusalem +IN +2232+08822 Asia/Kolkata +IO -0720+07225 Indian/Chagos +IQ +3321+04425 Asia/Baghdad +IR +3540+05126 Asia/Tehran +IT,SM,VA +4154+01229 Europe/Rome +JM +175805-0764736 America/Jamaica +JO +3157+03556 Asia/Amman +JP,AU +353916+1394441 Asia/Tokyo Eyre Bird Observatory +KE,DJ,ER,ET,KM,MG,SO,TZ,UG,YT -0117+03649 Africa/Nairobi +KG +4254+07436 Asia/Bishkek +KI,MH,TV,UM,WF +0125+17300 Pacific/Tarawa Gilberts, Marshalls, Wake +KI -0247-17143 Pacific/Kanton Phoenix Islands +KI +0152-15720 Pacific/Kiritimati Line Islands +KP +3901+12545 Asia/Pyongyang +KR +3733+12658 Asia/Seoul +KZ +4315+07657 Asia/Almaty most of Kazakhstan +KZ +4448+06528 Asia/Qyzylorda Qyzylorda/Kyzylorda/Kzyl-Orda +KZ +5312+06337 Asia/Qostanay Qostanay/Kostanay/Kustanay +KZ +5017+05710 Asia/Aqtobe Aqtöbe/Aktobe +KZ +4431+05016 Asia/Aqtau Mangghystaū/Mankistau +KZ +4707+05156 Asia/Atyrau Atyraū/Atirau/Gur’yev +KZ +5113+05121 Asia/Oral West Kazakhstan +LB +3353+03530 Asia/Beirut +LK +0656+07951 Asia/Colombo +LR +0618-01047 Africa/Monrovia +LT +5441+02519 Europe/Vilnius +LV +5657+02406 Europe/Riga +LY +3254+01311 Africa/Tripoli +MA +3339-00735 Africa/Casablanca +MD +4700+02850 Europe/Chisinau +MH +0905+16720 Pacific/Kwajalein Kwajalein +MM,CC +1647+09610 Asia/Yangon +MN +4755+10653 Asia/Ulaanbaatar most of Mongolia +MN +4801+09139 Asia/Hovd Bayan-Ölgii, Hovd, Uvs +MO +221150+1133230 Asia/Macau +MQ +1436-06105 America/Martinique +MT +3554+01431 Europe/Malta +MU -2010+05730 Indian/Mauritius +MV,TF +0410+07330 Indian/Maldives Kerguelen, St Paul I, Amsterdam I +MX +1924-09909 America/Mexico_City Central Mexico +MX +2105-08646 America/Cancun Quintana Roo +MX +2058-08937 America/Merida Campeche, Yucatán +MX +2540-10019 America/Monterrey Durango; Coahuila, Nuevo León, Tamaulipas (most areas) +MX +2550-09730 America/Matamoros Coahuila, Nuevo León, Tamaulipas (US border) +MX +2838-10605 America/Chihuahua Chihuahua (most areas) +MX +3144-10629 America/Ciudad_Juarez Chihuahua (US border - west) +MX +2934-10425 America/Ojinaga Chihuahua (US border - east) +MX +2313-10625 America/Mazatlan Baja California Sur, Nayarit (most areas), Sinaloa +MX +2048-10515 America/Bahia_Banderas Bahía de Banderas +MX +2904-11058 America/Hermosillo Sonora +MX +3232-11701 America/Tijuana Baja California +MY,BN +0133+11020 Asia/Kuching Sabah, Sarawak +MZ,BI,BW,CD,MW,RW,ZM,ZW -2558+03235 Africa/Maputo Central Africa Time +NA -2234+01706 Africa/Windhoek +NC -2216+16627 Pacific/Noumea +NF -2903+16758 Pacific/Norfolk +NG,AO,BJ,CD,CF,CG,CM,GA,GQ,NE +0627+00324 Africa/Lagos West Africa Time +NI +1209-08617 America/Managua +NP +2743+08519 Asia/Kathmandu +NR -0031+16655 Pacific/Nauru +NU -1901-16955 Pacific/Niue +NZ,AQ -3652+17446 Pacific/Auckland New Zealand time +NZ -4357-17633 Pacific/Chatham Chatham Islands +PA,CA,KY +0858-07932 America/Panama EST - ON (Atikokan), NU (Coral H) +PE -1203-07703 America/Lima +PF -1732-14934 Pacific/Tahiti Society Islands +PF -0900-13930 Pacific/Marquesas Marquesas Islands +PF -2308-13457 Pacific/Gambier Gambier Islands +PG,AQ,FM -0930+14710 Pacific/Port_Moresby Papua New Guinea (most areas), Chuuk, Yap, Dumont d’Urville +PG -0613+15534 Pacific/Bougainville Bougainville +PH +143512+1205804 Asia/Manila +PK +2452+06703 Asia/Karachi +PL +5215+02100 Europe/Warsaw +PM +4703-05620 America/Miquelon +PN -2504-13005 Pacific/Pitcairn +PR,AG,CA,AI,AW,BL,BQ,CW,DM,GD,GP,KN,LC,MF,MS,SX,TT,VC,VG,VI +182806-0660622 America/Puerto_Rico AST - QC (Lower North Shore) +PS +3130+03428 Asia/Gaza Gaza Strip +PS +313200+0350542 Asia/Hebron West Bank +PT +3843-00908 Europe/Lisbon Portugal (mainland) +PT +3238-01654 Atlantic/Madeira Madeira Islands +PT +3744-02540 Atlantic/Azores Azores +PW +0720+13429 Pacific/Palau +PY -2516-05740 America/Asuncion +QA,BH +2517+05132 Asia/Qatar +RO +4426+02606 Europe/Bucharest +RS,BA,HR,ME,MK,SI +4450+02030 Europe/Belgrade +RU +5443+02030 Europe/Kaliningrad MSK-01 - Kaliningrad +RU +554521+0373704 Europe/Moscow MSK+00 - Moscow area +# Mention RU and UA alphabetically. See “territorial claims” above. +RU,UA +4457+03406 Europe/Simferopol Crimea +RU +5836+04939 Europe/Kirov MSK+00 - Kirov +RU +4844+04425 Europe/Volgograd MSK+00 - Volgograd +RU +4621+04803 Europe/Astrakhan MSK+01 - Astrakhan +RU +5134+04602 Europe/Saratov MSK+01 - Saratov +RU +5420+04824 Europe/Ulyanovsk MSK+01 - Ulyanovsk +RU +5312+05009 Europe/Samara MSK+01 - Samara, Udmurtia +RU +5651+06036 Asia/Yekaterinburg MSK+02 - Urals +RU +5500+07324 Asia/Omsk MSK+03 - Omsk +RU +5502+08255 Asia/Novosibirsk MSK+04 - Novosibirsk +RU +5322+08345 Asia/Barnaul MSK+04 - Altai +RU +5630+08458 Asia/Tomsk MSK+04 - Tomsk +RU +5345+08707 Asia/Novokuznetsk MSK+04 - Kemerovo +RU +5601+09250 Asia/Krasnoyarsk MSK+04 - Krasnoyarsk area +RU +5216+10420 Asia/Irkutsk MSK+05 - Irkutsk, Buryatia +RU +5203+11328 Asia/Chita MSK+06 - Zabaykalsky +RU +6200+12940 Asia/Yakutsk MSK+06 - Lena River +RU +623923+1353314 Asia/Khandyga MSK+06 - Tomponsky, Ust-Maysky +RU +4310+13156 Asia/Vladivostok MSK+07 - Amur River +RU +643337+1431336 Asia/Ust-Nera MSK+07 - Oymyakonsky +RU +5934+15048 Asia/Magadan MSK+08 - Magadan +RU +4658+14242 Asia/Sakhalin MSK+08 - Sakhalin Island +RU +6728+15343 Asia/Srednekolymsk MSK+08 - Sakha (E), N Kuril Is +RU +5301+15839 Asia/Kamchatka MSK+09 - Kamchatka +RU +6445+17729 Asia/Anadyr MSK+09 - Bering Sea +SA,AQ,KW,YE +2438+04643 Asia/Riyadh Syowa +SB,FM -0932+16012 Pacific/Guadalcanal Pohnpei +SD +1536+03232 Africa/Khartoum +SG,AQ,MY +0117+10351 Asia/Singapore peninsular Malaysia, Concordia +SR +0550-05510 America/Paramaribo +SS +0451+03137 Africa/Juba +ST +0020+00644 Africa/Sao_Tome +SV +1342-08912 America/El_Salvador +SY +3330+03618 Asia/Damascus +TC +2128-07108 America/Grand_Turk +TD +1207+01503 Africa/Ndjamena +TH,CX,KH,LA,VN +1345+10031 Asia/Bangkok north Vietnam +TJ +3835+06848 Asia/Dushanbe +TK -0922-17114 Pacific/Fakaofo +TL -0833+12535 Asia/Dili +TM +3757+05823 Asia/Ashgabat +TN +3648+01011 Africa/Tunis +TO -210800-1751200 Pacific/Tongatapu +TR +4101+02858 Europe/Istanbul +TW +2503+12130 Asia/Taipei +UA +5026+03031 Europe/Kyiv most of Ukraine +US +404251-0740023 America/New_York Eastern (most areas) +US +421953-0830245 America/Detroit Eastern - MI (most areas) +US +381515-0854534 America/Kentucky/Louisville Eastern - KY (Louisville area) +US +364947-0845057 America/Kentucky/Monticello Eastern - KY (Wayne) +US +394606-0860929 America/Indiana/Indianapolis Eastern - IN (most areas) +US +384038-0873143 America/Indiana/Vincennes Eastern - IN (Da, Du, K, Mn) +US +410305-0863611 America/Indiana/Winamac Eastern - IN (Pulaski) +US +382232-0862041 America/Indiana/Marengo Eastern - IN (Crawford) +US +382931-0871643 America/Indiana/Petersburg Eastern - IN (Pike) +US +384452-0850402 America/Indiana/Vevay Eastern - IN (Switzerland) +US +415100-0873900 America/Chicago Central (most areas) +US +375711-0864541 America/Indiana/Tell_City Central - IN (Perry) +US +411745-0863730 America/Indiana/Knox Central - IN (Starke) +US +450628-0873651 America/Menominee Central - MI (Wisconsin border) +US +470659-1011757 America/North_Dakota/Center Central - ND (Oliver) +US +465042-1012439 America/North_Dakota/New_Salem Central - ND (Morton rural) +US +471551-1014640 America/North_Dakota/Beulah Central - ND (Mercer) +US +394421-1045903 America/Denver Mountain (most areas) +US +433649-1161209 America/Boise Mountain - ID (south), OR (east) +US,CA +332654-1120424 America/Phoenix MST - AZ (most areas), Creston BC +US +340308-1181434 America/Los_Angeles Pacific +US +611305-1495401 America/Anchorage Alaska (most areas) +US +581807-1342511 America/Juneau Alaska - Juneau area +US +571035-1351807 America/Sitka Alaska - Sitka area +US +550737-1313435 America/Metlakatla Alaska - Annette Island +US +593249-1394338 America/Yakutat Alaska - Yakutat +US +643004-1652423 America/Nome Alaska (west) +US +515248-1763929 America/Adak Alaska - western Aleutians +US +211825-1575130 Pacific/Honolulu Hawaii +UY -345433-0561245 America/Montevideo +UZ +3940+06648 Asia/Samarkand Uzbekistan (west) +UZ +4120+06918 Asia/Tashkent Uzbekistan (east) +VE +1030-06656 America/Caracas +VN +1045+10640 Asia/Ho_Chi_Minh south Vietnam +VU -1740+16825 Pacific/Efate +WS -1350-17144 Pacific/Apia +ZA,LS,SZ -2615+02800 Africa/Johannesburg +# +# The next section contains experimental tab-separated comments for +# use by user agents like tzselect that identify continents and oceans. +# +# For example, the comment ‘#@AQAntarctica/’ means the country code +# AQ is in the continent Antarctica regardless of the Zone name, +# so Pacific/Auckland should be listed under Antarctica as well as +# under the Pacific because its line’s country codes include AQ. +# +# If more than one country code is affected each is listed separated +# by commas, e.g., ‘#@IS,SHAtlantic/’. If a country code is in +# more than one continent or ocean, each is listed separated by +# commas, e.g., the second column of ‘#@CY,TRAsia/,Europe/’. +# +# These experimental comments are present only for country codes where +# the continent or ocean is not already obvious from the Zone name. +# For example, there is no such comment for RU since it already +# corresponds to Zone names starting with both ‘Europe/’ and ‘Asia/’. +# +#@AQ Antarctica/ +#@IS,SH Atlantic/ +#@CY,TR Asia/,Europe/ +#@SJ Arctic/ +#@CC,CX,KM,MG,YT Indian/ diff --git a/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/zonenow.tab b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/zonenow.tab new file mode 100644 index 0000000000000000000000000000000000000000..aa3a64f3d7b9fb14b6eaad1525f19fbe670a007d --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pytz/zoneinfo/zonenow.tab @@ -0,0 +1,293 @@ +# tzdb timezone descriptions, for users who do not care about old timestamps +# +# This file is in the public domain. +# +# From Paul Eggert (2023-12-18): +# This file contains a table where each row stands for a timezone +# where civil timestamps are predicted to agree from now on. +# This file is like zone1970.tab (see zone1970.tab’s comments), +# but with the following changes: +# +# 1. Each timezone corresponds to a set of clocks that are planned +# to agree from now on. This is a larger set of clocks than in +# zone1970.tab, where each timezone’s clocks must agree from 1970 on. +# 2. The first column is irrelevant and ignored. +# 3. The table is sorted in a different way: +# first by standard time UTC offset; +# then, if DST is used, by daylight saving UTC offset; +# then by time zone abbreviation. +# 4. Every timezone has a nonempty comments column, with wording +# distinguishing the timezone only from other timezones with the +# same UTC offset at some point during the year. +# +# The format of this table is experimental, and may change in future versions. +# +# This table is intended as an aid for users, to help them select timezones +# appropriate for their practical needs. It is not intended to take or +# endorse any position on legal or territorial claims. +# +#XX coordinates TZ comments +# +# -11 - SST +XX -1416-17042 Pacific/Pago_Pago Midway; Samoa (SST) +# +# -11 +XX -1901-16955 Pacific/Niue Niue +# +# -10 - HST +XX +211825-1575130 Pacific/Honolulu Hawaii (HST) +# +# -10 +XX -1732-14934 Pacific/Tahiti Tahiti; Cook Islands +# +# -10/-09 - HST / HDT (North America DST) +XX +515248-1763929 America/Adak western Aleutians in Alaska (HST/HDT) +# +# -09:30 +XX -0900-13930 Pacific/Marquesas Marquesas +# +# -09 +XX -2308-13457 Pacific/Gambier Gambier +# +# -09/-08 - AKST/AKDT (North America DST) +XX +611305-1495401 America/Anchorage most of Alaska (AKST/AKDT) +# +# -08 +XX -2504-13005 Pacific/Pitcairn Pitcairn +# +# -08/-07 - PST/PDT (North America DST) +XX +340308-1181434 America/Los_Angeles Pacific (PST/PDT) - US & Canada; Mexico near US border +# +# -07 - MST +XX +332654-1120424 America/Phoenix Mountain Standard (MST) - Arizona; western Mexico; Yukon +# +# -07/-06 - MST/MDT (North America DST) +XX +394421-1045903 America/Denver Mountain (MST/MDT) - US & Canada; Mexico near US border +# +# -06 +XX -0054-08936 Pacific/Galapagos Galápagos +# +# -06 - CST +XX +1924-09909 America/Mexico_City Central Standard (CST) - Saskatchewan; central Mexico; Central America +# +# -06/-05 (Chile DST) +XX -2709-10926 Pacific/Easter Easter Island +# +# -06/-05 - CST/CDT (North America DST) +XX +415100-0873900 America/Chicago Central (CST/CDT) - US & Canada; Mexico near US border +# +# -05 +XX -1203-07703 America/Lima eastern South America +# +# -05 - EST +XX +175805-0764736 America/Jamaica Eastern Standard (EST) - Caymans; Jamaica; eastern Mexico; Panama +# +# -05/-04 - CST/CDT (Cuba DST) +XX +2308-08222 America/Havana Cuba +# +# -05/-04 - EST/EDT (North America DST) +XX +404251-0740023 America/New_York Eastern (EST/EDT) - US & Canada +# +# -04 +XX +1030-06656 America/Caracas western South America +# +# -04 - AST +XX +1828-06954 America/Santo_Domingo Atlantic Standard (AST) - eastern Caribbean +# +# -04/-03 (Chile DST) +XX -3327-07040 America/Santiago most of Chile +# +# -04/-03 - AST/ADT (North America DST) +XX +4439-06336 America/Halifax Atlantic (AST/ADT) - Canada; Bermuda +# +# -03:30/-02:30 - NST/NDT (North America DST) +XX +4734-05243 America/St_Johns Newfoundland (NST/NDT) +# +# -03 +XX -2332-04637 America/Sao_Paulo eastern and southern South America +# +# -03/-02 (North America DST) +XX +4703-05620 America/Miquelon St Pierre & Miquelon +# +# -02 +XX -0351-03225 America/Noronha Fernando de Noronha; South Georgia +# +# -02/-01 (EU DST) +XX +6411-05144 America/Nuuk most of Greenland +# +# -01 +XX +1455-02331 Atlantic/Cape_Verde Cape Verde +# +# -01/+00 (EU DST) +XX +3744-02540 Atlantic/Azores Azores +# +# +00 - GMT +XX +0519-00402 Africa/Abidjan far western Africa; Iceland (GMT) +# +# +00/+01 - GMT/BST (EU DST) +XX +513030-0000731 Europe/London United Kingdom (GMT/BST) +# +# +00/+01 - WET/WEST (EU DST) +XX +3843-00908 Europe/Lisbon western Europe (WET/WEST) +# +# +00/+02 - Troll DST +XX -720041+0023206 Antarctica/Troll Troll Station in Antarctica +# +# +01 - CET +XX +3647+00303 Africa/Algiers Algeria, Tunisia (CET) +# +# +01 - WAT +XX +0627+00324 Africa/Lagos western Africa (WAT) +# +# +01/+00 - IST/GMT (EU DST in reverse) +XX +5320-00615 Europe/Dublin Ireland (IST/GMT) +# +# +01/+00 - (Morocco DST) +XX +3339-00735 Africa/Casablanca Morocco +# +# +01/+02 - CET/CEST (EU DST) +XX +4852+00220 Europe/Paris central Europe (CET/CEST) +# +# +02 - CAT +XX -2558+03235 Africa/Maputo central Africa (CAT) +# +# +02 - EET +XX +3254+01311 Africa/Tripoli Libya; Kaliningrad (EET) +# +# +02 - SAST +XX -2615+02800 Africa/Johannesburg southern Africa (SAST) +# +# +02/+03 - EET/EEST (EU DST) +XX +3758+02343 Europe/Athens eastern Europe (EET/EEST) +# +# +02/+03 - EET/EEST (Egypt DST) +XX +3003+03115 Africa/Cairo Egypt +# +# +02/+03 - EET/EEST (Lebanon DST) +XX +3353+03530 Asia/Beirut Lebanon +# +# +02/+03 - EET/EEST (Palestine DST) +XX +3130+03428 Asia/Gaza Palestine +# +# +02/+03 - IST/IDT (Israel DST) +XX +314650+0351326 Asia/Jerusalem Israel +# +# +03 +XX +4101+02858 Europe/Istanbul Near East; Belarus +# +# +03 - EAT +XX -0117+03649 Africa/Nairobi eastern Africa (EAT) +# +# +03 - MSK +XX +554521+0373704 Europe/Moscow Moscow (MSK) +# +# +03:30 +XX +3540+05126 Asia/Tehran Iran +# +# +04 +XX +2518+05518 Asia/Dubai Russia; Caucasus; Persian Gulf; Seychelles; Réunion +# +# +04:30 +XX +3431+06912 Asia/Kabul Afghanistan +# +# +05 +XX +4120+06918 Asia/Tashkent Russia; Kazakhstan; Tajikistan; Turkmenistan; Uzbekistan; Maldives +# +# +05 - PKT +XX +2452+06703 Asia/Karachi Pakistan (PKT) +# +# +05:30 +XX +0656+07951 Asia/Colombo Sri Lanka +# +# +05:30 - IST +XX +2232+08822 Asia/Kolkata India (IST) +# +# +05:45 +XX +2743+08519 Asia/Kathmandu Nepal +# +# +06 +XX +2343+09025 Asia/Dhaka Russia; Kyrgyzstan; Bhutan; Bangladesh; Chagos +# +# +06:30 +XX +1647+09610 Asia/Yangon Myanmar; Cocos +# +# +07 +XX +1345+10031 Asia/Bangkok Russia; Indochina; Christmas Island +# +# +07 - WIB +XX -0610+10648 Asia/Jakarta Indonesia (WIB) +# +# +08 +XX +0117+10351 Asia/Singapore Russia; Brunei; Malaysia; Singapore; Concordia +# +# +08 - AWST +XX -3157+11551 Australia/Perth Western Australia (AWST) +# +# +08 - CST +XX +3114+12128 Asia/Shanghai China (CST) +# +# +08 - HKT +XX +2217+11409 Asia/Hong_Kong Hong Kong (HKT) +# +# +08 - PHT +XX +143512+1205804 Asia/Manila Philippines (PHT) +# +# +08 - WITA +XX -0507+11924 Asia/Makassar Indonesia (WITA) +# +# +08:45 +XX -3143+12852 Australia/Eucla Eucla +# +# +09 +XX +5203+11328 Asia/Chita Russia; Palau; East Timor +# +# +09 - JST +XX +353916+1394441 Asia/Tokyo Japan (JST); Eyre Bird Observatory +# +# +09 - KST +XX +3733+12658 Asia/Seoul Korea (KST) +# +# +09 - WIT +XX -0232+14042 Asia/Jayapura Indonesia (WIT) +# +# +09:30 - ACST +XX -1228+13050 Australia/Darwin Northern Territory (ACST) +# +# +09:30/+10:30 - ACST/ACDT (Australia DST) +XX -3455+13835 Australia/Adelaide South Australia (ACST/ACDT) +# +# +10 +XX +4310+13156 Asia/Vladivostok Russia; Yap; Chuuk; Papua New Guinea; Dumont d’Urville +# +# +10 - AEST +XX -2728+15302 Australia/Brisbane Queensland (AEST) +# +# +10 - ChST +XX +1328+14445 Pacific/Guam Mariana Islands (ChST) +# +# +10/+11 - 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Production/Stable +Classifier: Intended Audience :: Developers +Classifier: License :: OSI Approved :: MIT License +Classifier: Operating System :: OS Independent +Classifier: Programming Language :: Cython +Classifier: Programming Language :: Python +Classifier: Programming Language :: Python :: 3 +Classifier: Programming Language :: Python :: 3.8 +Classifier: Programming Language :: Python :: 3.9 +Classifier: Programming Language :: Python :: 3.10 +Classifier: Programming Language :: Python :: 3.11 +Classifier: Programming Language :: Python :: 3.12 +Classifier: Programming Language :: Python :: 3.13 +Classifier: Programming Language :: Python :: 3.14 +Classifier: Programming Language :: Python :: Implementation :: CPython +Classifier: Programming Language :: Python :: Implementation :: PyPy +Classifier: Topic :: Software Development :: Libraries :: Python Modules +Classifier: Topic :: Text Processing :: Markup +Requires-Python: >=3.8 +License-File: LICENSE +Dynamic: author +Dynamic: author-email +Dynamic: classifier +Dynamic: description +Dynamic: download-url +Dynamic: home-page +Dynamic: license +Dynamic: license-file +Dynamic: platform +Dynamic: project-url +Dynamic: requires-python +Dynamic: summary + +YAML is a data serialization format designed for human readability +and interaction with scripting languages. PyYAML is a YAML parser +and emitter for Python. + +PyYAML features a complete YAML 1.1 parser, Unicode support, pickle +support, capable extension API, and sensible error messages. 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associated documentation files (the "Software"), to deal in +the Software without restriction, including without limitation the rights to +use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies +of the Software, and to permit persons to whom the Software is furnished to do +so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/.venv_haddock/lib/python3.12/site-packages/pyyaml-6.0.3.dist-info/top_level.txt b/.venv_haddock/lib/python3.12/site-packages/pyyaml-6.0.3.dist-info/top_level.txt new file mode 100644 index 0000000000000000000000000000000000000000..e6475e911f628412049bc4090d86f23ac403adde --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/pyyaml-6.0.3.dist-info/top_level.txt @@ -0,0 +1,2 @@ +_yaml +yaml diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/._.dylibs b/.venv_haddock/lib/python3.12/site-packages/scipy/._.dylibs new file mode 100644 index 0000000000000000000000000000000000000000..ee537d225f1b1eed0d0f4ed0b171fdc63ca71d82 Binary files /dev/null and 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DisplayModes(Enum): + stdout = "stdout" + dicts = "dicts" + + +def _cleanup(d): + """ + Removes empty values in a `dict` recursively + This ensures we remove values that Meson could not provide to CONFIG + """ + if isinstance(d, dict): + return { k: _cleanup(v) for k, v in d.items() if v != '' and _cleanup(v) != '' } + else: + return d + + +CONFIG = _cleanup( + { + "Compilers": { + "c": { + "name": "clang", + "linker": r"ld64", + "version": "15.0.0", + "commands": r"cc", + "args": r"", + "linker args": r"", + }, + "cython": { + "name": r"cython", + "linker": r"cython", + "version": r"3.2.4", + "commands": r"cython", + "args": r"", + "linker args": r"", + }, + "c++": { + "name": "clang", + "linker": r"ld64", + "version": "15.0.0", + "commands": r"c++", + "args": r"", + "linker args": r"", + }, + "fortran": { + "name": "gcc", + "linker": r"ld64", + "version": "13.4.0", + "commands": r"gfortran", + "args": r"", + "linker args": r"", + }, + "pythran": { + "version": r"0.18.1", + "include directory": r"../../../../../../private/var/folders/7x/mtlmm33x08j4_89tfb27m_x00000gn/T/build-env-wl6q4faf/lib/python3.12/site-packages/pythran" + }, + }, + "Machine Information": { + "host": { + "cpu": r"aarch64", + "family": r"aarch64", + "endian": r"little", + "system": r"darwin", + }, + "build": { + "cpu": r"aarch64", + "family": r"aarch64", + "endian": r"little", + "system": r"darwin", + }, + "cross-compiled": bool("False".lower().replace('false', '')), + }, + "Build Dependencies": { + "blas": { + "name": "Accelerate", + "found": bool("True".lower().replace('false', '')), + "version": "unknown", + "detection method": "extraframeworks", + "include directory": r"unknown", + "lib directory": r"unknown", + "openblas configuration": r"unknown", + "pc file directory": r"unknown", + "has ilp64": bool(r"False".lower().replace('false', '')), + }, + "lapack": { + "name": "Accelerate", + "found": bool("True".lower().replace('false', '')), + "version": "unknown", + "detection method": "extraframeworks", + "include directory": r"unknown", + "lib directory": r"unknown", + "openblas configuration": r"unknown", + "pc file directory": r"unknown", + "has ilp64": bool(r"False".lower().replace('false', '')), + }, + "pybind11": { + "name": "pybind11", + "version": "3.0.2", + "detection method": "config-tool", + "include directory": r"unknown", + }, + }, + "Python Information": { + "path": r"/private/var/folders/7x/mtlmm33x08j4_89tfb27m_x00000gn/T/build-env-wl6q4faf/bin/python", + "version": "3.12", + }, + } +) + + +def _check_pyyaml(): + import yaml + + return yaml + + +def show(mode=DisplayModes.stdout.value): + """ + Show libraries and system information on which SciPy was built + and is being used + + Parameters + ---------- + mode : {`'stdout'`, `'dicts'`}, optional. + Indicates how to display the config information. + `'stdout'` prints to console, `'dicts'` returns a dictionary + of the configuration. + + Returns + ------- + out : {`dict`, `None`} + If mode is `'dicts'`, a dict is returned, else None + + Examples + -------- + >>> import scipy + >>> scipy.show_config() + ... # formatted output is printed to the console + + >>> config_dict = scipy.show_config(mode='dicts') + >>> list(config_dict.keys()) + ['Compilers', 'Machine Information', 'Build Dependencies', 'Python Information'] + + Notes + ----- + 1. The `'stdout'` mode will give more readable + output if ``pyyaml`` is installed + + """ + if mode == DisplayModes.stdout.value: + try: # Non-standard library, check import + yaml = _check_pyyaml() + + print(yaml.dump(CONFIG)) + except ModuleNotFoundError: + import warnings + import json + + warnings.warn("Install `pyyaml` for better output", stacklevel=1) + print(json.dumps(CONFIG, indent=2)) + elif mode == DisplayModes.dicts.value: + return CONFIG + else: + raise AttributeError( + f"Invalid `mode`, use one of: {', '.join([e.value for e in DisplayModes])}" + ) diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..cbbe00ea4b7187aa9768a15ef2ef1dd7ef5a48c3 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/__init__.py @@ -0,0 +1,138 @@ +""" +SciPy: A scientific computing package for Python +================================================ + +Documentation is available in the docstrings and +online at https://docs.scipy.org/doc/scipy/ + +Subpackages +----------- +:: + + cluster --- Vector Quantization / Kmeans + constants --- Physical and mathematical constants and units + datasets --- Dataset methods + differentiate --- Finite difference differentiation tools + fft --- Discrete Fourier transforms + fftpack --- Legacy discrete Fourier transforms + integrate --- Integration routines + interpolate --- Interpolation Tools + io --- Data input and output + linalg --- Linear algebra routines + ndimage --- N-D image package + odr --- Orthogonal Distance Regression + optimize --- Optimization Tools + signal --- Signal Processing Tools + sparse --- Sparse Matrices + spatial --- Spatial data structures and algorithms + special --- Special functions + stats --- Statistical Functions + +Public API in the main SciPy namespace +-------------------------------------- +:: + + __version__ --- SciPy version string + LowLevelCallable --- Low-level callback function + show_config --- Show scipy build configuration + test --- Run scipy unittests + +""" + +import importlib as _importlib + +from numpy import __version__ as __numpy_version__ + + +try: + from scipy.__config__ import show as show_config +except ImportError as e: + msg = """Error importing SciPy: you cannot import SciPy while + being in scipy source directory; please exit the SciPy source + tree first and relaunch your Python interpreter.""" + raise ImportError(msg) from e + + +from scipy.version import version as __version__ + + +# Allow distributors to run custom init code +from . import _distributor_init +del _distributor_init + + +from scipy._lib import _pep440 +# In maintenance branch, change to np_maxversion N+3 if numpy is at N +np_minversion = '1.26.4' +np_maxversion = '2.7.0' +if (_pep440.parse(__numpy_version__) < _pep440.Version(np_minversion) or + _pep440.parse(__numpy_version__) >= _pep440.Version(np_maxversion)): + import warnings + warnings.warn(f"A NumPy version >={np_minversion} and <{np_maxversion}" + f" is required for this version of SciPy (detected " + f"version {__numpy_version__})", + UserWarning, stacklevel=2) +del _pep440 + + +# This is the first import of an extension module within SciPy. If there's +# a general issue with the install, such that extension modules are missing +# or cannot be imported, this is where we'll get a failure - so give an +# informative error message. +try: + from scipy._lib._ccallback import LowLevelCallable +except ImportError as e: + msg = "The `scipy` install you are using seems to be broken, " + \ + "(extension modules cannot be imported), " + \ + "please try reinstalling." + raise ImportError(msg) from e + + +from scipy._lib._testutils import PytestTester +test = PytestTester(__name__) +del PytestTester + + +submodules = [ + 'cluster', + 'constants', + 'datasets', + 'differentiate', + 'fft', + 'fftpack', + 'integrate', + 'interpolate', + 'io', + 'linalg', + 'ndimage', + 'odr', + 'optimize', + 'signal', + 'sparse', + 'spatial', + 'special', + 'stats' +] + +__all__ = submodules + [ + 'LowLevelCallable', + 'test', + 'show_config', + '__version__', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + if name in submodules: + return _importlib.import_module(f'scipy.{name}') + else: + try: + return globals()[name] + except KeyError: + raise AttributeError( + f"Module 'scipy' has no attribute '{name}'" + ) diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_cyutility.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/_cyutility.cpython-312-darwin.so new file mode 100644 index 0000000000000000000000000000000000000000..783ac03b7293a3463d2a041974cd7888d26be514 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_cyutility.cpython-312-darwin.so @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b9123c3e0c1516317fe646e8067694ed4d35f87ebc10044691a43f5bd1d7ce67 +size 169968 diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_distributor_init.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_distributor_init.py new file mode 100644 index 0000000000000000000000000000000000000000..5df134975aa27d31beaff74c3cbfd2d3fb0a55dd --- 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b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/._uarray.py new file mode 100644 index 0000000000000000000000000000000000000000..ee537d225f1b1eed0d0f4ed0b171fdc63ca71d82 Binary files /dev/null and b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/._uarray.py differ diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..2140970015d099763797d60a98a3a3b6f4b5f219 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/__init__.py @@ -0,0 +1,14 @@ +""" +Module containing private utility functions +=========================================== + +The ``scipy._lib`` namespace is empty (for now). Tests for all +utilities in submodules of ``_lib`` can be run with:: + + from scipy import _lib + _lib.test() + +""" +from scipy._lib._testutils import PytestTester +test = PytestTester(__name__) +del PytestTester diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api.py new file mode 100644 index 0000000000000000000000000000000000000000..127dae4dacb11099b127fc55ce3ae8cd9d67ddeb --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api.py @@ -0,0 +1,1036 @@ +"""Utility functions to use Python Array API compatible libraries. + +For the context about the Array API see: +https://data-apis.org/array-api/latest/purpose_and_scope.html + +The SciPy use case of the Array API is described on the following page: +https://data-apis.org/array-api/latest/use_cases.html#use-case-scipy +""" +import operator +import dataclasses +import functools +import textwrap + +from collections.abc import Generator +from contextlib import contextmanager +from contextvars import ContextVar +from types import ModuleType +from typing import Any, Literal, TypeAlias +from collections.abc import Iterable + +import numpy as np +import numpy.typing as npt + +from scipy._lib.array_api_compat import ( + is_array_api_obj, + is_lazy_array, + is_numpy_array, + is_cupy_array, + is_torch_array, + is_jax_array, + is_dask_array, + size as xp_size, + numpy as np_compat, + device as xp_device, + is_numpy_namespace as is_numpy, + is_cupy_namespace as is_cupy, + is_torch_namespace as is_torch, + is_jax_namespace as is_jax, + is_dask_namespace as is_dask, + is_array_api_strict_namespace as is_array_api_strict, +) +from scipy._lib.array_api_compat.common._helpers import _compat_module_name +from scipy._lib.array_api_extra.testing import lazy_xp_function +from scipy._lib._array_api_override import ( + array_namespace, SCIPY_ARRAY_API, SCIPY_DEVICE +) +from scipy._lib._docscrape import FunctionDoc +from scipy._lib import array_api_extra as xpx + + +__all__ = [ + '_asarray', 'array_namespace', 'assert_almost_equal', 'assert_array_almost_equal', + 'default_xp', 'eager_warns', 'is_lazy_array', 'is_marray', + 'is_array_api_strict', 'is_complex', 'is_cupy', 'is_jax', 'is_numpy', 'is_torch', + 'np_compat', 'get_native_namespace_name', + 'SCIPY_ARRAY_API', 'SCIPY_DEVICE', 'scipy_namespace_for', + 'xp_assert_close', 'xp_assert_equal', 'xp_assert_less', + 'xp_copy', 'xp_device', 'xp_ravel', 'xp_size', + 'xp_unsupported_param_msg', 'xp_vector_norm', 'xp_capabilities', + 'xp_result_type', 'xp_promote', + 'make_xp_test_case', 'make_xp_pytest_marks', 'make_xp_pytest_param', +] + + +Array: TypeAlias = Any # To be changed to a Protocol later (see array-api#589) +ArrayLike: TypeAlias = Array | npt.ArrayLike + + +def _check_finite(array: Array, xp: ModuleType) -> None: + """Check for NaNs or Infs.""" + if not xp.all(xp.isfinite(array)): + msg = "array must not contain infs or NaNs" + raise ValueError(msg) + +def _asarray( + array: ArrayLike, + dtype: Any = None, + order: Literal['K', 'A', 'C', 'F'] | None = None, + copy: bool | None = None, + *, + xp: ModuleType | None = None, + check_finite: bool = False, + subok: bool = False, + ) -> Array: + """SciPy-specific replacement for `np.asarray` with `order`, `check_finite`, and + `subok`. + + Memory layout parameter `order` is not exposed in the Array API standard. + `order` is only enforced if the input array implementation + is NumPy based, otherwise `order` is just silently ignored. + + `check_finite` is also not a keyword in the array API standard; included + here for convenience rather than that having to be a separate function + call inside SciPy functions. + + `subok` is included to allow this function to preserve the behaviour of + `np.asanyarray` for NumPy based inputs. + """ + if xp is None: + xp = array_namespace(array) + if is_numpy(xp): + # Use NumPy API to support order + if copy is True: + array = np.array(array, order=order, dtype=dtype, subok=subok) + elif subok: + array = np.asanyarray(array, order=order, dtype=dtype) + else: + array = np.asarray(array, order=order, dtype=dtype) + else: + try: + array = xp.asarray(array, dtype=dtype, copy=copy) + except TypeError: + coerced_xp = array_namespace(xp.asarray(3)) + array = coerced_xp.asarray(array, dtype=dtype, copy=copy) + + if check_finite: + _check_finite(array, xp) + + return array + + +def xp_copy(x: Array, *, xp: ModuleType | None = None) -> Array: + """ + Copies an array. + + Parameters + ---------- + x : array + + xp : array_namespace + + Returns + ------- + copy : array + Copied array + + Notes + ----- + This copy function does not offer all the semantics of `np.copy`, i.e. the + `subok` and `order` keywords are not used. + """ + # Note: for older NumPy versions, `np.asarray` did not support the `copy` kwarg, + # so this uses our other helper `_asarray`. + if xp is None: + xp = array_namespace(x) + + return _asarray(x, copy=True, xp=xp) + + +def _xp_copy_to_numpy(x: Array) -> np.ndarray: + """Copies a possibly on device array to a NumPy array. + + This function is intended only for converting alternative backend + arrays to numpy arrays within test code, to make it easier for use + of the alternative backend to be isolated only to the function being + tested. `_xp_copy_to_numpy` should NEVER be used except in test code + for the specific purpose mentioned above. In production code, attempts + to copy device arrays to NumPy arrays should fail, or else functions + may appear to be working on the GPU when they actually aren't. + + Parameters + ---------- + x : array + + Returns + ------- + ndarray + """ + xp = array_namespace(x) + if is_numpy(xp): + return x.copy() + if is_cupy(xp): + return x.get() + if is_torch(xp): + return x.cpu().numpy() + if is_array_api_strict(xp): + # array api strict supports multiple devices, so need to + # ensure x is on the cpu before copying to NumPy. + return np.asarray( + xp.asarray(x, device=xp.Device("CPU_DEVICE")), copy=True + ) + # Fall back to np.asarray. This works for dask.array. It + # currently works for jax.numpy, but hopefully JAX will make + # the transfer guard workable enough for use in scipy tests, in + # which case, JAX will have to be handled explicitly. + # If new backends are added, they may require explicit handling as + # well. + return np.asarray(x, copy=True) + + +_default_xp_ctxvar: ContextVar[ModuleType] = ContextVar("_default_xp") + +@contextmanager +def default_xp(xp: ModuleType) -> Generator[None, None, None]: + """In all ``xp_assert_*`` and ``assert_*`` function calls executed within this + context manager, test by default that the array namespace is + the provided across all arrays, unless one explicitly passes the ``xp=`` + parameter or ``check_namespace=False``. + + Without this context manager, the default value for `xp` is the namespace + for the desired array (the second parameter of the tests). + """ + token = _default_xp_ctxvar.set(xp) + try: + yield + finally: + _default_xp_ctxvar.reset(token) + + +def eager_warns(warning_type, *, match=None, xp): + """pytest.warns context manager if arrays of specified namespace are always eager. + + Otherwise, context manager that *ignores* specified warning. + """ + import pytest + from scipy._lib._util import ignore_warns + if is_numpy(xp) or is_array_api_strict(xp) or is_cupy(xp): + return pytest.warns(warning_type, match=match) + return ignore_warns(warning_type, match='' if match is None else match) + + +def _strict_check(actual, desired, xp, *, + check_namespace=True, check_dtype=True, check_shape=True, + check_0d=True): + __tracebackhide__ = True # Hide traceback for py.test + + if xp is None: + try: + xp = _default_xp_ctxvar.get() + except LookupError: + xp = array_namespace(desired) + + if check_namespace: + _assert_matching_namespace(actual, desired, xp) + + # only NumPy distinguishes between scalars and arrays; we do if check_0d=True. + # do this first so we can then cast to array (and thus use the array API) below. + if is_numpy(xp) and check_0d: + _msg = ("Array-ness does not match:\n Actual: " + f"{type(actual)}\n Desired: {type(desired)}") + assert ((xp.isscalar(actual) and xp.isscalar(desired)) + or (not xp.isscalar(actual) and not xp.isscalar(desired))), _msg + + actual = xp.asarray(actual) + desired = xp.asarray(desired) + + if check_dtype: + _msg = f"dtypes do not match.\nActual: {actual.dtype}\nDesired: {desired.dtype}" + assert actual.dtype == desired.dtype, _msg + + if check_shape: + if is_dask(xp): + actual.compute_chunk_sizes() + desired.compute_chunk_sizes() + _msg = f"Shapes do not match.\nActual: {actual.shape}\nDesired: {desired.shape}" + assert actual.shape == desired.shape, _msg + + desired = xp.broadcast_to(desired, actual.shape) + return actual, desired, xp + + +def _assert_matching_namespace(actual, desired, xp): + __tracebackhide__ = True # Hide traceback for py.test + + desired_arr_space = array_namespace(desired) + _msg = ("Namespace of desired array does not match expectations " + "set by the `default_xp` context manager or by the `xp`" + "pytest fixture.\n" + f"Desired array's space: {desired_arr_space.__name__}\n" + f"Expected namespace: {xp.__name__}") + assert desired_arr_space == xp, _msg + + actual_arr_space = array_namespace(actual) + _msg = ("Namespace of actual and desired arrays do not match.\n" + f"Actual: {actual_arr_space.__name__}\n" + f"Desired: {xp.__name__}") + assert actual_arr_space == xp, _msg + + +def xp_assert_equal(actual, desired, *, check_namespace=True, check_dtype=True, + check_shape=True, check_0d=True, err_msg='', xp=None): + __tracebackhide__ = True # Hide traceback for py.test + + actual, desired, xp = _strict_check( + actual, desired, xp, check_namespace=check_namespace, + check_dtype=check_dtype, check_shape=check_shape, + check_0d=check_0d + ) + + if is_cupy(xp): + return xp.testing.assert_array_equal(actual, desired, err_msg=err_msg) + elif is_torch(xp): + # PyTorch recommends using `rtol=0, atol=0` like this + # to test for exact equality + err_msg = None if err_msg == '' else err_msg + return xp.testing.assert_close(actual, desired, rtol=0, atol=0, equal_nan=True, + check_dtype=False, msg=err_msg) + # JAX uses `np.testing` + return np.testing.assert_array_equal(actual, desired, err_msg=err_msg) + + +def xp_assert_close(actual, desired, *, rtol=None, atol=0, check_namespace=True, + check_dtype=True, check_shape=True, check_0d=True, + err_msg='', xp=None): + __tracebackhide__ = True # Hide traceback for py.test + + actual, desired, xp = _strict_check( + actual, desired, xp, + check_namespace=check_namespace, check_dtype=check_dtype, + check_shape=check_shape, check_0d=check_0d + ) + + floating = xp.isdtype(actual.dtype, ('real floating', 'complex floating')) + if rtol is None and floating: + # multiplier of 4 is used as for `np.float64` this puts the default `rtol` + # roughly half way between sqrt(eps) and the default for + # `numpy.testing.assert_allclose`, 1e-7 + rtol = xp.finfo(actual.dtype).eps**0.5 * 4 + elif rtol is None: + rtol = 1e-7 + + if is_cupy(xp): + return xp.testing.assert_allclose(actual, desired, rtol=rtol, + atol=atol, err_msg=err_msg) + elif is_torch(xp): + err_msg = None if err_msg == '' else err_msg + return xp.testing.assert_close(actual, desired, rtol=rtol, atol=atol, + equal_nan=True, check_dtype=False, msg=err_msg) + # JAX uses `np.testing` + return np.testing.assert_allclose(actual, desired, rtol=rtol, + atol=atol, err_msg=err_msg) + + +def xp_assert_close_nulp(actual, desired, *, nulp=1, check_namespace=True, + check_dtype=True, check_shape=True, check_0d=True, + err_msg='', xp=None): + __tracebackhide__ = True # Hide traceback for py.test + + actual, desired, xp = _strict_check( + actual, desired, xp, + check_namespace=check_namespace, check_dtype=check_dtype, + check_shape=check_shape, check_0d=check_0d + ) + + actual, desired = map(_xp_copy_to_numpy, (actual, desired)) + return np.testing.assert_array_almost_equal_nulp(actual, desired, nulp=nulp) + + +def xp_assert_less(actual, desired, *, check_namespace=True, check_dtype=True, + check_shape=True, check_0d=True, err_msg='', verbose=True, xp=None): + __tracebackhide__ = True # Hide traceback for py.test + + actual, desired, xp = _strict_check( + actual, desired, xp, check_namespace=check_namespace, + check_dtype=check_dtype, check_shape=check_shape, + check_0d=check_0d + ) + + if is_cupy(xp): + return xp.testing.assert_array_less(actual, desired, + err_msg=err_msg, verbose=verbose) + elif is_torch(xp): + if actual.device.type != 'cpu': + actual = actual.cpu() + if desired.device.type != 'cpu': + desired = desired.cpu() + # JAX uses `np.testing` + return np.testing.assert_array_less(actual, desired, + err_msg=err_msg, verbose=verbose) + + +def assert_array_almost_equal(actual, desired, decimal=6, *args, **kwds): + """Backwards compatible replacement. In new code, use xp_assert_close instead. + """ + rtol, atol = 0, 1.5*10**(-decimal) + return xp_assert_close(actual, desired, + atol=atol, rtol=rtol, check_dtype=False, check_shape=False, + *args, **kwds) + + +def assert_almost_equal(actual, desired, decimal=7, *args, **kwds): + """Backwards compatible replacement. In new code, use xp_assert_close instead. + """ + rtol, atol = 0, 1.5*10**(-decimal) + return xp_assert_close(actual, desired, + atol=atol, rtol=rtol, check_dtype=False, check_shape=False, + *args, **kwds) + + +def xp_unsupported_param_msg(param: Any) -> str: + return f'Providing {param!r} is only supported for numpy arrays.' + + +def is_complex(x: Array, xp: ModuleType) -> bool: + return xp.isdtype(x.dtype, 'complex floating') + + +def get_native_namespace_name(xp: ModuleType) -> str: + """Return name for native namespace (without array_api_compat prefix).""" + name = xp.__name__ + return name.removeprefix(f"{_compat_module_name()}.") + + +def scipy_namespace_for(xp: ModuleType) -> ModuleType | None: + """Return the `scipy`-like namespace of a non-NumPy backend + + That is, return the namespace corresponding with backend `xp` that contains + `scipy` sub-namespaces like `linalg` and `special`. If no such namespace + exists, return ``None``. Useful for dispatching. + """ + + if is_cupy(xp): + import cupyx # type: ignore[import-not-found,import-untyped] + return cupyx.scipy + + if is_jax(xp): + import jax # type: ignore[import-not-found] + return jax.scipy + + if is_torch(xp): + return xp + + return None + + +# maybe use `scipy.linalg` if/when array API support is added +def xp_vector_norm(x: Array, /, *, + axis: int | tuple[int] | None = None, + keepdims: bool = False, + ord: int | float = 2, + xp: ModuleType | None = None) -> Array: + xp = array_namespace(x) if xp is None else xp + + if SCIPY_ARRAY_API: + # check for optional `linalg` extension + if hasattr(xp, 'linalg'): + return xp.linalg.vector_norm(x, axis=axis, keepdims=keepdims, ord=ord) + else: + if ord != 2: + raise ValueError( + "only the Euclidean norm (`ord=2`) is currently supported in " + "`xp_vector_norm` for backends not implementing the `linalg` " + "extension." + ) + # return (x @ x)**0.5 + # or to get the right behavior with nd, complex arrays + return xp.sum(xp.conj(x) * x, axis=axis, keepdims=keepdims)**0.5 + else: + # to maintain backwards compatibility + return np.linalg.norm(x, ord=ord, axis=axis, keepdims=keepdims) + + +def xp_ravel(x: Array, /, *, xp: ModuleType | None = None) -> Array: + # Equivalent of np.ravel written in terms of array API + # Even though it's one line, it comes up so often that it's worth having + # this function for readability + xp = array_namespace(x) if xp is None else xp + return xp.reshape(x, (-1,)) + + +def xp_swapaxes(a, axis1, axis2, xp=None): + # Equivalent of np.swapaxes written in terms of array API + xp = array_namespace(a) if xp is None else xp + axes = list(range(a.ndim)) + axes[axis1], axes[axis2] = axes[axis2], axes[axis1] + a = xp.permute_dims(a, axes) + return a + + +# utility to find common dtype with option to force floating +def xp_result_type(*args, force_floating=False, xp): + """ + Returns the dtype that results from applying type promotion rules + (see Array API Standard Type Promotion Rules) to the arguments. Augments + standard `result_type` in a few ways: + + - There is a `force_floating` argument that ensures that the result type + is floating point, even when all args are integer. + - When a TypeError is raised (e.g. due to an unsupported promotion) + and `force_floating=True`, we define a custom rule: use the result type + of the default float and any other floats passed. See + https://github.com/scipy/scipy/pull/22695/files#r1997905891 + for rationale. + - This function accepts array-like iterables, which are immediately converted + to the namespace's arrays before result type calculation. Consequently, the + result dtype may be different when an argument is `1.` vs `[1.]`. + + Typically, this function will be called shortly after `array_namespace` + on a subset of the arguments passed to `array_namespace`. + """ + # prevent double conversion of iterable to array + # avoid `np.iterable` for torch arrays due to pytorch/pytorch#143334 + # don't use `array_api_compat.is_array_api_obj` as it returns True for NumPy scalars + args = [(_asarray(arg, subok=True, xp=xp) if is_torch_array(arg) or np.iterable(arg) + else arg) for arg in args] + args_not_none = [arg for arg in args if arg is not None] + if force_floating: + args_not_none.append(1.0) + + if is_numpy(xp) and xp.__version__ < '2.0': + # Follow NEP 50 promotion rules anyway + args_not_none = [arg.dtype if getattr(arg, 'size', 0) == 1 else arg + for arg in args_not_none] + return xp.result_type(*args_not_none) + + try: # follow library's preferred promotion rules + return xp.result_type(*args_not_none) + except TypeError: # mixed type promotion isn't defined + if not force_floating: + raise + # use `result_type` of default floating point type and any floats present + # This can be revisited, but right now, the only backends that get here + # are array-api-strict (which is not for production use) and PyTorch + # (due to data-apis/array-api-compat#279). + float_args = [] + for arg in args_not_none: + arg_array = xp.asarray(arg) if np.isscalar(arg) else arg + dtype = getattr(arg_array, 'dtype', arg) + if xp.isdtype(dtype, ('real floating', 'complex floating')): + float_args.append(arg) + return xp.result_type(*float_args, xp_default_dtype(xp)) + + +def xp_promote(*args, broadcast=False, force_floating=False, xp): + """ + Promotes elements of *args to result dtype, ignoring `None`s. + Includes options for forcing promotion to floating point and + broadcasting the arrays, again ignoring `None`s. + Type promotion rules follow `xp_result_type` instead of `xp.result_type`. + + Typically, this function will be called shortly after `array_namespace` + on a subset of the arguments passed to `array_namespace`. + + This function accepts array-like iterables, which are immediately converted + to the namespace's arrays before result type calculation. Consequently, the + result dtype may be different when an argument is `1.` vs `[1.]`. + + See Also + -------- + xp_result_type + """ + if not args: + return args + + # prevent double conversion of iterable to array + # avoid `np.iterable` for torch arrays due to pytorch/pytorch#143334 + # don't use `array_api_compat.is_array_api_obj` as it returns True for NumPy scalars + args = [(_asarray(arg, subok=True, xp=xp) if is_torch_array(arg) or np.iterable(arg) + else arg) for arg in args] + + dtype = xp_result_type(*args, force_floating=force_floating, xp=xp) + + args = [(_asarray(arg, dtype=dtype, subok=True, xp=xp) if arg is not None else arg) + for arg in args] + + if not broadcast: + return args[0] if len(args)==1 else tuple(args) + + args_not_none = [arg for arg in args if arg is not None] + + # determine result shape + shapes = {arg.shape for arg in args_not_none} + try: + shape = (np.broadcast_shapes(*shapes) if len(shapes) != 1 + else args_not_none[0].shape) + except ValueError as e: + message = "Array shapes are incompatible for broadcasting." + raise ValueError(message) from e + + out = [] + for arg in args: + if arg is None: + out.append(arg) + continue + + # broadcast only if needed + # Even if two arguments need broadcasting, this is faster than + # `broadcast_arrays`, especially since we've already determined `shape` + if arg.shape != shape: + kwargs = {'subok': True} if is_numpy(xp) else {} + arg = xp.broadcast_to(arg, shape, **kwargs) + + # This is much faster than xp.astype(arg, dtype, copy=False) + if arg.dtype != dtype: + arg = xp.astype(arg, dtype) + + out.append(arg) + + return out[0] if len(out)==1 else tuple(out) + + +def xp_float_to_complex(arr: Array, xp: ModuleType | None = None) -> Array: + xp = array_namespace(arr) if xp is None else xp + arr_dtype = arr.dtype + # The standard float dtypes are float32 and float64. + # Convert float32 to complex64, + # and float64 (and non-standard real dtypes) to complex128 + if xp.isdtype(arr_dtype, xp.float32): + arr = xp.astype(arr, xp.complex64) + elif xp.isdtype(arr_dtype, 'real floating'): + arr = xp.astype(arr, xp.complex128) + + return arr + + +def xp_default_dtype(xp): + """Query the namespace-dependent default floating-point dtype. + """ + if is_torch(xp): + # historically, we allow pytorch to keep its default of float32 + return xp.get_default_dtype() + else: + # we default to float64 + return xp.float64 + + +### MArray Helpers ### +def xp_result_device(*args): + """Return the device of an array in `args`, for the purpose of + input-output device propagation. + If there are multiple devices, return an arbitrary one. + If there are no arrays, return None (this typically happens only on NumPy). + """ + for arg in args: + # Do not do a duck-type test for the .device attribute, as many backends today + # don't have it yet. See workarouunds in array_api_compat.device(). + if is_array_api_obj(arg): + return xp_device(arg) + return None + + +# np.r_ replacement +def concat_1d(xp: ModuleType | None, *arrays: Iterable[ArrayLike]) -> Array: + """A replacement for `np.r_` as `xp.concat` does not accept python scalars + or 0-D arrays. + """ + arys = [xpx.atleast_nd(xp.asarray(a), ndim=1, xp=xp) for a in arrays] + return xp.concat(arys) + + +def is_marray(xp): + """Returns True if `xp` is an MArray namespace; False otherwise.""" + return "marray" in xp.__name__ + + +def _length_nonmasked(x, axis, keepdims=False, xp=None): + xp = array_namespace(x) if xp is None else xp + if is_marray(xp): + if np.iterable(axis): + message = '`axis` must be an integer or None for use with `MArray`.' + raise NotImplementedError(message) + return xp.astype(xp.count(x, axis=axis, keepdims=keepdims), x.dtype) + return (xp_size(x) if axis is None else + # compact way to deal with axis tuples or ints + int(np.prod(np.asarray(x.shape)[np.asarray(axis)]))) + + +def _share_masks(*args, xp): + if is_marray(xp): + mask = functools.reduce(operator.or_, (arg.mask for arg in args)) + args = [xp.asarray(arg.data, mask=mask) for arg in args] + return args[0] if len(args) == 1 else args + +### End MArray Helpers ### + + +@dataclasses.dataclass(repr=False) +class _XPSphinxCapability: + cpu: bool | None # None if not applicable + gpu: bool | None + warnings: list[str] = dataclasses.field(default_factory=list) + + def _render(self, value): + if value is None: + return "n/a" + if not value: + return "⛔" + if self.warnings: + res = "⚠️ " + '; '.join(self.warnings) + assert len(res) <= 20, "Warnings too long" + return res + return "✅" + + def __str__(self): + cpu = self._render(self.cpu) + gpu = self._render(self.gpu) + return f"{cpu:20} {gpu:20}" + + +def _make_sphinx_capabilities( + # lists of tuples [(module name, reason), ...] + skip_backends=(), xfail_backends=(), + # @pytest.mark.skip/xfail_xp_backends kwargs + cpu_only=False, np_only=False, out_of_scope=False, exceptions=(), + # xpx.lazy_xp_backends kwargs + allow_dask_compute=False, jax_jit=True, + # list of tuples [(module name, reason), ...] + warnings = (), + # unused in documentation + reason=None, +): + if out_of_scope: + return {"out_of_scope": True} + + exceptions = set(exceptions) + + # Default capabilities + capabilities = { + "numpy": _XPSphinxCapability(cpu=True, gpu=None), + "array_api_strict": _XPSphinxCapability(cpu=True, gpu=None), + "cupy": _XPSphinxCapability(cpu=None, gpu=True), + "torch": _XPSphinxCapability(cpu=True, gpu=True), + "jax.numpy": _XPSphinxCapability(cpu=True, gpu=True, + warnings=[] if jax_jit else ["no JIT"]), + # Note: Dask+CuPy is currently untested and unsupported + "dask.array": _XPSphinxCapability(cpu=True, gpu=None, + warnings=["computes graph"] if allow_dask_compute else []), + } + + # documentation doesn't display the reason + for module, _ in list(skip_backends) + list(xfail_backends): + backend = capabilities[module] + if backend.cpu is not None: + backend.cpu = False + if backend.gpu is not None: + backend.gpu = False + + for module, backend in capabilities.items(): + if np_only and module not in exceptions | {"numpy"}: + if backend.cpu is not None: + backend.cpu = False + if backend.gpu is not None: + backend.gpu = False + elif cpu_only and module not in exceptions and backend.gpu is not None: + backend.gpu = False + + for module, warning in warnings: + backend = capabilities[module] + backend.warnings.append(warning) + + return capabilities + + +def _make_capabilities_note(fun_name, capabilities, extra_note=None): + if "out_of_scope" in capabilities: + # It will be better to link to a section of the dev-arrayapi docs + # that explains what is and isn't in-scope, but such a section + # doesn't exist yet. Using :ref:`dev-arrayapi` as a placeholder. + note = f""" + **Array API Standard Support** + + `{fun_name}` is not in-scope for support of Python Array API Standard compatible + backends other than NumPy. + + See :ref:`dev-arrayapi` for more information. + """ + return textwrap.dedent(note) + + # Note: deliberately not documenting array-api-strict + note = f""" + **Array API Standard Support** + + `{fun_name}` has experimental support for Python Array API Standard compatible + backends in addition to NumPy. Please consider testing these features + by setting an environment variable ``SCIPY_ARRAY_API=1`` and providing + CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following + combinations of backend and device (or other capability) are supported. + + ==================== ==================== ==================== + Library CPU GPU + ==================== ==================== ==================== + NumPy {capabilities['numpy'] } + CuPy {capabilities['cupy'] } + PyTorch {capabilities['torch'] } + JAX {capabilities['jax.numpy'] } + Dask {capabilities['dask.array'] } + ==================== ==================== ==================== + + """ + (extra_note or "") + " See :ref:`dev-arrayapi` for more information." + + return textwrap.dedent(note) + + +def xp_capabilities( + *, + # Alternative capabilities table. + # Used only for testing this decorator. + capabilities_table=None, + # Generate pytest.mark.skip/xfail_xp_backends. + # See documentation in conftest.py. + # lists of tuples [(module name, reason), ...] + skip_backends=(), xfail_backends=(), + cpu_only=False, np_only=False, reason=None, + out_of_scope=False, exceptions=(), + # lists of tuples [(module name, reason), ...] + warnings=(), + # xpx.testing.lazy_xp_function kwargs. + # Refer to array-api-extra documentation. + allow_dask_compute=False, jax_jit=True, + # Extra note to inject into the docstring + extra_note=None, +): + """Decorator for a function that states its support among various + Array API compatible backends. + + This decorator has two effects: + 1. It allows tagging tests with ``@make_xp_test_case`` or + ``make_xp_pytest_param`` (see below) to automatically generate + SKIP/XFAIL markers and perform additional backend-specific + testing, such as extra validation for Dask and JAX; + 2. It automatically adds a note to the function's docstring, containing + a table matching what has been tested. + + See Also + -------- + make_xp_test_case + make_xp_pytest_param + array_api_extra.testing.lazy_xp_function + """ + capabilities_table = (xp_capabilities_table if capabilities_table is None + else capabilities_table) + + if out_of_scope: + np_only = True + + capabilities = dict( + skip_backends=skip_backends, + xfail_backends=xfail_backends, + cpu_only=cpu_only, + np_only=np_only, + out_of_scope=out_of_scope, + reason=reason, + exceptions=exceptions, + allow_dask_compute=allow_dask_compute, + jax_jit=jax_jit, + warnings=warnings, + ) + sphinx_capabilities = _make_sphinx_capabilities(**capabilities) + + def decorator(f): + # Don't use a wrapper, as in some cases @xp_capabilities is + # applied to a ufunc + capabilities_table[f] = capabilities + note = _make_capabilities_note(f.__name__, sphinx_capabilities, extra_note) + doc = FunctionDoc(f) + doc['Notes'].append(note) + doc = str(doc).split("\n", 1)[1].lstrip(" \n") # remove signature + try: + f.__doc__ = doc + except AttributeError: + # Can't update __doc__ on ufuncs if SciPy + # was compiled against NumPy < 2.2. + pass + + return f + return decorator + + +def make_xp_test_case(*funcs, capabilities_table=None): + capabilities_table = (xp_capabilities_table if capabilities_table is None + else capabilities_table) + """Generate pytest decorator for a test function that tests functionality + of one or more Array API compatible functions. + + Read the parameters of the ``@xp_capabilities`` decorator applied to the + listed functions and: + + - Generate the ``@pytest.mark.skip_xp_backends`` and + ``@pytest.mark.xfail_xp_backends`` decorators + for the decorated test function + - Tag the function with `xpx.testing.lazy_xp_function` + + Example:: + + @make_xp_test_case(f1) + def test_f1(xp): + ... + + @make_xp_test_case(f2) + def test_f2(xp): + ... + + @make_xp_test_case(f1, f2) + def test_f1_and_f2(xp): + ... + + The above is equivalent to:: + @pytest.mark.skip_xp_backends(...) + @pytest.mark.skip_xp_backends(...) + @pytest.mark.xfail_xp_backends(...) + @pytest.mark.xfail_xp_backends(...) + def test_f1(xp): + ... + + etc., where the arguments of ``skip_xp_backends`` and ``xfail_xp_backends`` are + determined by the ``@xp_capabilities`` decorator applied to the functions. + + See Also + -------- + xp_capabilities + make_xp_pytest_marks + make_xp_pytest_param + array_api_extra.testing.lazy_xp_function + """ + marks = make_xp_pytest_marks(*funcs, capabilities_table=capabilities_table) + return lambda func: functools.reduce(lambda f, g: g(f), marks, func) + + +def make_xp_pytest_param(func, *args, capabilities_table=None): + """Variant of ``make_xp_test_case`` that returns a pytest.param for a function, + with all necessary skip_xp_backends and xfail_xp_backends marks applied:: + + @pytest.mark.parametrize( + "func", [make_xp_pytest_param(f1), make_xp_pytest_param(f2)] + ) + def test(func, xp): + ... + + The above is equivalent to:: + + @pytest.mark.parametrize( + "func", [ + pytest.param(f1, marks=[ + pytest.mark.skip_xp_backends(...), + pytest.mark.xfail_xp_backends(...), ...]), + pytest.param(f2, marks=[ + pytest.mark.skip_xp_backends(...), + pytest.mark.xfail_xp_backends(...), ...]), + ) + def test(func, xp): + ... + + Parameters + ---------- + func : Callable + Function to be tested. It must be decorated with ``@xp_capabilities``. + *args : Any, optional + Extra pytest parameters for the use case, e.g.:: + + @pytest.mark.parametrize("func,verb", [ + make_xp_pytest_param(f1, "hello"), + make_xp_pytest_param(f2, "world")]) + def test(func, verb, xp): + # iterates on (func=f1, verb="hello") + # and (func=f2, verb="world") + + See Also + -------- + xp_capabilities + make_xp_test_case + make_xp_pytest_marks + array_api_extra.testing.lazy_xp_function + """ + import pytest + + marks = make_xp_pytest_marks(func, capabilities_table=capabilities_table) + return pytest.param(func, *args, marks=marks, id=func.__name__) + + +def make_xp_pytest_marks(*funcs, capabilities_table=None): + """Variant of ``make_xp_test_case`` that returns a list of pytest marks, + which can be used with the module-level `pytestmark = ...` variable:: + + pytestmark = make_xp_pytest_marks(f1, f2) + + def test(xp): + ... + + In this example, the whole test module is dedicated to testing `f1` or `f2`, + and the two functions have the same capabilities, so it's unnecessary to + cherry-pick which test tests which function. + The above is equivalent to:: + + pytestmark = [ + pytest.mark.skip_xp_backends(...), + pytest.mark.xfail_xp_backends(...), ...]), + ] + + def test(xp): + ... + + See Also + -------- + xp_capabilities + make_xp_test_case + make_xp_pytest_param + array_api_extra.testing.lazy_xp_function + """ + capabilities_table = (xp_capabilities_table if capabilities_table is None + else capabilities_table) + import pytest + + marks = [] + for func in funcs: + capabilities = capabilities_table[func] + exceptions = capabilities['exceptions'] + reason = capabilities['reason'] + + if capabilities['cpu_only']: + marks.append(pytest.mark.skip_xp_backends( + cpu_only=True, exceptions=exceptions, reason=reason)) + if capabilities['np_only']: + marks.append(pytest.mark.skip_xp_backends( + np_only=True, exceptions=exceptions, reason=reason)) + + for mod_name, reason in capabilities['skip_backends']: + marks.append(pytest.mark.skip_xp_backends(mod_name, reason=reason)) + for mod_name, reason in capabilities['xfail_backends']: + marks.append(pytest.mark.xfail_xp_backends(mod_name, reason=reason)) + + lazy_kwargs = {k: capabilities[k] + for k in ('allow_dask_compute', 'jax_jit')} + lazy_xp_function(func, **lazy_kwargs) + + return marks + + +# Is it OK to have a dictionary that is mutated (once upon import) in many places? +xp_capabilities_table = {} # type: ignore[var-annotated] + + +def xp_device_type(a: Array) -> Literal["cpu", "cuda", None]: + if is_numpy_array(a): + return "cpu" + if is_cupy_array(a): + return "cuda" + if is_torch_array(a): + # TODO this can return other backends e.g. tpu but they're unsupported in scipy + return a.device.type + if is_jax_array(a): + # TODO this can return other backends e.g. tpu but they're unsupported in scipy + return "cuda" if (p := a.device.platform) == "gpu" else p + if is_dask_array(a): + return xp_device_type(a._meta) + # array-api-strict is a stand-in for unknown libraries; don't special-case it + return None diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_compat_vendor.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_compat_vendor.py new file mode 100644 index 0000000000000000000000000000000000000000..64d844ff46419252fd7b158700f0f4babc0f2258 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_compat_vendor.py @@ -0,0 +1,9 @@ +# DO NOT RENAME THIS FILE +# This is a hook for array_api_extra/src/array_api_extra/_lib/_compat.py +# to override functions of array_api_compat. + +from .array_api_compat import * # noqa: F403 +from ._array_api_override import array_namespace as scipy_array_namespace + +# overrides array_api_compat.array_namespace inside array-api-extra +array_namespace = scipy_array_namespace # type: ignore[assignment] diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_docs_tables.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_docs_tables.py new file mode 100644 index 0000000000000000000000000000000000000000..d3a14ee9257d58bbc558076493df5da253127d22 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_docs_tables.py @@ -0,0 +1,294 @@ +"""Generate flat tables showing Array API capabilities for use in docs. + +These tables are intended for presenting Array API capabilities across +a wide number of functions at once. Rows correspond to functions and +columns correspond to library/device/option combinations. +""" + +from collections import defaultdict +from enum import auto, Enum +from importlib import import_module +from types import ModuleType + +from scipy._lib._array_api import xp_capabilities_table +from scipy._lib._array_api import _make_sphinx_capabilities + +# For undocumented aliases of public functions which are kept around for +# backwards compatibility reasons. These should be excluded from the +# tables since they would be redundant. There are also no docs pages to +# link entries to. +ALIASES = { + "scipy.linalg": { + # Alias of scipy.linalg.solve_continuous_lyapunov + "solve_lyapunov", + }, + "scipy.ndimage": { + # Alias of scipy.ndimage.sum_labels + "sum", + }, + "scipy.special": { + # Alias of scipy.special.jv + "jn", + # Alias of scipy.special.roots_legendre + "p_roots", + # Alias of scipy.special.roots_chebyt + "t_roots", + # Alias of scipy.special.roots_chebyu + "u_roots", + # Alias of scipy.special.roots_chebyc + "c_roots", + # Alias of scipy.special.roots_chebys + "s_roots", + # Alias of scipy.special.roots_jacobi + "j_roots", + # Alias of scipy.special.roots_laguerre + "l_roots", + # Alias of scipy.special.roots_genlaguerre + "la_roots", + # Alias of scipy.special.roots_hermite + "h_roots", + # Alias of scipy.special.roots_hermitenorm + "he_roots", + # Alias of scipy.special.roots_gegenbauer + "cg_roots", + # Alias of scipy.special.roots_sh_legendre + "ps_roots", + # Alias of scipy.special.roots_sh_chebyt + "ts_roots", + # Alias of scipy.special.roots_chebyu + "us_roots", + # Alias of scipy.special.roots_sh_jacobi + "js_roots", + } +} + +# Shortened names for use in table. +BACKEND_NAMES_MAP = { + "jax.numpy": "jax", + "dask.array": "dask", +} + + +class BackendSupportStatus(Enum): + YES = auto() + NO = auto() + OUT_OF_SCOPE = auto() + UNKNOWN = auto() + + +def _process_capabilities_table_entry(entry: dict | None) -> dict[str, dict[str, bool]]: + """Returns dict showing alternative backend support in easy to consume form. + + Parameters + ---------- + entry : Optional[dict] + A dict with the structure of the values of the dict + scipy._lib._array_api.xp_capabilities_table. If None, it is + assumped that no alternative backends are supported. + Default: None. + + Returns + ------- + dict[str, dict[str, bool]] + The output dict currently has keys "cpu", "gpu", "jit" and "lazy". + The value associated to each key is itself a dict. The keys of + the inner dicts correspond to backends, with bool values stating + whether or not the backend is supported with a given device or + mode. Inapplicable backends do not appear in the inner dicts + (e.g. since cupy is gpu-only, it does not appear in the inner + dict keyed on "cpu"). Only alternative backends to NumPy are + included since NumPY support should be guaranteed. + + """ + # This is a template for the output format. If more backends and + # backend options are added, it will need to be updated manually. + # Entries start as boolean, but upon returning, will take values + # from the BackendSupportStatus Enum. + output = { + "cpu": {"torch": False, "jax": False, "dask": False}, + "gpu": {"cupy": False, "torch": False, "jax": False}, + "jit": {"jax": False}, + "lazy": {"dask": False}, + } + S = BackendSupportStatus + if entry is None: + # If there is no entry, assume no alternative backends are supported. + # If the list of supported backends will grows, this hard-coded dict + # will need to be updated. + return { + outer_key: {inner_key: S.UNKNOWN for inner_key in outer_value} + for outer_key, outer_value in output.items() + } + + if entry["out_of_scope"]: + # None is used to signify out-of-scope functions. + return { + outer_key: {inner_key: S.OUT_OF_SCOPE for inner_key in outer_value} + for outer_key, outer_value in output.items() + } + + # For now, use _make_sphinx_capabilities because that's where + # the relevant logic for determining what is and isn't + # supported based on xp_capabilities_table entries lives. + # Perhaps this logic should be decoupled from sphinx. + for backend, capabilities in _make_sphinx_capabilities(**entry).items(): + if backend in {"array_api_strict", "numpy"}: + continue + backend = BACKEND_NAMES_MAP.get(backend, backend) + cpu, gpu = capabilities.cpu, capabilities.gpu + if cpu is not None: + if backend not in output["cpu"]: + raise ValueError( + "Input capabilities table entry contains unhandled" + f" backend {backend} on cpu." + ) + output["cpu"][backend] = cpu + if gpu is not None: + if backend not in output["gpu"]: + raise ValueError( + "Input capabilities table entry contains unhandled" + f" backend {backend} on gpu." + ) + output["gpu"][backend] = gpu + if backend == "jax": + output["jit"]["jax"] = entry["jax_jit"] and output["cpu"]["jax"] + if backend == "dask.array": + support_lazy = not entry["allow_dask_compute"] and output["dask"] + output["lazy"]["dask"] = support_lazy + return { + outer_key: { + inner_key: S.YES if inner_value else S.NO + for inner_key, inner_value in outer_value.items() + } + for outer_key, outer_value in output.items() + } + + +def is_named_function_like_object(obj): + return ( + not isinstance(obj, ModuleType | type) + and callable(obj) and hasattr(obj, "__name__") + ) + + +def make_flat_capabilities_table( + modules: str | list[str], + backend_type: str, + /, + *, + capabilities_table: list[str] | None = None, +) -> list[dict[str, str]]: + """Generate full table of array api capabilities across public functions. + + Parameters + ---------- + modules : str | list[str] + A string containing single SciPy module, (e.g `scipy.stats`, `scipy.fft`) + or a list of such strings. + + backend_type : {'cpu', 'gpu', 'jit', 'lazy'} + + capabilities_table : Optional[list[str]] + Table in the form of `scipy._lib._array_api.xp_capabilities_table`. + If None, uses `scipy._lib._array_api.xp_capabilities_table`. + Default: None. + + Returns + ------- + output : list[dict[str, str]] + `output` is a table in dict format + (keys corresponding to column names). The first column is "module". + The other columns correspond to supported backends for the given + `backend_type`, e.g. jax.numpy, torch, and dask on cpu. + numpy is excluded because it should always be supported. + See the helper function + `_process_capabilities_table_entry` above). + + """ + if backend_type not in {"cpu", "gpu", "jit", "lazy"}: + raise ValueError(f"Received unhandled backend type {backend_type}") + + if isinstance(modules, str): + modules = [modules] + + if capabilities_table is None: + capabilities_table = xp_capabilities_table + + output = [] + + for module_name in modules: + module = import_module(module_name) + public_things = module.__all__ + for name in public_things: + if name in ALIASES.get(module_name, {}): + # Skip undocumented aliases that are kept + # for backwards compatibility reasons. + continue + thing = getattr(module, name) + if not is_named_function_like_object(thing): + continue + entry = xp_capabilities_table.get(thing, None) + capabilities = _process_capabilities_table_entry(entry)[backend_type] + row = {"module": module_name} + row.update({"function": name}) + row.update(capabilities) + output.append(row) + return output + + +def calculate_table_statistics( + flat_table: list[dict[str, str]] +) -> dict[str, tuple[dict[str, str], bool]]: + """Get counts of what is supported per module. + + Parameters + ---------- + flat_table : list[dict[str, str]] + A table as returned by `make_flat_capabilities_table` + + Returns + ------- + dict[str, tuple[dict[str, str], bool]] + dict mapping module names to 2-tuples containing an inner dict and a + bool. The inner dicts have a key "total" along with keys for each + backend column of the supplied flat capabilities table. The value + corresponding to total is the total count of functions in the given + module, and the value associated to the other keys is the count of + functions that support that particular backend. The bool is False if + the calculation may be innacurate due to missing xp_capabilities + decorators, and True if all functions for that particular module have + been decorated with xp_capabilities. + """ + if not flat_table: + return [] + + counter = defaultdict(lambda: defaultdict(int)) + + S = BackendSupportStatus + # Keep track of which modules have functions with missing xp_capabilities + # decorators so this information can be passed back to the caller. + missing_xp_capabilities = set() + for entry in flat_table: + entry = entry.copy() + entry.pop("function") + module = entry.pop("module") + current_counter = counter[module] + + # By design, all backends and options must be considered out-of-scope + # if one is, so just pick an arbitrary entry here to test if function is + # in-scope. + if next(iter(entry.values())) != S.OUT_OF_SCOPE: + current_counter["total"] += 1 + for key, value in entry.items(): + # Functions missing xp_capabilities will be tabulated as + # unsupported, but may actually be supported. There is a + # note about this in the documentation and this function is + # set up to return information needed to put asterisks next + # to percentages impacted by missing xp_capabilities decorators. + current_counter[key] += 1 if value == S.YES else 0 + if value == S.UNKNOWN: + missing_xp_capabilities.add(module) + return { + key: (dict(value), key not in missing_xp_capabilities) + for key, value in counter.items() + } diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_no_0d.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_no_0d.py new file mode 100644 index 0000000000000000000000000000000000000000..a6b6fe1affd172eea620760a20f185f192d37b69 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_no_0d.py @@ -0,0 +1,103 @@ +""" +Extra testing functions that forbid 0d-input, see #21044 + +While the xp_assert_* functions generally aim to follow the conventions of the +underlying `xp` library, NumPy in particular is inconsistent in its handling +of scalars vs. 0d-arrays, see https://github.com/numpy/numpy/issues/24897. + +For example, this means that the following operations (as of v2.0.1) currently +return scalars, even though a 0d-array would often be more appropriate: + + import numpy as np + np.array(0) * 2 # scalar, not 0d array + - np.array(0) # scalar, not 0d-array + np.sin(np.array(0)) # scalar, not 0d array + np.mean([1, 2, 3]) # scalar, not 0d array + +Libraries like CuPy tend to return a 0d-array in scenarios like those above, +and even `xp.asarray(0)[()]` remains a 0d-array there. To deal with the reality +of the inconsistencies present in NumPy, as well as 20+ years of code on top, +the `xp_assert_*` functions here enforce consistency in the only way that +doesn't go against the tide, i.e. by forbidding 0d-arrays as the return type. + +However, when scalars are not generally the expected NumPy return type, +it remains preferable to use the assert functions from +the `scipy._lib._array_api` module, which have less surprising behaviour. +""" +from scipy._lib._array_api import array_namespace, is_numpy +from scipy._lib._array_api import (xp_assert_close as xp_assert_close_base, + xp_assert_equal as xp_assert_equal_base, + xp_assert_less as xp_assert_less_base) + +__all__: list[str] = [] + + +def _check_scalar(actual, desired, *, xp=None, **kwargs): + __tracebackhide__ = True # Hide traceback for py.test + + if xp is None: + xp = array_namespace(actual) + + # necessary to handle non-numpy scalars, e.g. bare `0.0` has no shape + desired = xp.asarray(desired) + + # Only NumPy distinguishes between scalars and arrays; + # shape check in xp_assert_* is sufficient except for shape == () + if not (is_numpy(xp) and desired.shape == ()): + return + + _msg = ("Result is a NumPy 0d-array. Many SciPy functions intend to follow " + "the convention of many NumPy functions, returning a scalar when a " + "0d-array would be correct. The specialized `xp_assert_*` functions " + "in the `scipy._lib._array_api_no_0d` module err on the side of " + "caution and do not accept 0d-arrays by default. If the correct " + "result may legitimately be a 0d-array, pass `check_0d=True`, " + "or use the `xp_assert_*` functions from `scipy._lib._array_api`.") + assert xp.isscalar(actual), _msg + + +def xp_assert_equal(actual, desired, *, check_0d=False, **kwargs): + # in contrast to xp_assert_equal_base, this defaults to check_0d=False, + # but will do an extra check in that case, which forbids 0d-arrays for `actual` + __tracebackhide__ = True # Hide traceback for py.test + + # array-ness (check_0d == True) is taken care of by the *_base functions + if not check_0d: + _check_scalar(actual, desired, **kwargs) + return xp_assert_equal_base(actual, desired, check_0d=check_0d, **kwargs) + + +def xp_assert_close(actual, desired, *, check_0d=False, **kwargs): + # as for xp_assert_equal + __tracebackhide__ = True + + if not check_0d: + _check_scalar(actual, desired, **kwargs) + return xp_assert_close_base(actual, desired, check_0d=check_0d, **kwargs) + + +def xp_assert_less(actual, desired, *, check_0d=False, **kwargs): + # as for xp_assert_equal + __tracebackhide__ = True + + if not check_0d: + _check_scalar(actual, desired, **kwargs) + return xp_assert_less_base(actual, desired, check_0d=check_0d, **kwargs) + + +def assert_array_almost_equal(actual, desired, decimal=6, *args, **kwds): + """Backwards compatible replacement. In new code, use xp_assert_close instead. + """ + rtol, atol = 0, 1.5*10**(-decimal) + return xp_assert_close(actual, desired, + atol=atol, rtol=rtol, check_dtype=False, check_shape=False, + *args, **kwds) + + +def assert_almost_equal(actual, desired, decimal=7, *args, **kwds): + """Backwards compatible replacement. In new code, use xp_assert_close instead. + """ + rtol, atol = 0, 1.5*10**(-decimal) + return xp_assert_close(actual, desired, + atol=atol, rtol=rtol, check_dtype=False, check_shape=False, + *args, **kwds) diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_override.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_override.py new file mode 100644 index 0000000000000000000000000000000000000000..8c6965258b9b4bb35b5e5fe522b7bc1416c5ecb8 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_array_api_override.py @@ -0,0 +1,150 @@ +""" +Override functions from array_api_compat, for use by array-api-extra +and internally. + +See also _array_api_compat_vendor.py +""" +import enum +import os + +from functools import lru_cache +from types import ModuleType +from typing import Any, TypeAlias + +import numpy as np +import numpy.typing as npt + +from scipy._lib import array_api_compat +import scipy._lib.array_api_compat.numpy as np_compat +from scipy._lib.array_api_compat import is_array_api_obj, is_jax_array +from scipy._lib._sparse import SparseABC + + +Array: TypeAlias = Any # To be changed to a Protocol later (see array-api#589) +ArrayLike: TypeAlias = Array | npt.ArrayLike + +# To enable array API and strict array-like input validation +SCIPY_ARRAY_API: str | bool = os.environ.get("SCIPY_ARRAY_API", False) +# To control the default device - for use in the test suite only +SCIPY_DEVICE = os.environ.get("SCIPY_DEVICE", "cpu") + + +class _ArrayClsInfo(enum.Enum): + skip = 0 + numpy = 1 + array_like = 2 + unknown = 3 + + +@lru_cache(100) +def _validate_array_cls(cls: type) -> _ArrayClsInfo: + if issubclass(cls, (list, tuple)): + return _ArrayClsInfo.array_like + + # this comes from `_util._asarray_validated` + if issubclass(cls, SparseABC): + msg = ('Sparse arrays/matrices are not supported by this function. ' + 'Perhaps one of the `scipy.sparse.linalg` functions ' + 'would work instead.') + raise ValueError(msg) + + if issubclass(cls, np.ma.MaskedArray): + raise TypeError("Inputs of type `numpy.ma.MaskedArray` are not supported.") + + if issubclass(cls, np.matrix): + raise TypeError("Inputs of type `numpy.matrix` are not supported.") + + if issubclass(cls, (np.ndarray, np.generic)): + return _ArrayClsInfo.numpy + + # Note: this must happen after the test for np.generic, because + # np.float64 and np.complex128 are subclasses of float and complex respectively. + # This matches the behavior of array_api_compat. + if issubclass(cls, (int, float, complex, bool, type(None))): + return _ArrayClsInfo.skip + + return _ArrayClsInfo.unknown + + +def array_namespace(*arrays: Array) -> ModuleType: + """Get the array API compatible namespace for the arrays xs. + + Parameters + ---------- + *arrays : sequence of array_like + Arrays used to infer the common namespace. + + Returns + ------- + namespace : module + Common namespace. + + Notes + ----- + Wrapper around `array_api_compat.array_namespace`. + + 1. Check for the global switch `SCIPY_ARRAY_API`. If disabled, just + return array_api_compat.numpy namespace and skip all compliance checks. + + 2. Check for known-bad array classes. + The following subclasses are not supported and raise and error: + + - `numpy.ma.MaskedArray` + - `numpy.matrix` + - NumPy arrays which do not have a boolean or numerical dtype + - `scipy.sparse` arrays + + 3. Coerce array-likes to NumPy arrays and check their dtype. + Note that non-scalar array-likes can't be mixed with non-NumPy Array + API objects; e.g. + + - `array_namespace([1, 2])` returns NumPy namespace; + - `array_namespace(np.asarray([1, 2], [3, 4])` returns NumPy namespace; + - `array_namespace(cp.asarray([1, 2], [3, 4])` raises an error. + """ + if not SCIPY_ARRAY_API: + # here we could wrap the namespace if needed + return np_compat + + numpy_arrays = [] + api_arrays = [] + + for array in arrays: + arr_info = _validate_array_cls(type(array)) + if arr_info is _ArrayClsInfo.skip: + pass + + elif arr_info is _ArrayClsInfo.numpy: + if array.dtype.kind in 'iufcb': # Numeric or bool + numpy_arrays.append(array) + elif array.dtype.kind == 'V' and is_jax_array(array): + # Special case for JAX zero gradient arrays; + # see array_api_compat._common._helpers._is_jax_zero_gradient_array + api_arrays.append(array) # JAX zero gradient array + else: + raise TypeError(f"An argument has dtype `{array.dtype!r}`; " + "only boolean and numerical dtypes are supported.") + + elif arr_info is _ArrayClsInfo.unknown and is_array_api_obj(array): + api_arrays.append(array) + + else: + # list, tuple, or arbitrary object + try: + array = np.asanyarray(array) + except TypeError: + raise TypeError("An argument is neither array API compatible nor " + "coercible by NumPy.") + if array.dtype.kind not in 'iufcb': # Numeric or bool + raise TypeError(f"An argument has dtype `{array.dtype!r}`; " + "only boolean and numerical dtypes are supported.") + numpy_arrays.append(array) + + # When there are exclusively NumPy and ArrayLikes, skip calling + # array_api_compat.array_namespace for performance. + if not api_arrays: + return np_compat + + # In case of mix of NumPy/ArrayLike and non-NumPy Array API arrays, + # let array_api_compat.array_namespace raise an error. + return array_api_compat.array_namespace(*numpy_arrays, *api_arrays) diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_bunch.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_bunch.py new file mode 100644 index 0000000000000000000000000000000000000000..172e7dce1b25d0a70c1810e3d133f4b6bd12a538 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_bunch.py @@ -0,0 +1,229 @@ +import sys as _sys +from keyword import iskeyword as _iskeyword + + +def _validate_names(typename, field_names, extra_field_names): + """ + Ensure that all the given names are valid Python identifiers that + do not start with '_'. Also check that there are no duplicates + among field_names + extra_field_names. + """ + for name in [typename] + field_names + extra_field_names: + if not isinstance(name, str): + raise TypeError('typename and all field names must be strings') + if not name.isidentifier(): + raise ValueError('typename and all field names must be valid ' + f'identifiers: {name!r}') + if _iskeyword(name): + raise ValueError('typename and all field names cannot be a ' + f'keyword: {name!r}') + + seen = set() + for name in field_names + extra_field_names: + if name.startswith('_'): + raise ValueError('Field names cannot start with an underscore: ' + f'{name!r}') + if name in seen: + raise ValueError(f'Duplicate field name: {name!r}') + seen.add(name) + + +# Note: This code is adapted from CPython:Lib/collections/__init__.py +def _make_tuple_bunch(typename, field_names, extra_field_names=None, + module=None): + """ + Create a namedtuple-like class with additional attributes. + + This function creates a subclass of tuple that acts like a namedtuple + and that has additional attributes. + + The additional attributes are listed in `extra_field_names`. The + values assigned to these attributes are not part of the tuple. + + The reason this function exists is to allow functions in SciPy + that currently return a tuple or a namedtuple to returned objects + that have additional attributes, while maintaining backwards + compatibility. + + This should only be used to enhance *existing* functions in SciPy. + New functions are free to create objects as return values without + having to maintain backwards compatibility with an old tuple or + namedtuple return value. + + Parameters + ---------- + typename : str + The name of the type. + field_names : list of str + List of names of the values to be stored in the tuple. These names + will also be attributes of instances, so the values in the tuple + can be accessed by indexing or as attributes. At least one name + is required. See the Notes for additional restrictions. + extra_field_names : list of str, optional + List of names of values that will be stored as attributes of the + object. See the notes for additional restrictions. + + Returns + ------- + cls : type + The new class. + + Notes + ----- + There are restrictions on the names that may be used in `field_names` + and `extra_field_names`: + + * The names must be unique--no duplicates allowed. + * The names must be valid Python identifiers, and must not begin with + an underscore. + * The names must not be Python keywords (e.g. 'def', 'and', etc., are + not allowed). + + Examples + -------- + >>> from scipy._lib._bunch import _make_tuple_bunch + + Create a class that acts like a namedtuple with length 2 (with field + names `x` and `y`) that will also have the attributes `w` and `beta`: + + >>> Result = _make_tuple_bunch('Result', ['x', 'y'], ['w', 'beta']) + + `Result` is the new class. We call it with keyword arguments to create + a new instance with given values. + + >>> result1 = Result(x=1, y=2, w=99, beta=0.5) + >>> result1 + Result(x=1, y=2, w=99, beta=0.5) + + `result1` acts like a tuple of length 2: + + >>> len(result1) + 2 + >>> result1[:] + (1, 2) + + The values assigned when the instance was created are available as + attributes: + + >>> result1.y + 2 + >>> result1.beta + 0.5 + """ + if len(field_names) == 0: + raise ValueError('field_names must contain at least one name') + + if extra_field_names is None: + extra_field_names = [] + _validate_names(typename, field_names, extra_field_names) + + typename = _sys.intern(str(typename)) + field_names = tuple(map(_sys.intern, field_names)) + extra_field_names = tuple(map(_sys.intern, extra_field_names)) + + all_names = field_names + extra_field_names + arg_list = ', '.join(field_names) + full_list = ', '.join(all_names) + repr_fmt = ''.join(('(', + ', '.join(f'{name}=%({name})r' for name in all_names), + ')')) + tuple_new = tuple.__new__ + _dict, _tuple, _zip = dict, tuple, zip + + # Create all the named tuple methods to be added to the class namespace + + s = f"""\ +def __new__(_cls, {arg_list}, **extra_fields): + return _tuple_new(_cls, ({arg_list},)) + +def __init__(self, {arg_list}, **extra_fields): + for key in self._extra_fields: + if key not in extra_fields: + raise TypeError("missing keyword argument '%s'" % (key,)) + for key, val in extra_fields.items(): + if key not in self._extra_fields: + raise TypeError("unexpected keyword argument '%s'" % (key,)) + self.__dict__[key] = val + +def __setattr__(self, key, val): + if key in {repr(field_names)}: + raise AttributeError("can't set attribute %r of class %r" + % (key, self.__class__.__name__)) + else: + self.__dict__[key] = val +""" + del arg_list + namespace = {'_tuple_new': tuple_new, + '__builtins__': dict(TypeError=TypeError, + AttributeError=AttributeError), + '__name__': f'namedtuple_{typename}'} + exec(s, namespace) + __new__ = namespace['__new__'] + __new__.__doc__ = f'Create new instance of {typename}({full_list})' + __init__ = namespace['__init__'] + __init__.__doc__ = f'Instantiate instance of {typename}({full_list})' + __setattr__ = namespace['__setattr__'] + + def __repr__(self): + 'Return a nicely formatted representation string' + return self.__class__.__name__ + repr_fmt % self._asdict() + + def _asdict(self): + 'Return a new dict which maps field names to their values.' + out = _dict(_zip(self._fields, self)) + out.update(self.__dict__) + return out + + def __getnewargs_ex__(self): + 'Return self as a plain tuple. Used by copy and pickle.' + return _tuple(self), self.__dict__ + + # Modify function metadata to help with introspection and debugging + for method in (__new__, __repr__, _asdict, __getnewargs_ex__): + method.__qualname__ = f'{typename}.{method.__name__}' + + # Build-up the class namespace dictionary + # and use type() to build the result class + class_namespace = { + '__doc__': f'{typename}({full_list})', + '_fields': field_names, + '__new__': __new__, + '__init__': __init__, + '__repr__': __repr__, + '__setattr__': __setattr__, + '_asdict': _asdict, + '_extra_fields': extra_field_names, + '__getnewargs_ex__': __getnewargs_ex__, + # _field_defaults and _replace are added to get Polars to detect + # a bunch object as a namedtuple. See gh-22450 + '_field_defaults': {}, + '_replace': None, + } + for index, name in enumerate(field_names): + + def _get(self, index=index): + return self[index] + class_namespace[name] = property(_get) + for name in extra_field_names: + + def _get(self, name=name): + return self.__dict__[name] + class_namespace[name] = property(_get) + + result = type(typename, (tuple,), class_namespace) + + # For pickling to work, the __module__ variable needs to be set to the + # frame where the named tuple is created. Bypass this step in environments + # where sys._getframe is not defined (Jython for example) or sys._getframe + # is not defined for arguments greater than 0 (IronPython), or where the + # user has specified a particular module. + if module is None: + try: + module = _sys._getframe(1).f_globals.get('__name__', '__main__') + except (AttributeError, ValueError): + pass + if module is not None: + result.__module__ = module + __new__.__module__ = module + + return result diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_ccallback.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_ccallback.py new file mode 100644 index 0000000000000000000000000000000000000000..1980d06f5489e6633fb611c35bfb56903bd63e7f --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_ccallback.py @@ -0,0 +1,251 @@ +from . import _ccallback_c + +import ctypes + +PyCFuncPtr = ctypes.CFUNCTYPE(ctypes.c_void_p).__bases__[0] + +ffi = None + +class CData: + pass + +def _import_cffi(): + global ffi, CData + + if ffi is not None: + return + + try: + import cffi + ffi = cffi.FFI() + CData = ffi.CData + except ImportError: + ffi = False + + +class LowLevelCallable(tuple): + """ + Low-level callback function. + + Some functions in SciPy take as arguments callback functions, which + can either be python callables or low-level compiled functions. Using + compiled callback functions can improve performance somewhat by + avoiding wrapping data in Python objects. + + Such low-level functions in SciPy are wrapped in `LowLevelCallable` + objects, which can be constructed from function pointers obtained from + ctypes, cffi, Cython, or contained in Python `PyCapsule` objects. + + .. seealso:: + + Functions accepting low-level callables: + + `scipy.integrate.quad`, `scipy.ndimage.generic_filter`, + `scipy.ndimage.generic_filter1d`, `scipy.ndimage.geometric_transform` + + Usage examples: + + :ref:`ndimage-ccallbacks`, :ref:`quad-callbacks` + + Parameters + ---------- + function : {PyCapsule, ctypes function pointer, cffi function pointer} + Low-level callback function. + user_data : {PyCapsule, ctypes void pointer, cffi void pointer} + User data to pass on to the callback function. + signature : str, optional + Signature of the function. If omitted, determined from *function*, + if possible. + + Attributes + ---------- + function + Callback function given. + user_data + User data given. + signature + Signature of the function. + + Methods + ------- + from_cython + Class method for constructing callables from Cython C-exported + functions. + + Notes + ----- + The argument ``function`` can be one of: + + - PyCapsule, whose name contains the C function signature + - ctypes function pointer + - cffi function pointer + + The signature of the low-level callback must match one of those expected + by the routine it is passed to. + + If constructing low-level functions from a PyCapsule, the name of the + capsule must be the corresponding signature, in the format:: + + return_type (arg1_type, arg2_type, ...) + + For example:: + + "void (double)" + "double (double, int *, void *)" + + The context of a PyCapsule passed in as ``function`` is used as ``user_data``, + if an explicit value for ``user_data`` was not given. + + """ + + # Make the class immutable + __slots__ = () + + def __new__(cls, function, user_data=None, signature=None): + # We need to hold a reference to the function & user data, + # to prevent them going out of scope + item = cls._parse_callback(function, user_data, signature) + return tuple.__new__(cls, (item, function, user_data)) + + def __repr__(self): + return f"LowLevelCallable({self.function!r}, {self.user_data!r})" + + @property + def function(self): + return tuple.__getitem__(self, 1) + + @property + def user_data(self): + return tuple.__getitem__(self, 2) + + @property + def signature(self): + return _ccallback_c.get_capsule_signature(tuple.__getitem__(self, 0)) + + def __getitem__(self, idx): + raise ValueError() + + @classmethod + def from_cython(cls, module, name, user_data=None, signature=None): + """ + Create a low-level callback function from an exported Cython function. + + Parameters + ---------- + module : module + Cython module where the exported function resides + name : str + Name of the exported function + user_data : {PyCapsule, ctypes void pointer, cffi void pointer}, optional + User data to pass on to the callback function. + signature : str, optional + Signature of the function. If omitted, determined from *function*. + + """ + try: + function = module.__pyx_capi__[name] + except AttributeError as e: + message = "Given module is not a Cython module with __pyx_capi__ attribute" + raise ValueError(message) from e + except KeyError as e: + message = f"No function {name!r} found in __pyx_capi__ of the module" + raise ValueError(message) from e + return cls(function, user_data, signature) + + @classmethod + def _parse_callback(cls, obj, user_data=None, signature=None): + _import_cffi() + + if isinstance(obj, LowLevelCallable): + func = tuple.__getitem__(obj, 0) + elif isinstance(obj, PyCFuncPtr): + func, signature = _get_ctypes_func(obj, signature) + elif isinstance(obj, CData): + func, signature = _get_cffi_func(obj, signature) + elif _ccallback_c.check_capsule(obj): + func = obj + else: + raise ValueError("Given input is not a callable or a " + "low-level callable (pycapsule/ctypes/cffi)") + + if isinstance(user_data, ctypes.c_void_p): + context = _get_ctypes_data(user_data) + elif isinstance(user_data, CData): + context = _get_cffi_data(user_data) + elif user_data is None: + context = 0 + elif _ccallback_c.check_capsule(user_data): + context = user_data + else: + raise ValueError("Given user data is not a valid " + "low-level void* pointer (pycapsule/ctypes/cffi)") + + return _ccallback_c.get_raw_capsule(func, signature, context) + + +# +# ctypes helpers +# + +def _get_ctypes_func(func, signature=None): + # Get function pointer + func_ptr = ctypes.cast(func, ctypes.c_void_p).value + + # Construct function signature + if signature is None: + signature = _typename_from_ctypes(func.restype) + " (" + for j, arg in enumerate(func.argtypes): + if j == 0: + signature += _typename_from_ctypes(arg) + else: + signature += ", " + _typename_from_ctypes(arg) + signature += ")" + + return func_ptr, signature + + +def _typename_from_ctypes(item): + if item is None: + return "void" + elif item is ctypes.c_void_p: + return "void *" + + name = item.__name__ + + pointer_level = 0 + while name.startswith("LP_"): + pointer_level += 1 + name = name[3:] + + if name.startswith('c_'): + name = name[2:] + + if pointer_level > 0: + name += " " + "*"*pointer_level + + return name + + +def _get_ctypes_data(data): + # Get voidp pointer + return ctypes.cast(data, ctypes.c_void_p).value + + +# +# CFFI helpers +# + +def _get_cffi_func(func, signature=None): + # Get function pointer + func_ptr = ffi.cast('uintptr_t', func) + + # Get signature + if signature is None: + signature = ffi.getctype(ffi.typeof(func)).replace('(*)', ' ') + + return func_ptr, signature + + +def _get_cffi_data(data): + # Get pointer + return ffi.cast('uintptr_t', data) diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_ccallback_c.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_ccallback_c.cpython-312-darwin.so new file mode 100644 index 0000000000000000000000000000000000000000..1cee07f2f2960fa27fca708dbc0be9926c2c058e --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_ccallback_c.cpython-312-darwin.so @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c2a75e8b8e99ddc1ded49d67eba1b22b2fc2459da4fea343bbed4dab043943cc +size 114640 diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_disjoint_set.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_disjoint_set.py new file mode 100644 index 0000000000000000000000000000000000000000..683c5c8e518705e710212dafc01363f92a2f947d --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_disjoint_set.py @@ -0,0 +1,254 @@ +""" +Disjoint set data structure +""" + + +class DisjointSet: + """ Disjoint set data structure for incremental connectivity queries. + + .. versionadded:: 1.6.0 + + Attributes + ---------- + n_subsets : int + The number of subsets. + + Methods + ------- + add + merge + connected + subset + subset_size + subsets + __getitem__ + + Notes + ----- + This class implements the disjoint set [1]_, also known as the *union-find* + or *merge-find* data structure. The *find* operation (implemented in + `__getitem__`) implements the *path halving* variant. The *merge* method + implements the *merge by size* variant. + + References + ---------- + .. [1] https://en.wikipedia.org/wiki/Disjoint-set_data_structure + + Examples + -------- + >>> from scipy.cluster.hierarchy import DisjointSet + + Initialize a disjoint set: + + >>> disjoint_set = DisjointSet([1, 2, 3, 'a', 'b']) + + Merge some subsets: + + >>> disjoint_set.merge(1, 2) + True + >>> disjoint_set.merge(3, 'a') + True + >>> disjoint_set.merge('a', 'b') + True + >>> disjoint_set.merge('b', 'b') + False + + Find root elements: + + >>> disjoint_set[2] + 1 + >>> disjoint_set['b'] + 3 + + Test connectivity: + + >>> disjoint_set.connected(1, 2) + True + >>> disjoint_set.connected(1, 'b') + False + + List elements in disjoint set: + + >>> list(disjoint_set) + [1, 2, 3, 'a', 'b'] + + Get the subset containing 'a': + + >>> disjoint_set.subset('a') + {'a', 3, 'b'} + + Get the size of the subset containing 'a' (without actually instantiating + the subset): + + >>> disjoint_set.subset_size('a') + 3 + + Get all subsets in the disjoint set: + + >>> disjoint_set.subsets() + [{1, 2}, {'a', 3, 'b'}] + """ + def __init__(self, elements=None): + self.n_subsets = 0 + self._sizes = {} + self._parents = {} + # _nbrs is a circular linked list which links connected elements. + self._nbrs = {} + # _indices tracks the element insertion order in `__iter__`. + self._indices = {} + if elements is not None: + for x in elements: + self.add(x) + + def __iter__(self): + """Returns an iterator of the elements in the disjoint set. + + Elements are ordered by insertion order. + """ + return iter(self._indices) + + def __len__(self): + return len(self._indices) + + def __contains__(self, x): + return x in self._indices + + def __getitem__(self, x): + """Find the root element of `x`. + + Parameters + ---------- + x : hashable object + Input element. + + Returns + ------- + root : hashable object + Root element of `x`. + """ + if x not in self._indices: + raise KeyError(x) + + # find by "path halving" + parents = self._parents + while self._indices[x] != self._indices[parents[x]]: + parents[x] = parents[parents[x]] + x = parents[x] + return x + + def add(self, x): + """Add element `x` to disjoint set + """ + if x in self._indices: + return + + self._sizes[x] = 1 + self._parents[x] = x + self._nbrs[x] = x + self._indices[x] = len(self._indices) + self.n_subsets += 1 + + def merge(self, x, y): + """Merge the subsets of `x` and `y`. + + The smaller subset (the child) is merged into the larger subset (the + parent). If the subsets are of equal size, the root element which was + first inserted into the disjoint set is selected as the parent. + + Parameters + ---------- + x, y : hashable object + Elements to merge. + + Returns + ------- + merged : bool + True if `x` and `y` were in disjoint sets, False otherwise. + """ + xr = self[x] + yr = self[y] + if self._indices[xr] == self._indices[yr]: + return False + + sizes = self._sizes + if (sizes[xr], self._indices[yr]) < (sizes[yr], self._indices[xr]): + xr, yr = yr, xr + self._parents[yr] = xr + self._sizes[xr] += self._sizes[yr] + self._nbrs[xr], self._nbrs[yr] = self._nbrs[yr], self._nbrs[xr] + self.n_subsets -= 1 + return True + + def connected(self, x, y): + """Test whether `x` and `y` are in the same subset. + + Parameters + ---------- + x, y : hashable object + Elements to test. + + Returns + ------- + result : bool + True if `x` and `y` are in the same set, False otherwise. + """ + return self._indices[self[x]] == self._indices[self[y]] + + def subset(self, x): + """Get the subset containing `x`. + + Parameters + ---------- + x : hashable object + Input element. + + Returns + ------- + result : set + Subset containing `x`. + """ + if x not in self._indices: + raise KeyError(x) + + result = [x] + nxt = self._nbrs[x] + while self._indices[nxt] != self._indices[x]: + result.append(nxt) + nxt = self._nbrs[nxt] + return set(result) + + def subset_size(self, x): + """Get the size of the subset containing `x`. + + Note that this method is faster than ``len(self.subset(x))`` because + the size is directly read off an internal field, without the need to + instantiate the full subset. + + Parameters + ---------- + x : hashable object + Input element. + + Returns + ------- + result : int + Size of the subset containing `x`. + """ + return self._sizes[self[x]] + + def subsets(self): + """Get all the subsets in the disjoint set. + + Returns + ------- + result : list + Subsets in the disjoint set. + """ + result = [] + visited = set() + for x in self: + if x not in visited: + xset = self.subset(x) + visited.update(xset) + result.append(xset) + return result diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_docscrape.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_docscrape.py new file mode 100644 index 0000000000000000000000000000000000000000..c74d2c20001f102c86f88c7bfb1afe731de60668 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_docscrape.py @@ -0,0 +1,761 @@ +# copied from numpydoc/docscrape.py, commit 97a6026508e0dd5382865672e9563a72cc113bd2 +"""Extract reference documentation from the NumPy source tree.""" + +import copy +import inspect +import pydoc +import re +import sys +import textwrap +from collections import namedtuple +from collections.abc import Callable, Mapping +from functools import cached_property +from warnings import warn + + +def strip_blank_lines(l): + "Remove leading and trailing blank lines from a list of lines" + while l and not l[0].strip(): + del l[0] + while l and not l[-1].strip(): + del l[-1] + return l + + +class Reader: + """A line-based string reader.""" + + def __init__(self, data): + """ + Parameters + ---------- + data : str + String with lines separated by '\\n'. + + """ + if isinstance(data, list): + self._str = data + else: + self._str = data.split("\n") # store string as list of lines + + self.reset() + + def __getitem__(self, n): + return self._str[n] + + def reset(self): + self._l = 0 # current line nr + + def read(self): + if not self.eof(): + out = self[self._l] + self._l += 1 + return out + else: + return "" + + def seek_next_non_empty_line(self): + for l in self[self._l :]: + if l.strip(): + break + else: + self._l += 1 + + def eof(self): + return self._l >= len(self._str) + + def read_to_condition(self, condition_func): + start = self._l + for line in self[start:]: + if condition_func(line): + return self[start : self._l] + self._l += 1 + if self.eof(): + return self[start : self._l + 1] + return [] + + def read_to_next_empty_line(self): + self.seek_next_non_empty_line() + + def is_empty(line): + return not line.strip() + + return self.read_to_condition(is_empty) + + def read_to_next_unindented_line(self): + def is_unindented(line): + return line.strip() and (len(line.lstrip()) == len(line)) + + return self.read_to_condition(is_unindented) + + def peek(self, n=0): + if self._l + n < len(self._str): + return self[self._l + n] + else: + return "" + + def is_empty(self): + return not "".join(self._str).strip() + + +class ParseError(Exception): + def __str__(self): + message = self.args[0] + if hasattr(self, "docstring"): + message = f"{message} in {self.docstring!r}" + return message + + +Parameter = namedtuple("Parameter", ["name", "type", "desc"]) + + +class NumpyDocString(Mapping): + """Parses a numpydoc string to an abstract representation + + Instances define a mapping from section title to structured data. + + """ + + sections = { + "Signature": "", + "Summary": [""], + "Extended Summary": [], + "Parameters": [], + "Attributes": [], + "Methods": [], + "Returns": [], + "Yields": [], + "Receives": [], + "Other Parameters": [], + "Raises": [], + "Warns": [], + "Warnings": [], + "See Also": [], + "Notes": [], + "References": "", + "Examples": "", + "index": {}, + } + + def __init__(self, docstring, config=None): + orig_docstring = docstring + docstring = textwrap.dedent(docstring).split("\n") + + self._doc = Reader(docstring) + self._parsed_data = copy.deepcopy(self.sections) + + try: + self._parse() + except ParseError as e: + e.docstring = orig_docstring + raise + + def __getitem__(self, key): + return self._parsed_data[key] + + def __setitem__(self, key, val): + if key not in self._parsed_data: + self._error_location(f"Unknown section {key}", error=False) + else: + self._parsed_data[key] = val + + def __iter__(self): + return iter(self._parsed_data) + + def __len__(self): + return len(self._parsed_data) + + def _is_at_section(self): + self._doc.seek_next_non_empty_line() + + if self._doc.eof(): + return False + + l1 = self._doc.peek().strip() # e.g. Parameters + + if l1.startswith(".. index::"): + return True + + l2 = self._doc.peek(1).strip() # ---------- or ========== + if len(l2) >= 3 and (set(l2) in ({"-"}, {"="})) and len(l2) != len(l1): + snip = "\n".join(self._doc._str[:2]) + "..." + self._error_location( + f"potentially wrong underline length... \n{l1} \n{l2} in \n{snip}", + error=False, + ) + return l2.startswith("-" * len(l1)) or l2.startswith("=" * len(l1)) + + def _strip(self, doc): + i = 0 + j = 0 + for i, line in enumerate(doc): + if line.strip(): + break + + for j, line in enumerate(doc[::-1]): + if line.strip(): + break + + return doc[i : len(doc) - j] + + def _read_to_next_section(self): + section = self._doc.read_to_next_empty_line() + + while not self._is_at_section() and not self._doc.eof(): + if not self._doc.peek(-1).strip(): # previous line was empty + section += [""] + + section += self._doc.read_to_next_empty_line() + + return section + + def _read_sections(self): + while not self._doc.eof(): + data = self._read_to_next_section() + name = data[0].strip() + + if name.startswith(".."): # index section + yield name, data[1:] + elif len(data) < 2: + yield StopIteration + else: + yield name, self._strip(data[2:]) + + def _parse_param_list(self, content, single_element_is_type=False): + content = dedent_lines(content) + r = Reader(content) + params = [] + while not r.eof(): + header = r.read().strip() + if " : " in header: + arg_name, arg_type = header.split(" : ", maxsplit=1) + else: + # NOTE: param line with single element should never have a + # a " :" before the description line, so this should probably + # warn. + if header.endswith(" :"): + header = header[:-2] + if single_element_is_type: + arg_name, arg_type = "", header + else: + arg_name, arg_type = header, "" + + desc = r.read_to_next_unindented_line() + desc = dedent_lines(desc) + desc = strip_blank_lines(desc) + + params.append(Parameter(arg_name, arg_type, desc)) + + return params + + # See also supports the following formats. + # + # + # SPACE* COLON SPACE+ SPACE* + # ( COMMA SPACE+ )+ (COMMA | PERIOD)? SPACE* + # ( COMMA SPACE+ )* SPACE* COLON SPACE+ SPACE* + + # is one of + # + # COLON COLON BACKTICK BACKTICK + # where + # is a legal function name, and + # is any nonempty sequence of word characters. + # Examples: func_f1 :meth:`func_h1` :obj:`~baz.obj_r` :class:`class_j` + # is a string describing the function. + + _role = r":(?P(py:)?\w+):" + _funcbacktick = r"`(?P(?:~\w+\.)?[a-zA-Z0-9_\.-]+)`" + _funcplain = r"(?P[a-zA-Z0-9_\.-]+)" + _funcname = r"(" + _role + _funcbacktick + r"|" + _funcplain + r")" + _funcnamenext = _funcname.replace("role", "rolenext") + _funcnamenext = _funcnamenext.replace("name", "namenext") + _description = r"(?P\s*:(\s+(?P\S+.*))?)?\s*$" + _func_rgx = re.compile(r"^\s*" + _funcname + r"\s*") + _line_rgx = re.compile( + r"^\s*" + + r"(?P" + + _funcname # group for all function names + + r"(?P([,]\s+" + + _funcnamenext + + r")*)" + + r")" + + r"(?P[,\.])?" # end of "allfuncs" + + _description # Some function lists have a trailing comma (or period) '\s*' + ) + + # Empty elements are replaced with '..' + empty_description = ".." + + def _parse_see_also(self, content): + """ + func_name : Descriptive text + continued text + another_func_name : Descriptive text + func_name1, func_name2, :meth:`func_name`, func_name3 + + """ + + content = dedent_lines(content) + + items = [] + + def parse_item_name(text): + """Match ':role:`name`' or 'name'.""" + m = self._func_rgx.match(text) + if not m: + self._error_location(f"Error parsing See Also entry {line!r}") + role = m.group("role") + name = m.group("name") if role else m.group("name2") + return name, role, m.end() + + rest = [] + for line in content: + if not line.strip(): + continue + + line_match = self._line_rgx.match(line) + description = None + if line_match: + description = line_match.group("desc") + if line_match.group("trailing") and description: + self._error_location( + "Unexpected comma or period after function list at index %d of " + 'line "%s"' % (line_match.end("trailing"), line), + error=False, + ) + if not description and line.startswith(" "): + rest.append(line.strip()) + elif line_match: + funcs = [] + text = line_match.group("allfuncs") + while True: + if not text.strip(): + break + name, role, match_end = parse_item_name(text) + funcs.append((name, role)) + text = text[match_end:].strip() + if text and text[0] == ",": + text = text[1:].strip() + rest = list(filter(None, [description])) + items.append((funcs, rest)) + else: + self._error_location(f"Error parsing See Also entry {line!r}") + return items + + def _parse_index(self, section, content): + """ + .. index:: default + :refguide: something, else, and more + + """ + + def strip_each_in(lst): + return [s.strip() for s in lst] + + out = {} + section = section.split("::") + if len(section) > 1: + out["default"] = strip_each_in(section[1].split(","))[0] + for line in content: + line = line.split(":") + if len(line) > 2: + out[line[1]] = strip_each_in(line[2].split(",")) + return out + + def _parse_summary(self): + """Grab signature (if given) and summary""" + if self._is_at_section(): + return + + # If several signatures present, take the last one + while True: + summary = self._doc.read_to_next_empty_line() + summary_str = " ".join([s.strip() for s in summary]).strip() + compiled = re.compile(r"^([\w., ]+=)?\s*[\w\.]+\(.*\)$") + if compiled.match(summary_str): + self["Signature"] = summary_str + if not self._is_at_section(): + continue + break + + if summary is not None: + self["Summary"] = summary + + if not self._is_at_section(): + self["Extended Summary"] = self._read_to_next_section() + + def _parse(self): + self._doc.reset() + self._parse_summary() + + sections = list(self._read_sections()) + section_names = {section for section, content in sections} + + has_yields = "Yields" in section_names + # We could do more tests, but we are not. Arbitrarily. + if not has_yields and "Receives" in section_names: + msg = "Docstring contains a Receives section but not Yields." + raise ValueError(msg) + + for section, content in sections: + if not section.startswith(".."): + section = (s.capitalize() for s in section.split(" ")) + section = " ".join(section) + if self.get(section): + self._error_location( + "The section %s appears twice in %s" + % (section, "\n".join(self._doc._str)) + ) + + if section in ("Parameters", "Other Parameters", "Attributes", "Methods"): + self[section] = self._parse_param_list(content) + elif section in ("Returns", "Yields", "Raises", "Warns", "Receives"): + self[section] = self._parse_param_list( + content, single_element_is_type=True + ) + elif section.startswith(".. index::"): + self["index"] = self._parse_index(section, content) + elif section == "See Also": + self["See Also"] = self._parse_see_also(content) + else: + self[section] = content + + @property + def _obj(self): + if hasattr(self, "_cls"): + return self._cls + elif hasattr(self, "_f"): + return self._f + return None + + def _error_location(self, msg, error=True): + if self._obj is not None: + # we know where the docs came from: + try: + filename = inspect.getsourcefile(self._obj) + except TypeError: + filename = None + # Make UserWarning more descriptive via object introspection. + # Skip if introspection fails + name = getattr(self._obj, "__name__", None) + if name is None: + name = getattr(getattr(self._obj, "__class__", None), "__name__", None) + if name is not None: + msg += f" in the docstring of {name}" + msg += f" in {filename}." if filename else "" + if error: + raise ValueError(msg) + else: + warn(msg, stacklevel=3) + + # string conversion routines + + def _str_header(self, name, symbol="-"): + return [name, len(name) * symbol] + + def _str_indent(self, doc, indent=4): + return [" " * indent + line for line in doc] + + def _str_signature(self): + if self["Signature"]: + return [self["Signature"].replace("*", r"\*")] + [""] + return [""] + + def _str_summary(self): + if self["Summary"]: + return self["Summary"] + [""] + return [] + + def _str_extended_summary(self): + if self["Extended Summary"]: + return self["Extended Summary"] + [""] + return [] + + def _str_param_list(self, name): + out = [] + if self[name]: + out += self._str_header(name) + for param in self[name]: + parts = [] + if param.name: + parts.append(param.name) + if param.type: + parts.append(param.type) + out += [" : ".join(parts)] + if param.desc and "".join(param.desc).strip(): + out += self._str_indent(param.desc) + out += [""] + return out + + def _str_section(self, name): + out = [] + if self[name]: + out += self._str_header(name) + out += self[name] + out += [""] + return out + + def _str_see_also(self, func_role): + if not self["See Also"]: + return [] + out = [] + out += self._str_header("See Also") + out += [""] + last_had_desc = True + for funcs, desc in self["See Also"]: + assert isinstance(funcs, list) + links = [] + for func, role in funcs: + if role: + link = f":{role}:`{func}`" + elif func_role: + link = f":{func_role}:`{func}`" + else: + link = f"`{func}`_" + links.append(link) + link = ", ".join(links) + out += [link] + if desc: + out += self._str_indent([" ".join(desc)]) + last_had_desc = True + else: + last_had_desc = False + out += self._str_indent([self.empty_description]) + + if last_had_desc: + out += [""] + out += [""] + return out + + def _str_index(self): + idx = self["index"] + out = [] + output_index = False + default_index = idx.get("default", "") + if default_index: + output_index = True + out += [f".. index:: {default_index}"] + for section, references in idx.items(): + if section == "default": + continue + output_index = True + out += [f" :{section}: {', '.join(references)}"] + if output_index: + return out + return "" + + def __str__(self, func_role=""): + out = [] + out += self._str_signature() + out += self._str_summary() + out += self._str_extended_summary() + out += self._str_param_list("Parameters") + for param_list in ("Attributes", "Methods"): + out += self._str_param_list(param_list) + for param_list in ( + "Returns", + "Yields", + "Receives", + "Other Parameters", + "Raises", + "Warns", + ): + out += self._str_param_list(param_list) + out += self._str_section("Warnings") + out += self._str_see_also(func_role) + for s in ("Notes", "References", "Examples"): + out += self._str_section(s) + out += self._str_index() + return "\n".join(out) + + +def dedent_lines(lines): + """Deindent a list of lines maximally""" + return textwrap.dedent("\n".join(lines)).split("\n") + + +class FunctionDoc(NumpyDocString): + def __init__(self, func, role="func", doc=None, config=None): + self._f = func + self._role = role # e.g. "func" or "meth" + + if doc is None: + if func is None: + raise ValueError("No function or docstring given") + doc = inspect.getdoc(func) or "" + if config is None: + config = {} + NumpyDocString.__init__(self, doc, config) + + def get_func(self): + func_name = getattr(self._f, "__name__", self.__class__.__name__) + if inspect.isclass(self._f): + func = getattr(self._f, "__call__", self._f.__init__) + else: + func = self._f + return func, func_name + + def __str__(self): + out = "" + + func, func_name = self.get_func() + + roles = {"func": "function", "meth": "method"} + + if self._role: + if self._role not in roles: + print(f"Warning: invalid role {self._role}") + out += f".. {roles.get(self._role, '')}:: {func_name}\n \n\n" + + out += super().__str__(func_role=self._role) + return out + + +class ObjDoc(NumpyDocString): + def __init__(self, obj, doc=None, config=None): + self._f = obj + if config is None: + config = {} + NumpyDocString.__init__(self, doc, config=config) + + +class ClassDoc(NumpyDocString): + extra_public_methods = ["__call__"] + + def __init__(self, cls, doc=None, modulename="", func_doc=FunctionDoc, config=None): + if not inspect.isclass(cls) and cls is not None: + raise ValueError(f"Expected a class or None, but got {cls!r}") + self._cls = cls + + if "sphinx" in sys.modules: + from sphinx.ext.autodoc import ALL + else: + ALL = object() + + if config is None: + config = {} + self.show_inherited_members = config.get("show_inherited_class_members", True) + + if modulename and not modulename.endswith("."): + modulename += "." + self._mod = modulename + + if doc is None: + if cls is None: + raise ValueError("No class or documentation string given") + doc = pydoc.getdoc(cls) + + NumpyDocString.__init__(self, doc) + + _members = config.get("members", []) + if _members is ALL: + _members = None + _exclude = config.get("exclude-members", []) + + if config.get("show_class_members", True) and _exclude is not ALL: + + def splitlines_x(s): + if not s: + return [] + else: + return s.splitlines() + + for field, items in [ + ("Methods", self.methods), + ("Attributes", self.properties), + ]: + if not self[field]: + doc_list = [] + for name in sorted(items): + if name in _exclude or (_members and name not in _members): + continue + try: + doc_item = pydoc.getdoc(getattr(self._cls, name)) + doc_list.append(Parameter(name, "", splitlines_x(doc_item))) + except AttributeError: + pass # method doesn't exist + self[field] = doc_list + + @property + def methods(self): + if self._cls is None: + return [] + return [ + name + for name, func in inspect.getmembers(self._cls) + if ( + (not name.startswith("_") or name in self.extra_public_methods) + and isinstance(func, Callable) + and self._is_show_member(name) + ) + ] + + @property + def properties(self): + if self._cls is None: + return [] + return [ + name + for name, func in inspect.getmembers(self._cls) + if ( + not name.startswith("_") + and not self._should_skip_member(name, self._cls) + and ( + func is None + or isinstance(func, property | cached_property) + or inspect.isdatadescriptor(func) + ) + and self._is_show_member(name) + ) + ] + + @staticmethod + def _should_skip_member(name, klass): + return ( + # Namedtuples should skip everything in their ._fields as the + # docstrings for each of the members is: "Alias for field number X" + issubclass(klass, tuple) + and hasattr(klass, "_asdict") + and hasattr(klass, "_fields") + and name in klass._fields + ) + + def _is_show_member(self, name): + return ( + # show all class members + self.show_inherited_members + # or class member is not inherited + or name in self._cls.__dict__ + ) + + +def get_doc_object( + obj, + what=None, + doc=None, + config=None, + class_doc=ClassDoc, + func_doc=FunctionDoc, + obj_doc=ObjDoc, +): + if what is None: + if inspect.isclass(obj): + what = "class" + elif inspect.ismodule(obj): + what = "module" + elif isinstance(obj, Callable): + what = "function" + else: + what = "object" + if config is None: + config = {} + + if what == "class": + return class_doc(obj, func_doc=func_doc, doc=doc, config=config) + elif what in ("function", "method"): + return func_doc(obj, doc=doc, config=config) + else: + if doc is None: + doc = pydoc.getdoc(obj) + return obj_doc(obj, doc, config=config) \ No newline at end of file diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_elementwise_iterative_method.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_elementwise_iterative_method.py new file mode 100644 index 0000000000000000000000000000000000000000..14c5c1949ddf407e1aecce0a51a1a834647ac523 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_elementwise_iterative_method.py @@ -0,0 +1,346 @@ +# `_elementwise_iterative_method.py` includes tools for writing functions that +# - are vectorized to work elementwise on arrays, +# - implement non-trivial, iterative algorithms with a callback interface, and +# - return rich objects with iteration count, termination status, etc. +# +# Examples include: +# `scipy.optimize._chandrupatla._chandrupatla for scalar rootfinding, +# `scipy.optimize._chandrupatla._chandrupatla_minimize for scalar minimization, +# `scipy.optimize._differentiate._differentiate for numerical differentiation, +# `scipy.optimize._bracket._bracket_root for finding rootfinding brackets, +# `scipy.optimize._bracket._bracket_minimize for finding minimization brackets, +# `scipy.integrate._tanhsinh._tanhsinh` for numerical quadrature, +# `scipy.differentiate.derivative` for finite difference based differentiation. + +import math +import numpy as np +from ._util import _RichResult, _call_callback_maybe_halt +from ._array_api import array_namespace, xp_size, xp_result_type +import scipy._lib.array_api_extra as xpx + +_ESIGNERR = -1 +_ECONVERR = -2 +_EVALUEERR = -3 +_ECALLBACK = -4 +_EINPUTERR = -5 +_ECONVERGED = 0 +_EINPROGRESS = 1 + +def _initialize(func, xs, args, complex_ok=False, preserve_shape=None, xp=None): + """Initialize abscissa, function, and args arrays for elementwise function + + Parameters + ---------- + func : callable + An elementwise function with signature + + func(x: ndarray, *args) -> ndarray + + where each element of ``x`` is a finite real and ``args`` is a tuple, + which may contain an arbitrary number of arrays that are broadcastable + with ``x``. + xs : tuple of arrays + Finite real abscissa arrays. Must be broadcastable. + args : tuple, optional + Additional positional arguments to be passed to `func`. + preserve_shape : bool, default:False + When ``preserve_shape=False`` (default), `func` may be passed + arguments of any shape; `_scalar_optimization_loop` is permitted + to reshape and compress arguments at will. When + ``preserve_shape=False``, arguments passed to `func` must have shape + `shape` or ``shape + (n,)``, where ``n`` is any integer. + xp : namespace + Namespace of array arguments in `xs`. + + Returns + ------- + xs, fs, args : tuple of arrays + Broadcasted, writeable, 1D abscissa and function value arrays (or + NumPy floats, if appropriate). The dtypes of the `xs` and `fs` are + `xfat`; the dtype of the `args` are unchanged. + shape : tuple of ints + Original shape of broadcasted arrays. + xfat : NumPy dtype + Result dtype of abscissae, function values, and args determined using + `np.result_type`, except integer types are promoted to `np.float64`. + + Raises + ------ + ValueError + If the result dtype is not that of a real scalar + + Notes + ----- + Useful for initializing the input of SciPy functions that accept + an elementwise callable, abscissae, and arguments; e.g. + `scipy.optimize._chandrupatla`. + """ + nx = len(xs) + xp = array_namespace(*xs) if xp is None else xp + + # Try to preserve `dtype`, but we need to ensure that the arguments are at + # least floats before passing them into the function; integers can overflow + # and cause failure. + # There might be benefit to combining the `xs` into a single array and + # calling `func` once on the combined array. For now, keep them separate. + xat = xp_result_type(*xs, force_floating=True, xp=xp) + xas = xp.broadcast_arrays(*xs, *args) # broadcast and rename + xs, args = xas[:nx], xas[nx:] + xs = [xp.asarray(x, dtype=xat) for x in xs] # use copy=False when implemented + fs = [xp.asarray(func(x, *args)) for x in xs] + shape = xs[0].shape + fshape = fs[0].shape + + if preserve_shape: + # bind original shape/func now to avoid late-binding gotcha + def func(x, *args, shape=shape, func=func, **kwargs): + i = (0,)*(len(fshape) - len(shape)) + return func(x[i], *args, **kwargs) + shape = np.broadcast_shapes(fshape, shape) # just shapes; use of NumPy OK + xs = [xp.broadcast_to(x, shape) for x in xs] + args = [xp.broadcast_to(arg, shape) for arg in args] + + message = ("The shape of the array returned by `func` must be the same as " + "the broadcasted shape of `x` and all other `args`.") + if preserve_shape is not None: # only in tanhsinh for now + message = f"When `preserve_shape=False`, {message.lower()}" + shapes_equal = [f.shape == shape for f in fs] + if not all(shapes_equal): # use Python all to reduce overhead + raise ValueError(message) + + # These algorithms tend to mix the dtypes of the abscissae and function + # values, so figure out what the result will be and convert them all to + # that type from the outset. + xfat = xp.result_type(*([f.dtype for f in fs] + [xat])) + if not complex_ok and not xp.isdtype(xfat, "real floating"): + raise ValueError("Abscissae and function output must be real numbers.") + xs = [xp.asarray(x, dtype=xfat, copy=True) for x in xs] + fs = [xp.asarray(f, dtype=xfat, copy=True) for f in fs] + + # To ensure that we can do indexing, we'll work with at least 1d arrays, + # but remember the appropriate shape of the output. + xs = [xp.reshape(x, (-1,)) for x in xs] + fs = [xp.reshape(f, (-1,)) for f in fs] + args = [xp.reshape(xp.asarray(arg, copy=True), (-1,)) for arg in args] + return func, xs, fs, args, shape, xfat, xp + + +def _loop(work, callback, shape, maxiter, func, args, dtype, pre_func_eval, + post_func_eval, check_termination, post_termination_check, + customize_result, res_work_pairs, xp, preserve_shape=False): + """Main loop of a vectorized scalar optimization algorithm + + Parameters + ---------- + work : _RichResult + All variables that need to be retained between iterations. Must + contain attributes `nit`, `nfev`, and `success`. All arrays are + subject to being "compressed" if `preserve_shape is False`; nest + arrays that should not be compressed inside another object (e.g. + `dict` or `_RichResult`). + callback : callable + User-specified callback function + shape : tuple of ints + The shape of all output arrays + maxiter : + Maximum number of iterations of the algorithm + func : callable + The user-specified callable that is being optimized or solved + args : tuple + Additional positional arguments to be passed to `func`. + dtype : NumPy dtype + The common dtype of all abscissae and function values + pre_func_eval : callable + A function that accepts `work` and returns `x`, the active elements + of `x` at which `func` will be evaluated. May modify attributes + of `work` with any algorithmic steps that need to happen + at the beginning of an iteration, before `func` is evaluated, + post_func_eval : callable + A function that accepts `x`, `func(x)`, and `work`. May modify + attributes of `work` with any algorithmic steps that need to happen + in the middle of an iteration, after `func` is evaluated but before + the termination check. + check_termination : callable + A function that accepts `work` and returns `stop`, a boolean array + indicating which of the active elements have met a termination + condition. + post_termination_check : callable + A function that accepts `work`. May modify `work` with any algorithmic + steps that need to happen after the termination check and before the + end of the iteration. + customize_result : callable + A function that accepts `res` and `shape` and returns `shape`. May + modify `res` (in-place) according to preferences (e.g. rearrange + elements between attributes) and modify `shape` if needed. + res_work_pairs : list of (str, str) + Identifies correspondence between attributes of `res` and attributes + of `work`; i.e., attributes of active elements of `work` will be + copied to the appropriate indices of `res` when appropriate. The order + determines the order in which _RichResult attributes will be + pretty-printed. + preserve_shape : bool, default: False + Whether to compress the attributes of `work` (to avoid unnecessary + computation on elements that have already converged). + + Returns + ------- + res : _RichResult + The final result object + + Notes + ----- + Besides providing structure, this framework provides several important + services for a vectorized optimization algorithm. + + - It handles common tasks involving iteration count, function evaluation + count, a user-specified callback, and associated termination conditions. + - It compresses the attributes of `work` to eliminate unnecessary + computation on elements that have already converged. + + """ + if xp is None: + raise NotImplementedError("Must provide xp.") + + cb_terminate = False + + # Initialize the result object and active element index array + n_elements = math.prod(shape) + active = xp.arange(n_elements) # in-progress element indices + res_dict = {i: xp.zeros(n_elements, dtype=dtype) for i, j in res_work_pairs} + res_dict['success'] = xp.zeros(n_elements, dtype=xp.bool) + res_dict['status'] = xp.full(n_elements, xp.asarray(_EINPROGRESS), dtype=xp.int32) + res_dict['nit'] = xp.zeros(n_elements, dtype=xp.int32) + res_dict['nfev'] = xp.zeros(n_elements, dtype=xp.int32) + res = _RichResult(res_dict) + work.args = args + + active = _check_termination(work, res, res_work_pairs, active, + check_termination, preserve_shape, xp) + + if callback is not None: + temp = _prepare_result(work, res, res_work_pairs, active, shape, + customize_result, preserve_shape, xp) + if _call_callback_maybe_halt(callback, temp): + cb_terminate = True + + while work.nit < maxiter and xp_size(active) and not cb_terminate and n_elements: + x = pre_func_eval(work) + + if work.args and work.args[0].ndim != x.ndim: + # `x` always starts as 1D. If the SciPy function that uses + # _loop added dimensions to `x`, we need to + # add them to the elements of `args`. + args = [] + for arg in work.args: + n_new_dims = x.ndim - arg.ndim + new_shape = arg.shape + (1,)*n_new_dims + args.append(xp.reshape(arg, new_shape)) + work.args = args + + x_shape = x.shape + if preserve_shape: + x = xp.reshape(x, (shape + (-1,))) + f = func(x, *work.args) + f = xp.asarray(f, dtype=dtype) + if preserve_shape: + x = xp.reshape(x, x_shape) + f = xp.reshape(f, x_shape) + work.nfev += 1 if x.ndim == 1 else x.shape[-1] + + post_func_eval(x, f, work) + + work.nit += 1 + active = _check_termination(work, res, res_work_pairs, active, + check_termination, preserve_shape, xp) + + if callback is not None: + temp = _prepare_result(work, res, res_work_pairs, active, shape, + customize_result, preserve_shape, xp) + if _call_callback_maybe_halt(callback, temp): + cb_terminate = True + break + if xp_size(active) == 0: + break + + post_termination_check(work) + + work.status = xpx.at(work.status)[:].set(_ECALLBACK if cb_terminate else _ECONVERR) + return _prepare_result(work, res, res_work_pairs, active, shape, + customize_result, preserve_shape, xp) + + +def _check_termination(work, res, res_work_pairs, active, check_termination, + preserve_shape, xp): + # Checks termination conditions, updates elements of `res` with + # corresponding elements of `work`, and compresses `work`. + + stop = check_termination(work) + + if xp.any(stop): + # update the active elements of the result object with the active + # elements for which a termination condition has been met + _update_active(work, res, res_work_pairs, active, stop, preserve_shape, xp) + + if preserve_shape: + stop = stop[active] + + proceed = ~stop + active = active[proceed] + + if not preserve_shape: + # compress the arrays to avoid unnecessary computation + for key, val in work.items(): + # `continued_fraction` hacks `n`; improve if this becomes a problem + if key in {'args', 'n'}: + continue + work[key] = val[proceed] if getattr(val, 'ndim', 0) > 0 else val + work.args = [arg[proceed] for arg in work.args] + + return active + + +def _update_active(work, res, res_work_pairs, active, mask, preserve_shape, xp): + # Update `active` indices of the arrays in result object `res` with the + # contents of the scalars and arrays in `update_dict`. When provided, + # `mask` is a boolean array applied both to the arrays in `update_dict` + # that are to be used and to the arrays in `res` that are to be updated. + update_dict = {key1: work[key2] for key1, key2 in res_work_pairs} + update_dict['success'] = work.status == 0 + + if mask is not None: + if preserve_shape: + active_mask = xp.zeros_like(mask) + active_mask = xpx.at(active_mask)[active].set(True) + active_mask = active_mask & mask + for key, val in update_dict.items(): + val = val[active_mask] if getattr(val, 'ndim', 0) > 0 else val + res[key] = xpx.at(res[key])[active_mask].set(val) + else: + active_mask = active[mask] + for key, val in update_dict.items(): + val = val[mask] if getattr(val, 'ndim', 0) > 0 else val + res[key] = xpx.at(res[key])[active_mask].set(val) + else: + for key, val in update_dict.items(): + if preserve_shape and getattr(val, 'ndim', 0) > 0: + val = val[active] + res[key] = xpx.at(res[key])[active].set(val) + + +def _prepare_result(work, res, res_work_pairs, active, shape, customize_result, + preserve_shape, xp): + # Prepare the result object `res` by creating a copy, copying the latest + # data from work, running the provided result customization function, + # and reshaping the data to the original shapes. + res = res.copy() + _update_active(work, res, res_work_pairs, active, None, preserve_shape, xp) + + shape = customize_result(res, shape) + + for key, val in res.items(): + # this looks like it won't work for xp != np if val is not numeric + temp = xp.reshape(val, shape) + res[key] = temp[()] if temp.ndim == 0 else temp + + res['_order_keys'] = ['success'] + [i for i, j in res_work_pairs] + return _RichResult(**res) diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_fpumode.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_fpumode.cpython-312-darwin.so new file mode 100644 index 0000000000000000000000000000000000000000..e4596a6ed97f2734fe82d613e7fc0ddabc28866c Binary files /dev/null and b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_fpumode.cpython-312-darwin.so differ diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_gcutils.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_gcutils.py new file mode 100644 index 0000000000000000000000000000000000000000..854ae36228614f3eb8849e9f95abf0dd387b5d35 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_gcutils.py @@ -0,0 +1,105 @@ +""" +Module for testing automatic garbage collection of objects + +.. autosummary:: + :toctree: generated/ + + set_gc_state - enable or disable garbage collection + gc_state - context manager for given state of garbage collector + assert_deallocated - context manager to check for circular references on object + +""" +import weakref +import gc + +from contextlib import contextmanager +from platform import python_implementation + +__all__ = ['set_gc_state', 'gc_state', 'assert_deallocated'] + + +IS_PYPY = python_implementation() == 'PyPy' + + +class ReferenceError(AssertionError): + pass + + +def set_gc_state(state): + """ Set status of garbage collector """ + if gc.isenabled() == state: + return + if state: + gc.enable() + else: + gc.disable() + + +@contextmanager +def gc_state(state): + """ Context manager to set state of garbage collector to `state` + + Parameters + ---------- + state : bool + True for gc enabled, False for disabled + + Examples + -------- + >>> with gc_state(False): + ... assert not gc.isenabled() + >>> with gc_state(True): + ... assert gc.isenabled() + """ + orig_state = gc.isenabled() + set_gc_state(state) + yield + set_gc_state(orig_state) + + +@contextmanager +def assert_deallocated(func, *args, **kwargs): + """Context manager to check that object is deallocated + + This is useful for checking that an object can be freed directly by + reference counting, without requiring gc to break reference cycles. + GC is disabled inside the context manager. + + This check is not available on PyPy. + + Parameters + ---------- + func : callable + Callable to create object to check + \\*args : sequence + positional arguments to `func` in order to create object to check + \\*\\*kwargs : dict + keyword arguments to `func` in order to create object to check + + Examples + -------- + >>> class C: pass + >>> with assert_deallocated(C) as c: + ... # do something + ... del c + + >>> class C: + ... def __init__(self): + ... self._circular = self # Make circular reference + >>> with assert_deallocated(C) as c: #doctest: +IGNORE_EXCEPTION_DETAIL + ... # do something + ... del c + Traceback (most recent call last): + ... + ReferenceError: Remaining reference(s) to object + """ + if IS_PYPY: + raise RuntimeError("assert_deallocated is unavailable on PyPy") + + with gc_state(False): + obj = func(*args, **kwargs) + ref = weakref.ref(obj) + yield obj + del obj + if ref() is not None: + raise ReferenceError("Remaining reference(s) to object") diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_pep440.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_pep440.py new file mode 100644 index 0000000000000000000000000000000000000000..d546e32a0349461a0aab76bfb4636ebf25227ca0 --- /dev/null +++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_pep440.py @@ -0,0 +1,487 @@ +"""Utility to compare pep440 compatible version strings. + +The LooseVersion and StrictVersion classes that distutils provides don't +work; they don't recognize anything like alpha/beta/rc/dev versions. +""" + +# Copyright (c) Donald Stufft and individual contributors. +# All rights reserved. + +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions are met: + +# 1. Redistributions of source code must retain the above copyright notice, +# this list of conditions and the following disclaimer. + +# 2. Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in the +# documentation and/or other materials provided with the distribution. + +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE +# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. + +import collections +import itertools +import re + + +__all__ = [ + "parse", "Version", "LegacyVersion", "InvalidVersion", "VERSION_PATTERN", +] + + +# BEGIN packaging/_structures.py + + +class Infinity: + def __repr__(self): + return "Infinity" + + def __hash__(self): + return hash(repr(self)) + + def __lt__(self, other): + return False + + def __le__(self, other): + return False + + def __eq__(self, other): + return isinstance(other, self.__class__) + + def __ne__(self, other): + return not isinstance(other, self.__class__) + + def __gt__(self, other): + return True + + def __ge__(self, other): + return True + + def __neg__(self): + return NegativeInfinity + + +Infinity = Infinity() + + +class NegativeInfinity: + def __repr__(self): + return "-Infinity" + + def __hash__(self): + return hash(repr(self)) + + def __lt__(self, other): + return True + + def __le__(self, other): + return True + + def __eq__(self, other): + return isinstance(other, self.__class__) + + def __ne__(self, other): + return not isinstance(other, self.__class__) + + def __gt__(self, other): + return False + + def __ge__(self, other): + return False + + def __neg__(self): + return Infinity + + +# BEGIN packaging/version.py + + +NegativeInfinity = NegativeInfinity() + +_Version = collections.namedtuple( + "_Version", + ["epoch", "release", "dev", "pre", "post", "local"], +) + + +def parse(version): + """ + Parse the given version string and return either a :class:`Version` object + or a :class:`LegacyVersion` object depending on if the given version is + a valid PEP 440 version or a legacy version. + """ + try: + return Version(version) + except InvalidVersion: + return LegacyVersion(version) + + +class InvalidVersion(ValueError): + """ + An invalid version was found, users should refer to PEP 440. + """ + + +class _BaseVersion: + + def __hash__(self): + return hash(self._key) + + def __lt__(self, other): + return self._compare(other, lambda s, o: s < o) + + def __le__(self, other): + return self._compare(other, lambda s, o: s <= o) + + def __eq__(self, other): + return self._compare(other, lambda s, o: s == o) + + def __ge__(self, other): + return self._compare(other, lambda s, o: s >= o) + + def __gt__(self, other): + return self._compare(other, lambda s, o: s > o) + + def __ne__(self, other): + return self._compare(other, lambda s, o: s != o) + + def _compare(self, other, method): + if not isinstance(other, _BaseVersion): + return NotImplemented + + return method(self._key, other._key) + + +class LegacyVersion(_BaseVersion): + + def __init__(self, version): + self._version = str(version) + self._key = _legacy_cmpkey(self._version) + + def __str__(self): + return self._version + + def __repr__(self): + return f"" + + @property + def public(self): + return self._version + + @property + def base_version(self): + return self._version + + @property + def local(self): + return None + + @property + def is_prerelease(self): + return False + + @property + def is_postrelease(self): + return False + + +_legacy_version_component_re = re.compile( + r"(\d+ | [a-z]+ | \.| -)", re.VERBOSE, +) + +_legacy_version_replacement_map = { + "pre": "c", "preview": "c", "-": "final-", "rc": "c", "dev": "@", +} + + +def _parse_version_parts(s): + for part in _legacy_version_component_re.split(s): + part = _legacy_version_replacement_map.get(part, part) + + if not part or part == ".": + continue + + if part[:1] in "0123456789": + # pad for numeric comparison + yield part.zfill(8) + else: + yield "*" + part + + # ensure that alpha/beta/candidate are before final + yield "*final" + + +def _legacy_cmpkey(version): + # We hardcode an epoch of -1 here. A PEP 440 version can only have an epoch + # greater than or equal to 0. This will effectively put the LegacyVersion, + # which uses the defacto standard originally implemented by setuptools, + # as before all PEP 440 versions. + epoch = -1 + + # This scheme is taken from pkg_resources.parse_version setuptools prior to + # its adoption of the packaging library. + parts = [] + for part in _parse_version_parts(version.lower()): + if part.startswith("*"): + # remove "-" before a prerelease tag + if part < "*final": + while parts and parts[-1] == "*final-": + parts.pop() + + # remove trailing zeros from each series of numeric parts + while parts and parts[-1] == "00000000": + parts.pop() + + parts.append(part) + parts = tuple(parts) + + return epoch, parts + + +# Deliberately not anchored to the start and end of the string, to make it +# easier for 3rd party code to reuse +VERSION_PATTERN = r""" + v? + (?: + (?:(?P[0-9]+)!)? # epoch + (?P[0-9]+(?:\.[0-9]+)*) # release segment + (?P
                                          # pre-release
+            [-_\.]?
+            (?P(a|b|c|rc|alpha|beta|pre|preview))
+            [-_\.]?
+            (?P[0-9]+)?
+        )?
+        (?P                                         # post release
+            (?:-(?P[0-9]+))
+            |
+            (?:
+                [-_\.]?
+                (?Ppost|rev|r)
+                [-_\.]?
+                (?P[0-9]+)?
+            )
+        )?
+        (?P                                          # dev release
+            [-_\.]?
+            (?Pdev)
+            [-_\.]?
+            (?P[0-9]+)?
+        )?
+    )
+    (?:\+(?P[a-z0-9]+(?:[-_\.][a-z0-9]+)*))?       # local version
+"""
+
+
+class Version(_BaseVersion):
+
+    _regex = re.compile(
+        r"^\s*" + VERSION_PATTERN + r"\s*$",
+        re.VERBOSE | re.IGNORECASE,
+    )
+
+    def __init__(self, version):
+        # Validate the version and parse it into pieces
+        match = self._regex.search(version)
+        if not match:
+            raise InvalidVersion(f"Invalid version: '{version}'")
+
+        # Store the parsed out pieces of the version
+        self._version = _Version(
+            epoch=int(match.group("epoch")) if match.group("epoch") else 0,
+            release=tuple(int(i) for i in match.group("release").split(".")),
+            pre=_parse_letter_version(
+                match.group("pre_l"),
+                match.group("pre_n"),
+            ),
+            post=_parse_letter_version(
+                match.group("post_l"),
+                match.group("post_n1") or match.group("post_n2"),
+            ),
+            dev=_parse_letter_version(
+                match.group("dev_l"),
+                match.group("dev_n"),
+            ),
+            local=_parse_local_version(match.group("local")),
+        )
+
+        # Generate a key which will be used for sorting
+        self._key = _cmpkey(
+            self._version.epoch,
+            self._version.release,
+            self._version.pre,
+            self._version.post,
+            self._version.dev,
+            self._version.local,
+        )
+
+    def __repr__(self):
+        return f""
+
+    def __str__(self):
+        parts = []
+
+        # Epoch
+        if self._version.epoch != 0:
+            parts.append(f"{self._version.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self._version.release))
+
+        # Pre-release
+        if self._version.pre is not None:
+            parts.append("".join(str(x) for x in self._version.pre))
+
+        # Post-release
+        if self._version.post is not None:
+            parts.append(f".post{self._version.post[1]}")
+
+        # Development release
+        if self._version.dev is not None:
+            parts.append(f".dev{self._version.dev[1]}")
+
+        # Local version segment
+        if self._version.local is not None:
+            parts.append(
+                "+{}".format(".".join(str(x) for x in self._version.local))
+            )
+
+        return "".join(parts)
+
+    @property
+    def public(self):
+        return str(self).split("+", 1)[0]
+
+    @property
+    def base_version(self):
+        parts = []
+
+        # Epoch
+        if self._version.epoch != 0:
+            parts.append(f"{self._version.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self._version.release))
+
+        return "".join(parts)
+
+    @property
+    def local(self):
+        version_string = str(self)
+        if "+" in version_string:
+            return version_string.split("+", 1)[1]
+
+    @property
+    def is_prerelease(self):
+        return bool(self._version.dev or self._version.pre)
+
+    @property
+    def is_postrelease(self):
+        return bool(self._version.post)
+
+
+def _parse_letter_version(letter, number):
+    if letter:
+        # We assume there is an implicit 0 in a pre-release if there is
+        # no numeral associated with it.
+        if number is None:
+            number = 0
+
+        # We normalize any letters to their lower-case form
+        letter = letter.lower()
+
+        # We consider some words to be alternate spellings of other words and
+        # in those cases we want to normalize the spellings to our preferred
+        # spelling.
+        if letter == "alpha":
+            letter = "a"
+        elif letter == "beta":
+            letter = "b"
+        elif letter in ["c", "pre", "preview"]:
+            letter = "rc"
+        elif letter in ["rev", "r"]:
+            letter = "post"
+
+        return letter, int(number)
+    if not letter and number:
+        # We assume that if we are given a number but not given a letter,
+        # then this is using the implicit post release syntax (e.g., 1.0-1)
+        letter = "post"
+
+        return letter, int(number)
+
+
+_local_version_seperators = re.compile(r"[\._-]")
+
+
+def _parse_local_version(local):
+    """
+    Takes a string like abc.1.twelve and turns it into ("abc", 1, "twelve").
+    """
+    if local is not None:
+        return tuple(
+            part.lower() if not part.isdigit() else int(part)
+            for part in _local_version_seperators.split(local)
+        )
+
+
+def _cmpkey(epoch, release, pre, post, dev, local):
+    # When we compare a release version, we want to compare it with all of the
+    # trailing zeros removed. So we'll use a reverse the list, drop all the now
+    # leading zeros until we come to something non-zero, then take the rest,
+    # re-reverse it back into the correct order, and make it a tuple and use
+    # that for our sorting key.
+    release = tuple(
+        reversed(list(
+            itertools.dropwhile(
+                lambda x: x == 0,
+                reversed(release),
+            )
+        ))
+    )
+
+    # We need to "trick" the sorting algorithm to put 1.0.dev0 before 1.0a0.
+    # We'll do this by abusing the pre-segment, but we _only_ want to do this
+    # if there is no pre- or a post-segment. If we have one of those, then
+    # the normal sorting rules will handle this case correctly.
+    if pre is None and post is None and dev is not None:
+        pre = -Infinity
+    # Versions without a pre-release (except as noted above) should sort after
+    # those with one.
+    elif pre is None:
+        pre = Infinity
+
+    # Versions without a post-segment should sort before those with one.
+    if post is None:
+        post = -Infinity
+
+    # Versions without a development segment should sort after those with one.
+    if dev is None:
+        dev = Infinity
+
+    if local is None:
+        # Versions without a local segment should sort before those with one.
+        local = -Infinity
+    else:
+        # Versions with a local segment need that segment parsed to implement
+        # the sorting rules in PEP440.
+        # - Alphanumeric segments sort before numeric segments
+        # - Alphanumeric segments sort lexicographically
+        # - Numeric segments sort numerically
+        # - Shorter versions sort before longer versions when the prefixes
+        #   match exactly
+        local = tuple(
+            (i, "") if isinstance(i, int) else (-Infinity, i)
+            for i in local
+        )
+
+    return epoch, release, pre, post, dev, local
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_public_api.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_public_api.py
new file mode 100644
index 0000000000000000000000000000000000000000..0bfd6c7710381e16c78be017756de614057b6028
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_public_api.py
@@ -0,0 +1,56 @@
+"""PUBLIC_MODULES was once included in scipy._lib.tests.test_public_api.
+
+It has been separated into this file so that this list of public modules
+could be used when generating tables showing support for alternative
+array API backends across modules in
+scipy/doc/source/array_api_capabilities.py.
+"""
+
+# Historically SciPy has not used leading underscores for private submodules
+# much.  This has resulted in lots of things that look like public modules
+# (i.e. things that can be imported as `import scipy.somesubmodule.somefile`),
+# but were never intended to be public.  The PUBLIC_MODULES list contains
+# modules that are either public because they were meant to be, or because they
+# contain public functions/objects that aren't present in any other namespace
+# for whatever reason and therefore should be treated as public.
+PUBLIC_MODULES = ["scipy." + s for s in [
+    "cluster",
+    "cluster.vq",
+    "cluster.hierarchy",
+    "constants",
+    "datasets",
+    "differentiate",
+    "fft",
+    "fftpack",
+    "integrate",
+    "interpolate",
+    "io",
+    "io.arff",
+    "io.matlab",
+    "io.wavfile",
+    "linalg",
+    "linalg.blas",
+    "linalg.cython_blas",
+    "linalg.lapack",
+    "linalg.cython_lapack",
+    "linalg.interpolative",
+    "ndimage",
+    "odr",
+    "optimize",
+    "optimize.elementwise",
+    "signal",
+    "signal.windows",
+    "sparse",
+    "sparse.linalg",
+    "sparse.csgraph",
+    "spatial",
+    "spatial.distance",
+    "spatial.transform",
+    "special",
+    "stats",
+    "stats.contingency",
+    "stats.distributions",
+    "stats.mstats",
+    "stats.qmc",
+    "stats.sampling"
+]]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_sparse.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_sparse.py
new file mode 100644
index 0000000000000000000000000000000000000000..e7deb32dd6e5d19bb8fceae4a7d22f2c6eddda7a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_sparse.py
@@ -0,0 +1,41 @@
+from abc import ABC
+
+__all__ = ["SparseABC", "issparse"]
+
+
+class SparseABC(ABC):
+    pass
+
+
+def issparse(x):
+    """Is `x` of a sparse array or sparse matrix type?
+
+    Parameters
+    ----------
+    x
+        object to check for being a sparse array or sparse matrix
+
+    Returns
+    -------
+    bool
+        True if `x` is a sparse array or a sparse matrix, False otherwise
+
+    Notes
+    -----
+    Use `isinstance(x, sp.sparse.sparray)` to check between an array or matrix.
+    Use `a.format` to check the sparse format, e.g. `a.format == 'csr'`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import csr_array, csr_matrix, issparse
+    >>> issparse(csr_matrix([[5]]))
+    True
+    >>> issparse(csr_array([[5]]))
+    True
+    >>> issparse(np.array([[5]]))
+    False
+    >>> issparse(5)
+    False
+    """
+    return isinstance(x, SparseABC)
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_testutils.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_testutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..442bb539db3bbedf0a64876fea124c107f3d0383
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_testutils.py
@@ -0,0 +1,373 @@
+"""
+Generic test utilities.
+
+"""
+
+import inspect
+import os
+import re
+import shutil
+import subprocess
+import sys
+import sysconfig
+import threading
+from importlib.util import module_from_spec, spec_from_file_location
+
+import numpy as np
+import scipy
+
+try:
+    # Need type: ignore[import-untyped] for mypy >= 1.6
+    import cython  # type: ignore[import-untyped]
+    from Cython.Compiler.Version import (  # type: ignore[import-untyped]
+        version as cython_version,
+    )
+except ImportError:
+    cython = None
+else:
+    from scipy._lib import _pep440
+    required_version = '3.0.8'
+    if _pep440.parse(cython_version) < _pep440.Version(required_version):
+        # too old or wrong cython, skip Cython API tests
+        cython = None
+
+
+__all__ = ['PytestTester', 'check_free_memory', '_TestPythranFunc', 'IS_MUSL']
+
+
+IS_MUSL = False
+# alternate way is
+# from packaging.tags import sys_tags
+#     _tags = list(sys_tags())
+#     if 'musllinux' in _tags[0].platform:
+_v = sysconfig.get_config_var('HOST_GNU_TYPE') or ''
+if 'musl' in _v:
+    IS_MUSL = True
+
+
+IS_EDITABLE = 'editable' in scipy.__path__[0]
+
+
+class FPUModeChangeWarning(RuntimeWarning):
+    """Warning about FPU mode change"""
+    pass
+
+
+class PytestTester:
+    """
+    Run tests for this namespace
+
+    ``scipy.test()`` runs tests for all of SciPy, with the default settings.
+    When used from a submodule (e.g., ``scipy.cluster.test()``, only the tests
+    for that namespace are run.
+
+    Parameters
+    ----------
+    label : {'fast', 'full'}, optional
+        Whether to run only the fast tests, or also those marked as slow.
+        Default is 'fast'.
+    verbose : int, optional
+        Test output verbosity. Default is 1.
+    extra_argv : list, optional
+        Arguments to pass through to Pytest.
+    doctests : bool, optional
+        Whether to run doctests or not. Default is False.
+    coverage : bool, optional
+        Whether to run tests with code coverage measurements enabled.
+        Default is False.
+    tests : list of str, optional
+        List of module names to run tests for. By default, uses the module
+        from which the ``test`` function is called.
+    parallel : int, optional
+        Run tests in parallel with pytest-xdist, if number given is larger than
+        1. Default is 1.
+
+    """
+    def __init__(self, module_name):
+        self.module_name = module_name
+
+    def __call__(self, label="fast", verbose=1, extra_argv=None, doctests=False,
+                 coverage=False, tests=None, parallel=None):
+        import pytest
+
+        module = sys.modules[self.module_name]
+        module_path = os.path.abspath(module.__path__[0])
+
+        pytest_args = ['--showlocals', '--tb=short']
+
+        if extra_argv is None:
+            extra_argv = []
+        pytest_args += extra_argv
+        if any(arg == "-m" or arg == "--markers" for arg in extra_argv):
+            # Likely conflict with default --mode=fast
+            raise ValueError("Must specify -m before --")
+
+        if verbose and int(verbose) > 1:
+            pytest_args += ["-" + "v"*(int(verbose)-1)]
+
+        if coverage:
+            pytest_args += ["--cov=" + module_path]
+
+        if label == "fast":
+            pytest_args += ["-m", "not slow"]
+        elif label != "full":
+            pytest_args += ["-m", label]
+
+        if tests is None:
+            tests = [self.module_name]
+
+        if parallel is not None and parallel > 1:
+            if _pytest_has_xdist():
+                pytest_args += ['-n', str(parallel)]
+            else:
+                import warnings
+                warnings.warn('Could not run tests in parallel because '
+                              'pytest-xdist plugin is not available.',
+                              stacklevel=2)
+
+        pytest_args += ['--pyargs'] + list(tests)
+
+        try:
+            code = pytest.main(pytest_args)
+        except SystemExit as exc:
+            code = exc.code
+
+        return (code == 0)
+
+
+class _TestPythranFunc:
+    '''
+    These are situations that can be tested in our pythran tests:
+    - A function with multiple array arguments and then
+      other positional and keyword arguments.
+    - A function with array-like keywords (e.g. `def somefunc(x0, x1=None)`.
+    Note: list/tuple input is not yet tested!
+
+    `self.arguments`: A dictionary which key is the index of the argument,
+                      value is tuple(array value, all supported dtypes)
+    `self.partialfunc`: A function used to freeze some non-array argument
+                        that of no interests in the original function
+    '''
+    ALL_INTEGER = [np.int8, np.int16, np.int32, np.int64, np.intc, np.intp]
+    ALL_FLOAT = [np.float32, np.float64]
+    ALL_COMPLEX = [np.complex64, np.complex128]
+
+    def setup_method(self):
+        self.arguments = {}
+        self.partialfunc = None
+        self.expected = None
+
+    def get_optional_args(self, func):
+        # get optional arguments with its default value,
+        # used for testing keywords
+        signature = inspect.signature(func)
+        optional_args = {}
+        for k, v in signature.parameters.items():
+            if v.default is not inspect.Parameter.empty:
+                optional_args[k] = v.default
+        return optional_args
+
+    def get_max_dtype_list_length(self):
+        # get the max supported dtypes list length in all arguments
+        max_len = 0
+        for arg_idx in self.arguments:
+            cur_len = len(self.arguments[arg_idx][1])
+            if cur_len > max_len:
+                max_len = cur_len
+        return max_len
+
+    def get_dtype(self, dtype_list, dtype_idx):
+        # get the dtype from dtype_list via index
+        # if the index is out of range, then return the last dtype
+        if dtype_idx > len(dtype_list)-1:
+            return dtype_list[-1]
+        else:
+            return dtype_list[dtype_idx]
+
+    def test_all_dtypes(self):
+        for type_idx in range(self.get_max_dtype_list_length()):
+            args_array = []
+            for arg_idx in self.arguments:
+                new_dtype = self.get_dtype(self.arguments[arg_idx][1],
+                                           type_idx)
+                args_array.append(self.arguments[arg_idx][0].astype(new_dtype))
+            self.pythranfunc(*args_array)
+
+    def test_views(self):
+        args_array = []
+        for arg_idx in self.arguments:
+            args_array.append(self.arguments[arg_idx][0][::-1][::-1])
+        self.pythranfunc(*args_array)
+
+    def test_strided(self):
+        args_array = []
+        for arg_idx in self.arguments:
+            args_array.append(np.repeat(self.arguments[arg_idx][0],
+                                        2, axis=0)[::2])
+        self.pythranfunc(*args_array)
+
+
+def _pytest_has_xdist():
+    """
+    Check if the pytest-xdist plugin is installed, providing parallel tests
+    """
+    # Check xdist exists without importing, otherwise pytests emits warnings
+    from importlib.util import find_spec
+    return find_spec('xdist') is not None
+
+
+def check_free_memory(free_mb):
+    """
+    Check *free_mb* of memory is available, otherwise do pytest.skip
+    """
+    import pytest
+
+    try:
+        mem_free = _parse_size(os.environ['SCIPY_AVAILABLE_MEM'])
+        msg = '{} MB memory required, but environment SCIPY_AVAILABLE_MEM={}'.format(
+            free_mb, os.environ['SCIPY_AVAILABLE_MEM'])
+    except KeyError:
+        mem_free = _get_mem_available()
+        if mem_free is None:
+            pytest.skip("Could not determine available memory; set SCIPY_AVAILABLE_MEM "
+                        "variable to free memory in MB to run the test.")
+        msg = f'{free_mb} MB memory required, but {mem_free/1e6} MB available'
+
+    if mem_free < free_mb * 1e6:
+        pytest.skip(msg)
+
+
+def _parse_size(size_str):
+    suffixes = {'': 1e6,
+                'b': 1.0,
+                'k': 1e3, 'M': 1e6, 'G': 1e9, 'T': 1e12,
+                'kb': 1e3, 'Mb': 1e6, 'Gb': 1e9, 'Tb': 1e12,
+                'kib': 1024.0, 'Mib': 1024.0**2, 'Gib': 1024.0**3, 'Tib': 1024.0**4}
+    m = re.match(r'^\s*(\d+)\s*({})\s*$'.format('|'.join(suffixes.keys())),
+                 size_str,
+                 re.I)
+    if not m or m.group(2) not in suffixes:
+        raise ValueError("Invalid size string")
+
+    return float(m.group(1)) * suffixes[m.group(2)]
+
+
+def _get_mem_available():
+    """
+    Get information about memory available, not counting swap.
+    """
+    try:
+        import psutil
+        return psutil.virtual_memory().available
+    except (ImportError, AttributeError):
+        pass
+
+    if sys.platform.startswith('linux'):
+        info = {}
+        with open('/proc/meminfo') as f:
+            for line in f:
+                p = line.split()
+                info[p[0].strip(':').lower()] = float(p[1]) * 1e3
+
+        if 'memavailable' in info:
+            # Linux >= 3.14
+            return info['memavailable']
+        else:
+            return info['memfree'] + info['cached']
+
+    return None
+
+def _test_cython_extension(tmp_path, srcdir):
+    """
+    Helper function to test building and importing Cython modules that
+    make use of the Cython APIs for BLAS, LAPACK, optimize, and special.
+    """
+    import pytest
+    try:
+        subprocess.check_call(["meson", "--version"])
+    except FileNotFoundError:
+        pytest.skip("No usable 'meson' found")
+
+    # Make safe for being called by multiple threads within one test
+    tmp_path = tmp_path / str(threading.get_ident())
+
+    # build the examples in a temporary directory
+    mod_name = os.path.split(srcdir)[1]
+    shutil.copytree(srcdir, tmp_path / mod_name)
+    build_dir = tmp_path / mod_name / 'tests' / '_cython_examples'
+    target_dir = build_dir / 'build'
+    os.makedirs(target_dir, exist_ok=True)
+
+    # Ensure we use the correct Python interpreter even when `meson` is
+    # installed in a different Python environment (see numpy#24956)
+    native_file = str(build_dir / 'interpreter-native-file.ini')
+    with open(native_file, 'w') as f:
+        f.write("[binaries]\n")
+        f.write(f"python = '{sys.executable}'")
+
+    if sys.platform == "win32":
+        subprocess.check_call(["meson", "setup",
+                               "--buildtype=release",
+                               "--native-file", native_file,
+                               "--vsenv", str(build_dir)],
+                              cwd=target_dir,
+                              )
+    else:
+        subprocess.check_call(["meson", "setup",
+                               "--native-file", native_file, str(build_dir)],
+                              cwd=target_dir
+                              )
+    subprocess.check_call(["meson", "compile", "-vv"], cwd=target_dir)
+
+    # import without adding the directory to sys.path
+    suffix = sysconfig.get_config_var('EXT_SUFFIX')
+
+    def load(modname):
+        so = (target_dir / modname).with_suffix(suffix)
+        spec = spec_from_file_location(modname, so)
+        mod = module_from_spec(spec)
+        spec.loader.exec_module(mod)
+        return mod
+
+    # test that the module can be imported
+    return load("extending"), load("extending_cpp")
+
+
+def _run_concurrent_barrier(n_workers, fn, *args, **kwargs):
+    """
+    Run a given function concurrently across a given number of threads.
+
+    This is equivalent to using a ThreadPoolExecutor, but using the threading
+    primitives instead. This function ensures that the closure passed by
+    parameter gets called concurrently by setting up a barrier before it gets
+    called before any of the threads.
+
+    Arguments
+    ---------
+    n_workers: int
+        Number of concurrent threads to spawn.
+    fn: callable
+        Function closure to execute concurrently. Its first argument will
+        be the thread id.
+    *args: tuple
+        Variable number of positional arguments to pass to the function.
+    **kwargs: dict
+        Keyword arguments to pass to the function.
+    """
+    barrier = threading.Barrier(n_workers)
+
+    def closure(i, *args, **kwargs):
+        barrier.wait()
+        fn(i, *args, **kwargs)
+
+    workers = []
+    for i in range(0, n_workers):
+        workers.append(threading.Thread(
+            target=closure,
+            args=(i,) + args, kwargs=kwargs))
+
+    for worker in workers:
+        worker.start()
+
+    for worker in workers:
+        worker.join()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_tmpdirs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_tmpdirs.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f9fd546a9d2ae3e9a20c0684f79eb0b3d61ee92
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_tmpdirs.py
@@ -0,0 +1,86 @@
+''' Contexts for *with* statement providing temporary directories
+'''
+import os
+from contextlib import contextmanager
+from shutil import rmtree
+from tempfile import mkdtemp
+
+
+@contextmanager
+def tempdir():
+    """Create and return a temporary directory. This has the same
+    behavior as mkdtemp but can be used as a context manager.
+
+    Upon exiting the context, the directory and everything contained
+    in it are removed.
+
+    Examples
+    --------
+    >>> import os
+    >>> with tempdir() as tmpdir:
+    ...     fname = os.path.join(tmpdir, 'example_file.txt')
+    ...     with open(fname, 'wt') as fobj:
+    ...         _ = fobj.write('a string\\n')
+    >>> os.path.exists(tmpdir)
+    False
+    """
+    d = mkdtemp()
+    yield d
+    rmtree(d)
+
+
+@contextmanager
+def in_tempdir():
+    ''' Create, return, and change directory to a temporary directory
+
+    Examples
+    --------
+    >>> import os
+    >>> my_cwd = os.getcwd()
+    >>> with in_tempdir() as tmpdir:
+    ...     _ = open('test.txt', 'wt').write('some text')
+    ...     assert os.path.isfile('test.txt')
+    ...     assert os.path.isfile(os.path.join(tmpdir, 'test.txt'))
+    >>> os.path.exists(tmpdir)
+    False
+    >>> os.getcwd() == my_cwd
+    True
+    '''
+    pwd = os.getcwd()
+    d = mkdtemp()
+    os.chdir(d)
+    yield d
+    os.chdir(pwd)
+    rmtree(d)
+
+
+@contextmanager
+def in_dir(dir=None):
+    """ Change directory to given directory for duration of ``with`` block
+
+    Useful when you want to use `in_tempdir` for the final test, but
+    you are still debugging. For example, you may want to do this in the end:
+
+    >>> with in_tempdir() as tmpdir:
+    ...     # do something complicated which might break
+    ...     pass
+
+    But, indeed, the complicated thing does break, and meanwhile, the
+    ``in_tempdir`` context manager wiped out the directory with the
+    temporary files that you wanted for debugging. So, while debugging, you
+    replace with something like:
+
+    >>> with in_dir() as tmpdir: # Use working directory by default
+    ...     # do something complicated which might break
+    ...     pass
+
+    You can then look at the temporary file outputs to debug what is happening,
+    fix, and finally replace ``in_dir`` with ``in_tempdir`` again.
+    """
+    cwd = os.getcwd()
+    if dir is None:
+        yield cwd
+        return
+    os.chdir(dir)
+    yield dir
+    os.chdir(cwd)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/._LICENSE b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/._LICENSE
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/LICENSE b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..5f2b90a026aaecbdc090b3d3234954ab29fce8ae
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/LICENSE
@@ -0,0 +1,29 @@
+BSD 3-Clause License
+
+Copyright (c) 2018, Quansight-Labs
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation
+  and/or other materials provided with the distribution.
+
+* Neither the name of the copyright holder nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..91afdcedb180599a41758cdd8c03416cf6c20d76
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/__init__.py
@@ -0,0 +1,116 @@
+"""
+.. note:
+    If you are looking for overrides for NumPy-specific methods, see the
+    documentation for :obj:`unumpy`. This page explains how to write
+    back-ends and multimethods.
+
+``uarray`` is built around a back-end protocol, and overridable multimethods.
+It is necessary to define multimethods for back-ends to be able to override them.
+See the documentation of :obj:`generate_multimethod` on how to write multimethods.
+
+
+
+Let's start with the simplest:
+
+``__ua_domain__`` defines the back-end *domain*. The domain consists of period-
+separated string consisting of the modules you extend plus the submodule. For
+example, if a submodule ``module2.submodule`` extends ``module1``
+(i.e., it exposes dispatchables marked as types available in ``module1``),
+then the domain string should be ``"module1.module2.submodule"``.
+
+
+For the purpose of this demonstration, we'll be creating an object and setting
+its attributes directly. However, note that you can use a module or your own type
+as a backend as well.
+
+>>> class Backend: pass
+>>> be = Backend()
+>>> be.__ua_domain__ = "ua_examples"
+
+It might be useful at this point to sidetrack to the documentation of
+:obj:`generate_multimethod` to find out how to generate a multimethod
+overridable by :obj:`uarray`. Needless to say, writing a backend and
+creating multimethods are mostly orthogonal activities, and knowing
+one doesn't necessarily require knowledge of the other, although it
+is certainly helpful. We expect core API designers/specifiers to write the
+multimethods, and implementors to override them. But, as is often the case,
+similar people write both.
+
+Without further ado, here's an example multimethod:
+
+>>> import uarray as ua
+>>> from uarray import Dispatchable
+>>> def override_me(a, b):
+...   return Dispatchable(a, int),
+>>> def override_replacer(args, kwargs, dispatchables):
+...     return (dispatchables[0], args[1]), {}
+>>> overridden_me = ua.generate_multimethod(
+...     override_me, override_replacer, "ua_examples"
+... )
+
+Next comes the part about overriding the multimethod. This requires
+the ``__ua_function__`` protocol, and the ``__ua_convert__``
+protocol. The ``__ua_function__`` protocol has the signature
+``(method, args, kwargs)`` where ``method`` is the passed
+multimethod, ``args``/``kwargs`` specify the arguments and ``dispatchables``
+is the list of converted dispatchables passed in.
+
+>>> def __ua_function__(method, args, kwargs):
+...     return method.__name__, args, kwargs
+>>> be.__ua_function__ = __ua_function__
+
+The other protocol of interest is the ``__ua_convert__`` protocol. It has the
+signature ``(dispatchables, coerce)``. When ``coerce`` is ``False``, conversion
+between the formats should ideally be an ``O(1)`` operation, but it means that
+no memory copying should be involved, only views of the existing data.
+
+>>> def __ua_convert__(dispatchables, coerce):
+...     for d in dispatchables:
+...         if d.type is int:
+...             if coerce and d.coercible:
+...                 yield str(d.value)
+...             else:
+...                 yield d.value
+>>> be.__ua_convert__ = __ua_convert__
+
+Now that we have defined the backend, the next thing to do is to call the multimethod.
+
+>>> with ua.set_backend(be):
+...      overridden_me(1, "2")
+('override_me', (1, '2'), {})
+
+Note that the marked type has no effect on the actual type of the passed object.
+We can also coerce the type of the input.
+
+>>> with ua.set_backend(be, coerce=True):
+...     overridden_me(1, "2")
+...     overridden_me(1.0, "2")
+('override_me', ('1', '2'), {})
+('override_me', ('1.0', '2'), {})
+
+Another feature is that if you remove ``__ua_convert__``, the arguments are not
+converted at all and it's up to the backend to handle that.
+
+>>> del be.__ua_convert__
+>>> with ua.set_backend(be):
+...     overridden_me(1, "2")
+('override_me', (1, '2'), {})
+
+You also have the option to return ``NotImplemented``, in which case processing moves on
+to the next back-end, which in this case, doesn't exist. The same applies to
+``__ua_convert__``.
+
+>>> be.__ua_function__ = lambda *a, **kw: NotImplemented
+>>> with ua.set_backend(be):
+...     overridden_me(1, "2")
+Traceback (most recent call last):
+    ...
+uarray.BackendNotImplementedError: ...
+
+The last possibility is if we don't have ``__ua_convert__``, in which case the job is
+left up to ``__ua_function__``, but putting things back into arrays after conversion
+will not be possible.
+"""
+
+from ._backend import *
+__version__ = '0.8.8.dev0+aa94c5a4.scipy'
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/_backend.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/_backend.py
new file mode 100644
index 0000000000000000000000000000000000000000..87ea71965761ca6916485828ee23d3402bfb1b7d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/_backend.py
@@ -0,0 +1,707 @@
+import typing
+import types
+import inspect
+import functools
+from . import _uarray
+import copyreg
+import pickle
+import contextlib
+import threading
+
+from ._uarray import (  # type: ignore
+    BackendNotImplementedError,
+    _Function,
+    _SkipBackendContext,
+    _SetBackendContext,
+    _BackendState,
+)
+
+__all__ = [
+    "set_backend",
+    "set_global_backend",
+    "skip_backend",
+    "register_backend",
+    "determine_backend",
+    "determine_backend_multi",
+    "clear_backends",
+    "create_multimethod",
+    "generate_multimethod",
+    "_Function",
+    "BackendNotImplementedError",
+    "Dispatchable",
+    "wrap_single_convertor",
+    "wrap_single_convertor_instance",
+    "all_of_type",
+    "mark_as",
+    "set_state",
+    "get_state",
+    "reset_state",
+    "_BackendState",
+    "_SkipBackendContext",
+    "_SetBackendContext",
+]
+
+ArgumentExtractorType = typing.Callable[..., tuple["Dispatchable", ...]]
+ArgumentReplacerType = typing.Callable[
+    [tuple, dict, tuple], tuple[tuple, dict]
+]
+
+def unpickle_function(mod_name, qname, self_):
+    import importlib
+
+    try:
+        module = importlib.import_module(mod_name)
+        qname = qname.split(".")
+        func = module
+        for q in qname:
+            func = getattr(func, q)
+
+        if self_ is not None:
+            func = types.MethodType(func, self_)
+
+        return func
+    except (ImportError, AttributeError) as e:
+        from pickle import UnpicklingError
+
+        raise UnpicklingError from e
+
+
+def pickle_function(func):
+    mod_name = getattr(func, "__module__", None)
+    qname = getattr(func, "__qualname__", None)
+    self_ = getattr(func, "__self__", None)
+
+    try:
+        test = unpickle_function(mod_name, qname, self_)
+    except pickle.UnpicklingError:
+        test = None
+
+    if test is not func:
+        raise pickle.PicklingError(
+            f"Can't pickle {func}: it's not the same object as {test}"
+        )
+
+    return unpickle_function, (mod_name, qname, self_)
+
+
+def pickle_state(state):
+    return _uarray._BackendState._unpickle, state._pickle()
+
+
+def pickle_set_backend_context(ctx):
+    return _SetBackendContext, ctx._pickle()
+
+
+def pickle_skip_backend_context(ctx):
+    return _SkipBackendContext, ctx._pickle()
+
+
+copyreg.pickle(_Function, pickle_function)
+copyreg.pickle(_uarray._BackendState, pickle_state)
+copyreg.pickle(_SetBackendContext, pickle_set_backend_context)
+copyreg.pickle(_SkipBackendContext, pickle_skip_backend_context)
+
+
+def get_state():
+    """
+    Returns an opaque object containing the current state of all the backends.
+
+    Can be used for synchronization between threads/processes.
+
+    See Also
+    --------
+    set_state
+        Sets the state returned by this function.
+    """
+    return _uarray.get_state()
+
+
+@contextlib.contextmanager
+def reset_state():
+    """
+    Returns a context manager that resets all state once exited.
+
+    See Also
+    --------
+    set_state
+        Context manager that sets the backend state.
+    get_state
+        Gets a state to be set by this context manager.
+    """
+    with set_state(get_state()):
+        yield
+
+
+@contextlib.contextmanager
+def set_state(state):
+    """
+    A context manager that sets the state of the backends to one returned by :obj:`get_state`.
+
+    See Also
+    --------
+    get_state
+        Gets a state to be set by this context manager.
+    """  # noqa: E501
+    old_state = get_state()
+    _uarray.set_state(state)
+    try:
+        yield
+    finally:
+        _uarray.set_state(old_state, True)
+
+
+def create_multimethod(*args, **kwargs):
+    """
+    Creates a decorator for generating multimethods.
+
+    This function creates a decorator that can be used with an argument
+    extractor in order to generate a multimethod. Other than for the
+    argument extractor, all arguments are passed on to
+    :obj:`generate_multimethod`.
+
+    See Also
+    --------
+    generate_multimethod
+        Generates a multimethod.
+    """
+
+    def wrapper(a):
+        return generate_multimethod(a, *args, **kwargs)
+
+    return wrapper
+
+
+def generate_multimethod(
+    argument_extractor: ArgumentExtractorType,
+    argument_replacer: ArgumentReplacerType,
+    domain: str,
+    default: typing.Callable | None = None,
+):
+    """
+    Generates a multimethod.
+
+    Parameters
+    ----------
+    argument_extractor : ArgumentExtractorType
+        A callable which extracts the dispatchable arguments. Extracted arguments
+        should be marked by the :obj:`Dispatchable` class. It has the same signature
+        as the desired multimethod.
+    argument_replacer : ArgumentReplacerType
+        A callable with the signature (args, kwargs, dispatchables), which should also
+        return an (args, kwargs) pair with the dispatchables replaced inside the
+        args/kwargs.
+    domain : str
+        A string value indicating the domain of this multimethod.
+    default: Optional[Callable], optional
+        The default implementation of this multimethod, where ``None`` (the default)
+        specifies there is no default implementation.
+
+    Examples
+    --------
+    In this example, ``a`` is to be dispatched over, so we return it, while marking it
+    as an ``int``.
+    The trailing comma is needed because the args have to be returned as an iterable.
+
+    >>> def override_me(a, b):
+    ...   return Dispatchable(a, int),
+
+    Next, we define the argument replacer that replaces the dispatchables inside
+    args/kwargs with the supplied ones.
+
+    >>> def override_replacer(args, kwargs, dispatchables):
+    ...     return (dispatchables[0], args[1]), {}
+
+    Next, we define the multimethod.
+
+    >>> overridden_me = generate_multimethod(
+    ...     override_me, override_replacer, "ua_examples"
+    ... )
+
+    Notice that there's no default implementation, unless you supply one.
+
+    >>> overridden_me(1, "a")
+    Traceback (most recent call last):
+        ...
+    uarray.BackendNotImplementedError: ...
+
+    >>> overridden_me2 = generate_multimethod(
+    ...     override_me, override_replacer, "ua_examples", default=lambda x, y: (x, y)
+    ... )
+    >>> overridden_me2(1, "a")
+    (1, 'a')
+
+    See Also
+    --------
+    uarray
+        See the module documentation for how to override the method by creating
+        backends.
+    """
+    kw_defaults, arg_defaults, opts = get_defaults(argument_extractor)
+    ua_func = _Function(
+        argument_extractor,
+        argument_replacer,
+        domain,
+        arg_defaults,
+        kw_defaults,
+        default,
+    )
+
+    return functools.update_wrapper(ua_func, argument_extractor)
+
+
+def set_backend(backend, coerce=False, only=False):
+    """
+    A context manager that sets the preferred backend.
+
+    Parameters
+    ----------
+    backend
+        The backend to set.
+    coerce
+        Whether or not to coerce to a specific backend's types. Implies ``only``.
+    only
+        Whether or not this should be the last backend to try.
+
+    See Also
+    --------
+    skip_backend: A context manager that allows skipping of backends.
+    set_global_backend: Set a single, global backend for a domain.
+    """
+    tid = threading.get_native_id()
+    try:
+        return backend.__ua_cache__[tid, "set", coerce, only]
+    except AttributeError:
+        backend.__ua_cache__ = {}
+    except KeyError:
+        pass
+
+    ctx = _SetBackendContext(backend, coerce, only)
+    backend.__ua_cache__[tid, "set", coerce, only] = ctx
+    return ctx
+
+
+def skip_backend(backend):
+    """
+    A context manager that allows one to skip a given backend from processing
+    entirely. This allows one to use another backend's code in a library that
+    is also a consumer of the same backend.
+
+    Parameters
+    ----------
+    backend
+        The backend to skip.
+
+    See Also
+    --------
+    set_backend: A context manager that allows setting of backends.
+    set_global_backend: Set a single, global backend for a domain.
+    """
+    tid = threading.get_native_id()
+    try:
+        return backend.__ua_cache__[tid, "skip"]
+    except AttributeError:
+        backend.__ua_cache__ = {}
+    except KeyError:
+        pass
+
+    ctx = _SkipBackendContext(backend)
+    backend.__ua_cache__[tid, "skip"] = ctx
+    return ctx
+
+
+def get_defaults(f):
+    sig = inspect.signature(f)
+    kw_defaults = {}
+    arg_defaults = []
+    opts = set()
+    for k, v in sig.parameters.items():
+        if v.default is not inspect.Parameter.empty:
+            kw_defaults[k] = v.default
+        if v.kind in (
+            inspect.Parameter.POSITIONAL_ONLY,
+            inspect.Parameter.POSITIONAL_OR_KEYWORD,
+        ):
+            arg_defaults.append(v.default)
+        opts.add(k)
+
+    return kw_defaults, tuple(arg_defaults), opts
+
+
+def set_global_backend(backend, coerce=False, only=False, *, try_last=False):
+    """
+    This utility method replaces the default backend for permanent use. It
+    will be tried in the list of backends automatically, unless the
+    ``only`` flag is set on a backend. This will be the first tried
+    backend outside the :obj:`set_backend` context manager.
+
+    Note that this method is not thread-safe.
+
+    .. warning::
+        We caution library authors against using this function in
+        their code. We do *not* support this use-case. This function
+        is meant to be used only by users themselves, or by a reference
+        implementation, if one exists.
+
+    Parameters
+    ----------
+    backend
+        The backend to register.
+    coerce : bool
+        Whether to coerce input types when trying this backend.
+    only : bool
+        If ``True``, no more backends will be tried if this fails.
+        Implied by ``coerce=True``.
+    try_last : bool
+        If ``True``, the global backend is tried after registered backends.
+
+    See Also
+    --------
+    set_backend: A context manager that allows setting of backends.
+    skip_backend: A context manager that allows skipping of backends.
+    """
+    _uarray.set_global_backend(backend, coerce, only, try_last)
+
+
+def register_backend(backend):
+    """
+    This utility method sets registers backend for permanent use. It
+    will be tried in the list of backends automatically, unless the
+    ``only`` flag is set on a backend.
+
+    Note that this method is not thread-safe.
+
+    Parameters
+    ----------
+    backend
+        The backend to register.
+    """
+    _uarray.register_backend(backend)
+
+
+def clear_backends(domain, registered=True, globals=False):
+    """
+    This utility method clears registered backends.
+
+    .. warning::
+        We caution library authors against using this function in
+        their code. We do *not* support this use-case. This function
+        is meant to be used only by users themselves.
+
+    .. warning::
+        Do NOT use this method inside a multimethod call, or the
+        program is likely to crash.
+
+    Parameters
+    ----------
+    domain : Optional[str]
+        The domain for which to de-register backends. ``None`` means
+        de-register for all domains.
+    registered : bool
+        Whether or not to clear registered backends. See :obj:`register_backend`.
+    globals : bool
+        Whether or not to clear global backends. See :obj:`set_global_backend`.
+
+    See Also
+    --------
+    register_backend : Register a backend globally.
+    set_global_backend : Set a global backend.
+    """
+    _uarray.clear_backends(domain, registered, globals)
+
+
+class Dispatchable:
+    """
+    A utility class which marks an argument with a specific dispatch type.
+
+
+    Attributes
+    ----------
+    value
+        The value of the Dispatchable.
+
+    type
+        The type of the Dispatchable.
+
+    Examples
+    --------
+    >>> x = Dispatchable(1, str)
+    >>> x
+    , value=1>
+
+    See Also
+    --------
+    all_of_type
+        Marks all unmarked parameters of a function.
+
+    mark_as
+        Allows one to create a utility function to mark as a given type.
+    """
+
+    def __init__(self, value, dispatch_type, coercible=True):
+        self.value = value
+        self.type = dispatch_type
+        self.coercible = coercible
+
+    def __getitem__(self, index):
+        return (self.type, self.value)[index]
+
+    def __str__(self):
+        return f"<{type(self).__name__}: type={self.type!r}, value={self.value!r}>"
+
+    __repr__ = __str__
+
+
+def mark_as(dispatch_type):
+    """
+    Creates a utility function to mark something as a specific type.
+
+    Examples
+    --------
+    >>> mark_int = mark_as(int)
+    >>> mark_int(1)
+    , value=1>
+    """
+    return functools.partial(Dispatchable, dispatch_type=dispatch_type)
+
+
+def all_of_type(arg_type):
+    """
+    Marks all unmarked arguments as a given type.
+
+    Examples
+    --------
+    >>> @all_of_type(str)
+    ... def f(a, b):
+    ...     return a, Dispatchable(b, int)
+    >>> f('a', 1)
+    (, value='a'>,
+     , value=1>)
+    """
+
+    def outer(func):
+        @functools.wraps(func)
+        def inner(*args, **kwargs):
+            extracted_args = func(*args, **kwargs)
+            return tuple(
+                Dispatchable(arg, arg_type)
+                if not isinstance(arg, Dispatchable)
+                else arg
+                for arg in extracted_args
+            )
+
+        return inner
+
+    return outer
+
+
+def wrap_single_convertor(convert_single):
+    """
+    Wraps a ``__ua_convert__`` defined for a single element to all elements.
+    If any of them return ``NotImplemented``, the operation is assumed to be
+    undefined.
+
+    Accepts a signature of (value, type, coerce).
+    """
+
+    @functools.wraps(convert_single)
+    def __ua_convert__(dispatchables, coerce):
+        converted = []
+        for d in dispatchables:
+            c = convert_single(d.value, d.type, coerce and d.coercible)
+
+            if c is NotImplemented:
+                return NotImplemented
+
+            converted.append(c)
+
+        return converted
+
+    return __ua_convert__
+
+
+def wrap_single_convertor_instance(convert_single):
+    """
+    Wraps a ``__ua_convert__`` defined for a single element to all elements.
+    If any of them return ``NotImplemented``, the operation is assumed to be
+    undefined.
+
+    Accepts a signature of (value, type, coerce).
+    """
+
+    @functools.wraps(convert_single)
+    def __ua_convert__(self, dispatchables, coerce):
+        converted = []
+        for d in dispatchables:
+            c = convert_single(self, d.value, d.type, coerce and d.coercible)
+
+            if c is NotImplemented:
+                return NotImplemented
+
+            converted.append(c)
+
+        return converted
+
+    return __ua_convert__
+
+
+def determine_backend(value, dispatch_type, *, domain, only=True, coerce=False):
+    """Set the backend to the first active backend that supports ``value``
+
+    This is useful for functions that call multimethods without any dispatchable
+    arguments. You can use :func:`determine_backend` to ensure the same backend
+    is used everywhere in a block of multimethod calls.
+
+    Parameters
+    ----------
+    value
+        The value being tested
+    dispatch_type
+        The dispatch type associated with ``value``, aka
+        ":ref:`marking `".
+    domain: string
+        The domain to query for backends and set.
+    coerce: bool
+        Whether or not to allow coercion to the backend's types. Implies ``only``.
+    only: bool
+        Whether or not this should be the last backend to try.
+
+    See Also
+    --------
+    set_backend: For when you know which backend to set
+
+    Notes
+    -----
+
+    Support is determined by the ``__ua_convert__`` protocol. Backends not
+    supporting the type must return ``NotImplemented`` from their
+    ``__ua_convert__`` if they don't support input of that type.
+
+    Examples
+    --------
+
+    Suppose we have two backends ``BackendA`` and ``BackendB`` each supporting
+    different types, ``TypeA`` and ``TypeB``. Neither supporting the other type:
+
+    >>> with ua.set_backend(ex.BackendA):
+    ...     ex.call_multimethod(ex.TypeB(), ex.TypeB())
+    Traceback (most recent call last):
+        ...
+    uarray.BackendNotImplementedError: ...
+
+    Now consider a multimethod that creates a new object of ``TypeA``, or
+    ``TypeB`` depending on the active backend.
+
+    >>> with ua.set_backend(ex.BackendA), ua.set_backend(ex.BackendB):
+    ...         res = ex.creation_multimethod()
+    ...         ex.call_multimethod(res, ex.TypeA())
+    Traceback (most recent call last):
+        ...
+    uarray.BackendNotImplementedError: ...
+
+    ``res`` is an object of ``TypeB`` because ``BackendB`` is set in the
+    innermost with statement. So, ``call_multimethod`` fails since the types
+    don't match.
+
+    Instead, we need to first find a backend suitable for all of our objects.
+
+    >>> with ua.set_backend(ex.BackendA), ua.set_backend(ex.BackendB):
+    ...     x = ex.TypeA()
+    ...     with ua.determine_backend(x, "mark", domain="ua_examples"):
+    ...         res = ex.creation_multimethod()
+    ...         ex.call_multimethod(res, x)
+    TypeA
+
+    """
+    dispatchables = (Dispatchable(value, dispatch_type, coerce),)
+    backend = _uarray.determine_backend(domain, dispatchables, coerce)
+
+    return set_backend(backend, coerce=coerce, only=only)
+
+
+def determine_backend_multi(
+    dispatchables, *, domain, only=True, coerce=False, **kwargs
+):
+    """Set a backend supporting all ``dispatchables``
+
+    This is useful for functions that call multimethods without any dispatchable
+    arguments. You can use :func:`determine_backend_multi` to ensure the same
+    backend is used everywhere in a block of multimethod calls involving
+    multiple arrays.
+
+    Parameters
+    ----------
+    dispatchables: Sequence[Union[uarray.Dispatchable, Any]]
+        The dispatchables that must be supported
+    domain: string
+        The domain to query for backends and set.
+    coerce: bool
+        Whether or not to allow coercion to the backend's types. Implies ``only``.
+    only: bool
+        Whether or not this should be the last backend to try.
+    dispatch_type: Optional[Any]
+        The default dispatch type associated with ``dispatchables``, aka
+        ":ref:`marking `".
+
+    See Also
+    --------
+    determine_backend: For a single dispatch value
+    set_backend: For when you know which backend to set
+
+    Notes
+    -----
+
+    Support is determined by the ``__ua_convert__`` protocol. Backends not
+    supporting the type must return ``NotImplemented`` from their
+    ``__ua_convert__`` if they don't support input of that type.
+
+    Examples
+    --------
+
+    :func:`determine_backend` allows the backend to be set from a single
+    object. :func:`determine_backend_multi` allows multiple objects to be
+    checked simultaneously for support in the backend. Suppose we have a
+    ``BackendAB`` which supports ``TypeA`` and ``TypeB`` in the same call,
+    and a ``BackendBC`` that doesn't support ``TypeA``.
+
+    >>> with ua.set_backend(ex.BackendAB), ua.set_backend(ex.BackendBC):
+    ...     a, b = ex.TypeA(), ex.TypeB()
+    ...     with ua.determine_backend_multi(
+    ...         [ua.Dispatchable(a, "mark"), ua.Dispatchable(b, "mark")],
+    ...         domain="ua_examples"
+    ...     ):
+    ...         res = ex.creation_multimethod()
+    ...         ex.call_multimethod(res, a, b)
+    TypeA
+
+    This won't call ``BackendBC`` because it doesn't support ``TypeA``.
+
+    We can also use leave out the ``ua.Dispatchable`` if we specify the
+    default ``dispatch_type`` for the ``dispatchables`` argument.
+
+    >>> with ua.set_backend(ex.BackendAB), ua.set_backend(ex.BackendBC):
+    ...     a, b = ex.TypeA(), ex.TypeB()
+    ...     with ua.determine_backend_multi(
+    ...         [a, b], dispatch_type="mark", domain="ua_examples"
+    ...     ):
+    ...         res = ex.creation_multimethod()
+    ...         ex.call_multimethod(res, a, b)
+    TypeA
+
+    """
+    if "dispatch_type" in kwargs:
+        disp_type = kwargs.pop("dispatch_type")
+        dispatchables = tuple(
+            d if isinstance(d, Dispatchable) else Dispatchable(d, disp_type)
+            for d in dispatchables
+        )
+    else:
+        dispatchables = tuple(dispatchables)
+        if not all(isinstance(d, Dispatchable) for d in dispatchables):
+            raise TypeError("dispatchables must be instances of uarray.Dispatchable")
+
+    if len(kwargs) != 0:
+        raise TypeError(f"Received unexpected keyword arguments: {kwargs}")
+
+    backend = _uarray.determine_backend(domain, dispatchables, coerce)
+
+    return set_backend(backend, coerce=coerce, only=only)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/_uarray.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/_uarray.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..b4360f1443449c7be372ebd8be476a640658df57
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_uarray/_uarray.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9047dbd782d4d3a95c337a45951ebfa14dfc115ae14b366b028fe067b8549961
+size 120656
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_util.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_util.py
new file mode 100644
index 0000000000000000000000000000000000000000..fd8130ad008d6eaa0cc022a4d6f50da2dab47f96
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/_util.py
@@ -0,0 +1,1251 @@
+import re
+from contextlib import contextmanager
+import functools
+import operator
+import warnings
+import numbers
+from collections import namedtuple
+import inspect
+import math
+import os
+import sys
+import textwrap
+from types import ModuleType
+from typing import Literal, TypeAlias, TypeVar
+
+import numpy as np
+from scipy._lib._array_api import (Array, array_namespace, is_lazy_array, is_numpy,
+                                   is_marray, xp_size, xp_result_device, xp_result_type)
+from scipy._lib._docscrape import FunctionDoc, Parameter
+from scipy._lib._sparse import issparse
+
+from numpy.exceptions import AxisError
+
+
+np_long: type
+np_ulong: type
+
+if np.lib.NumpyVersion(np.__version__) >= "2.0.0.dev0":
+    try:
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                r".*In the future `np\.long` will be defined as.*",
+                FutureWarning,
+            )
+            np_long = np.long  # type: ignore[attr-defined]
+            np_ulong = np.ulong  # type: ignore[attr-defined]
+    except AttributeError:
+            np_long = np.int_
+            np_ulong = np.uint
+else:
+    np_long = np.int_
+    np_ulong = np.uint
+
+IntNumber = int | np.integer
+DecimalNumber = float | np.floating | np.integer
+
+copy_if_needed: bool | None
+
+if np.lib.NumpyVersion(np.__version__) >= "2.0.0":
+    copy_if_needed = None
+elif np.lib.NumpyVersion(np.__version__) < "1.28.0":
+    copy_if_needed = False
+else:
+    # 2.0.0 dev versions, handle cases where copy may or may not exist
+    try:
+        np.array([1]).__array__(copy=None)  # type: ignore[call-overload]
+        copy_if_needed = None
+    except TypeError:
+        copy_if_needed = False
+
+
+# Wrapped function for inspect.signature for compatibility with Python 3.14+
+# See gh-23913
+#
+# PEP 649/749 allows for underfined annotations at runtime, and added the
+# `annotation_format` parameter to handle these cases.
+# `annotationlib.Format.FORWARDREF` is the closest to previous behavior,
+# returning ForwardRef objects fornew undefined annotations cases.
+#
+# Consider dropping this wrapper when support for Python 3.13 is dropped.
+if sys.version_info >= (3, 14):
+    import annotationlib
+    def wrapped_inspect_signature(callable):
+        """Get a signature object for the passed callable."""
+        return inspect.signature(callable,
+                                 annotation_format=annotationlib.Format.FORWARDREF)
+else:
+    wrapped_inspect_signature = inspect.signature
+
+
+_RNG: TypeAlias = np.random.Generator | np.random.RandomState
+SeedType: TypeAlias = IntNumber | _RNG | None
+
+GeneratorType = TypeVar("GeneratorType", bound=_RNG)
+
+
+def _lazyselect(condlist, choicelist, arrays, default=0):
+    """
+    Mimic `np.select(condlist, choicelist)`.
+
+    Notice, it assumes that all `arrays` are of the same shape or can be
+    broadcasted together.
+
+    All functions in `choicelist` must accept array arguments in the order
+    given in `arrays` and must return an array of the same shape as broadcasted
+    `arrays`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6)
+    >>> np.select([x <3, x > 3], [x**2, x**3], default=0)
+    array([  0,   1,   4,   0,  64, 125])
+
+    >>> _lazyselect([x < 3, x > 3], [lambda x: x**2, lambda x: x**3], (x,))
+    array([   0.,    1.,    4.,   0.,   64.,  125.])
+
+    >>> a = -np.ones_like(x)
+    >>> _lazyselect([x < 3, x > 3],
+    ...             [lambda x, a: x**2, lambda x, a: a * x**3],
+    ...             (x, a), default=np.nan)
+    array([   0.,    1.,    4.,   nan,  -64., -125.])
+
+    """
+    arrays = np.broadcast_arrays(*arrays)
+    tcode = np.mintypecode([a.dtype.char for a in arrays])
+    out = np.full(np.shape(arrays[0]), fill_value=default, dtype=tcode)
+    for func, cond in zip(choicelist, condlist):
+        if np.all(cond is False):
+            continue
+        cond, _ = np.broadcast_arrays(cond, arrays[0])
+        temp = tuple(np.extract(cond, arr) for arr in arrays)
+        np.place(out, cond, func(*temp))
+    return out
+
+
+def _aligned_zeros(shape, dtype=float, order="C", align=None):
+    """Allocate a new ndarray with aligned memory.
+
+    Primary use case for this currently is working around a f2py issue
+    in NumPy 1.9.1, where dtype.alignment is such that np.zeros() does
+    not necessarily create arrays aligned up to it.
+
+    """
+    dtype = np.dtype(dtype)
+    if align is None:
+        align = dtype.alignment
+    if not hasattr(shape, '__len__'):
+        shape = (shape,)
+    size = functools.reduce(operator.mul, shape) * dtype.itemsize
+    buf = np.empty(size + align + 1, np.uint8)
+    offset = buf.__array_interface__['data'][0] % align
+    if offset != 0:
+        offset = align - offset
+    # Note: slices producing 0-size arrays do not necessarily change
+    # data pointer --- so we use and allocate size+1
+    buf = buf[offset:offset+size+1][:-1]
+    data = np.ndarray(shape, dtype, buf, order=order)
+    data.fill(0)
+    return data
+
+
+def _prune_array(array):
+    """Return an array equivalent to the input array. If the input
+    array is a view of a much larger array, copy its contents to a
+    newly allocated array. Otherwise, return the input unchanged.
+    """
+    if array.base is not None and array.size < array.base.size // 2:
+        return array.copy()
+    return array
+
+
+def float_factorial(n: int) -> float:
+    """Compute the factorial and return as a float
+
+    Returns infinity when result is too large for a double
+    """
+    return float(math.factorial(n)) if n < 171 else np.inf
+
+
+_rng_desc = (
+    r"""If `rng` is passed by keyword, types other than `numpy.random.Generator` are
+    passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+    If `rng` is already a ``Generator`` instance, then the provided instance is
+    used. Specify `rng` for repeatable function behavior.
+
+    If this argument is passed by position or `{old_name}` is passed by keyword,
+    legacy behavior for the argument `{old_name}` applies:
+
+    - If `{old_name}` is None (or `numpy.random`), the `numpy.random.RandomState`
+      singleton is used.
+    - If `{old_name}` is an int, a new ``RandomState`` instance is used,
+      seeded with `{old_name}`.
+    - If `{old_name}` is already a ``Generator`` or ``RandomState`` instance then
+      that instance is used.
+
+    .. versionchanged:: 1.15.0
+        As part of the `SPEC-007 `_
+        transition from use of `numpy.random.RandomState` to
+        `numpy.random.Generator`, this keyword was changed from `{old_name}` to `rng`.
+        For an interim period, both keywords will continue to work, although only one
+        may be specified at a time. After the interim period, function calls using the
+        `{old_name}` keyword will emit warnings. The behavior of both `{old_name}` and
+        `rng` are outlined above, but only the `rng` keyword should be used in new code.
+        """
+)
+
+
+# SPEC 7
+def _transition_to_rng(old_name, *, position_num=None, end_version=None,
+                       replace_doc=True):
+    """Example decorator to transition from old PRNG usage to new `rng` behavior
+
+    Suppose the decorator is applied to a function that used to accept parameter
+    `old_name='random_state'` either by keyword or as a positional argument at
+    `position_num=1`. At the time of application, the name of the argument in the
+    function signature is manually changed to the new name, `rng`. If positional
+    use was allowed before, this is not changed.*
+
+    - If the function is called with both `random_state` and `rng`, the decorator
+      raises an error.
+    - If `random_state` is provided as a keyword argument, the decorator passes
+      `random_state` to the function's `rng` argument as a keyword. If `end_version`
+      is specified, the decorator will emit a `DeprecationWarning` about the
+      deprecation of keyword `random_state`.
+    - If `random_state` is provided as a positional argument, the decorator passes
+      `random_state` to the function's `rng` argument by position. If `end_version`
+      is specified, the decorator will emit a `FutureWarning` about the changing
+      interpretation of the argument.
+    - If `rng` is provided as a keyword argument, the decorator validates `rng` using
+      `numpy.random.default_rng` before passing it to the function.
+    - If `end_version` is specified and neither `random_state` nor `rng` is provided
+      by the user, the decorator checks whether `np.random.seed` has been used to set
+      the global seed. If so, it emits a `FutureWarning`, noting that usage of
+      `numpy.random.seed` will eventually have no effect. Either way, the decorator
+      calls the function without explicitly passing the `rng` argument.
+
+    If `end_version` is specified, a user must pass `rng` as a keyword to avoid
+    warnings.
+
+    After the deprecation period, the decorator can be removed, and the function
+    can simply validate the `rng` argument by calling `np.random.default_rng(rng)`.
+
+    * A `FutureWarning` is emitted when the PRNG argument is used by
+      position. It indicates that the "Hinsen principle" (same
+      code yielding different results in two versions of the software)
+      will be violated, unless positional use is deprecated. Specifically:
+
+      - If `None` is passed by position and `np.random.seed` has been used,
+        the function will change from being seeded to being unseeded.
+      - If an integer is passed by position, the random stream will change.
+      - If `np.random` or an instance of `RandomState` is passed by position,
+        an error will be raised.
+
+      We suggest that projects consider deprecating positional use of
+      `random_state`/`rng` (i.e., change their function signatures to
+      ``def my_func(..., *, rng=None)``); that might not make sense
+      for all projects, so this SPEC does not make that
+      recommendation, neither does this decorator enforce it.
+
+    Parameters
+    ----------
+    old_name : str
+        The old name of the PRNG argument (e.g. `seed` or `random_state`).
+    position_num : int, optional
+        The (0-indexed) position of the old PRNG argument (if accepted by position).
+        Maintainers are welcome to eliminate this argument and use, for example,
+        `inspect`, if preferred.
+    end_version : str, optional
+        The full version number of the library when the behavior described in
+        `DeprecationWarning`s and `FutureWarning`s will take effect. If left
+        unspecified, no warnings will be emitted by the decorator.
+    replace_doc : bool, default: True
+        Whether the decorator should replace the documentation for parameter `rng` with
+        `_rng_desc` (defined above), which documents both new `rng` keyword behavior
+        and typical legacy `random_state`/`seed` behavior. If True, manually replace
+        the first paragraph of the function's old `random_state`/`seed` documentation
+        with the desired *final* `rng` documentation; this way, no changes to
+        documentation are needed when the decorator is removed. Documentation of `rng`
+        after the first blank line is preserved. Use False if the function's old
+        `random_state`/`seed` behavior does not match that described by `_rng_desc`.
+
+    """
+    NEW_NAME = "rng"
+
+    cmn_msg = (
+        "To silence this warning and ensure consistent behavior in SciPy "
+        f"{end_version}, control the RNG using argument `{NEW_NAME}`. Arguments passed "
+        f"to keyword `{NEW_NAME}` will be validated by `np.random.default_rng`, so the "
+        "behavior corresponding with a given value may change compared to use of "
+        f"`{old_name}`. For example, "
+        "1) `None` will result in unpredictable random numbers, "
+        "2) an integer will result in a different stream of random numbers, (with the "
+        "same distribution), and "
+        "3) `np.random` or `RandomState` instances will result in an error. "
+        "See the documentation of `default_rng` for more information."
+    )
+
+    def decorator(fun):
+        @functools.wraps(fun)
+        def wrapper(*args, **kwargs):
+            # Determine how PRNG was passed
+            as_old_kwarg = old_name in kwargs
+            as_new_kwarg = NEW_NAME in kwargs
+            as_pos_arg = position_num is not None and len(args) >= position_num + 1
+            emit_warning = end_version is not None
+
+            # Can only specify PRNG one of the three ways
+            if int(as_old_kwarg) + int(as_new_kwarg) + int(as_pos_arg) > 1:
+                message = (
+                    f"{fun.__name__}() got multiple values for "
+                    f"argument now known as `{NEW_NAME}`. Specify one of "
+                    f"`{NEW_NAME}` or `{old_name}`."
+                )
+                raise TypeError(message)
+
+            # Check whether global random state has been set
+            global_seed_set = np.random.mtrand._rand._bit_generator._seed_seq is None
+
+            if as_old_kwarg:  # warn about deprecated use of old kwarg
+                kwargs[NEW_NAME] = kwargs.pop(old_name)
+                if emit_warning:
+                    message = (
+                        f"Use of keyword argument `{old_name}` is "
+                        f"deprecated and replaced by `{NEW_NAME}`.  "
+                        f"Support for `{old_name}` will be removed "
+                        f"in SciPy {end_version}. "
+                    ) + cmn_msg
+                    warnings.warn(message, DeprecationWarning, stacklevel=2)
+
+            elif as_pos_arg:
+                # Warn about changing meaning of positional arg
+
+                # Note that this decorator does not deprecate positional use of the
+                # argument; it only warns that the behavior will change in the future.
+                # Simultaneously transitioning to keyword-only use is another option.
+
+                arg = args[position_num]
+                # If the argument is None and the global seed wasn't set, or if the
+                # argument is one of a few new classes, the user will not notice change
+                # in behavior.
+                ok_classes = (
+                    np.random.Generator,
+                    np.random.SeedSequence,
+                    np.random.BitGenerator,
+                )
+                if (arg is None and not global_seed_set) or isinstance(arg, ok_classes):
+                    pass
+                elif emit_warning:
+                    message = (
+                        f"Positional use of `{NEW_NAME}` (formerly known as "
+                        f"`{old_name}`) is still allowed, but the behavior is "
+                        "changing: the argument will be normalized using "
+                        f"`np.random.default_rng` beginning in SciPy {end_version}, "
+                        "and the resulting `Generator` will be used to generate "
+                        "random numbers."
+                    ) + cmn_msg
+                    warnings.warn(message, FutureWarning, stacklevel=2)
+
+            elif as_new_kwarg:  # no warnings; this is the preferred use
+                # After the removal of the decorator, normalization with
+                # np.random.default_rng will be done inside the decorated function
+                kwargs[NEW_NAME] = np.random.default_rng(kwargs[NEW_NAME])
+
+            elif global_seed_set and emit_warning:
+                # Emit FutureWarning if `np.random.seed` was used and no PRNG was passed
+                message = (
+                    "The NumPy global RNG was seeded by calling "
+                    f"`np.random.seed`. Beginning in {end_version}, this "
+                    "function will no longer use the global RNG."
+                ) + cmn_msg
+                warnings.warn(message, FutureWarning, stacklevel=2)
+
+            return fun(*args, **kwargs)
+
+        # Add the old parameter name to the function signature
+        wrapped_signature = inspect.signature(fun)
+        wrapper.__signature__ = wrapped_signature.replace(parameters=[
+            *wrapped_signature.parameters.values(),
+            inspect.Parameter(old_name, inspect.Parameter.KEYWORD_ONLY, default=None),
+        ])
+
+        if replace_doc:
+            doc = FunctionDoc(wrapper)
+            parameter_names = [param.name for param in doc['Parameters']]
+            if 'rng' in parameter_names:
+                _type = "{None, int, `numpy.random.Generator`}, optional"
+                _desc = _rng_desc.replace("{old_name}", old_name)
+                old_doc = doc['Parameters'][parameter_names.index('rng')].desc
+                old_doc_keep = old_doc[old_doc.index("") + 1:] if "" in old_doc else []
+                new_doc = [_desc] + old_doc_keep
+                _rng_parameter_doc = Parameter('rng', _type, new_doc)
+                doc['Parameters'][parameter_names.index('rng')] = _rng_parameter_doc
+                doc = str(doc).split("\n", 1)[1].lstrip(" \n")  # remove signature
+                wrapper.__doc__ = str(doc)
+        return wrapper
+
+    return decorator
+
+
+# copy-pasted from scikit-learn utils/validation.py
+def check_random_state(seed):
+    """Turn `seed` into a `np.random.RandomState` instance.
+
+    Parameters
+    ----------
+    seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional
+        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
+        singleton is used.
+        If `seed` is an int, a new ``RandomState`` instance is used,
+        seeded with `seed`.
+        If `seed` is already a ``Generator`` or ``RandomState`` instance then
+        that instance is used.
+
+    Returns
+    -------
+    seed : {`numpy.random.Generator`, `numpy.random.RandomState`}
+        Random number generator.
+
+    """
+    if seed is None or seed is np.random:
+        return np.random.mtrand._rand
+    if isinstance(seed, numbers.Integral | np.integer):
+        return np.random.RandomState(seed)
+    if isinstance(seed, np.random.RandomState | np.random.Generator):
+        return seed
+
+    raise ValueError(f"'{seed}' cannot be used to seed a numpy.random.RandomState"
+                     " instance")
+
+
+def _asarray_validated(a, check_finite=True,
+                       sparse_ok=False, objects_ok=False, mask_ok=False,
+                       as_inexact=False):
+    """
+    Helper function for SciPy argument validation.
+
+    Many SciPy linear algebra functions do support arbitrary array-like
+    input arguments. Examples of commonly unsupported inputs include
+    matrices containing inf/nan, sparse matrix representations, and
+    matrices with complicated elements.
+
+    Parameters
+    ----------
+    a : array_like
+        The array-like input.
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+    sparse_ok : bool, optional
+        True if scipy sparse matrices are allowed.
+    objects_ok : bool, optional
+        True if arrays with dype('O') are allowed.
+    mask_ok : bool, optional
+        True if masked arrays are allowed.
+    as_inexact : bool, optional
+        True to convert the input array to a np.inexact dtype.
+
+    Returns
+    -------
+    ret : ndarray
+        The converted validated array.
+
+    """
+    if not sparse_ok:
+        if issparse(a):
+            msg = ('Sparse arrays/matrices are not supported by this function. '
+                   'Perhaps one of the `scipy.sparse.linalg` functions '
+                   'would work instead.')
+            raise ValueError(msg)
+    if not mask_ok:
+        if np.ma.isMaskedArray(a):
+            raise ValueError('masked arrays are not supported')
+    toarray = np.asarray_chkfinite if check_finite else np.asarray
+    a = toarray(a)
+    if not objects_ok:
+        if a.dtype is np.dtype('O'):
+            raise ValueError('object arrays are not supported')
+    if as_inexact:
+        if not np.issubdtype(a.dtype, np.inexact):
+            a = toarray(a, dtype=np.float64)
+    return a
+
+
+def _validate_int(k, name, minimum=None):
+    """
+    Validate a scalar integer.
+
+    This function can be used to validate an argument to a function
+    that expects the value to be an integer.  It uses `operator.index`
+    to validate the value (so, for example, k=2.0 results in a
+    TypeError).
+
+    Parameters
+    ----------
+    k : int
+        The value to be validated.
+    name : str
+        The name of the parameter.
+    minimum : int, optional
+        An optional lower bound.
+    """
+    try:
+        k = operator.index(k)
+    except TypeError:
+        raise TypeError(f'{name} must be an integer.') from None
+    if minimum is not None and k < minimum:
+        raise ValueError(f'{name} must be an integer not less '
+                         f'than {minimum}') from None
+    return k
+
+
+# Add a replacement for inspect.getfullargspec()/
+# The version below is borrowed from Django,
+# https://github.com/django/django/pull/4846.
+
+# Note an inconsistency between inspect.getfullargspec(func) and
+# inspect.signature(func). If `func` is a bound method, the latter does *not*
+# list `self` as a first argument, while the former *does*.
+# Hence, cook up a common ground replacement: `getfullargspec_no_self` which
+# mimics `inspect.getfullargspec` but does not list `self`.
+#
+# This way, the caller code does not need to know whether it uses a legacy
+# .getfullargspec or a bright and shiny .signature.
+
+FullArgSpec = namedtuple('FullArgSpec',
+                         ['args', 'varargs', 'varkw', 'defaults',
+                          'kwonlyargs', 'kwonlydefaults', 'annotations'])
+
+
+def getfullargspec_no_self(func):
+    """inspect.getfullargspec replacement using inspect.signature.
+
+    If func is a bound method, do not list the 'self' parameter.
+
+    Parameters
+    ----------
+    func : callable
+        A callable to inspect
+
+    Returns
+    -------
+    fullargspec : FullArgSpec(args, varargs, varkw, defaults, kwonlyargs,
+                              kwonlydefaults, annotations)
+
+        NOTE: if the first argument of `func` is self, it is *not*, I repeat
+        *not*, included in fullargspec.args.
+        This is done for consistency between inspect.getargspec() under
+        Python 2.x, and inspect.signature() under Python 3.x.
+
+    """
+    sig = wrapped_inspect_signature(func)
+    args = [
+        p.name for p in sig.parameters.values()
+        if p.kind in [inspect.Parameter.POSITIONAL_OR_KEYWORD,
+                      inspect.Parameter.POSITIONAL_ONLY]
+    ]
+    varargs = [
+        p.name for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.VAR_POSITIONAL
+    ]
+    varargs = varargs[0] if varargs else None
+    varkw = [
+        p.name for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.VAR_KEYWORD
+    ]
+    varkw = varkw[0] if varkw else None
+    defaults = tuple(
+        p.default for p in sig.parameters.values()
+        if (p.kind == inspect.Parameter.POSITIONAL_OR_KEYWORD and
+            p.default is not p.empty)
+    ) or None
+    kwonlyargs = [
+        p.name for p in sig.parameters.values()
+        if p.kind == inspect.Parameter.KEYWORD_ONLY
+    ]
+    kwdefaults = {p.name: p.default for p in sig.parameters.values()
+                  if p.kind == inspect.Parameter.KEYWORD_ONLY and
+                  p.default is not p.empty}
+    annotations = {p.name: p.annotation for p in sig.parameters.values()
+                   if p.annotation is not p.empty}
+    return FullArgSpec(args, varargs, varkw, defaults, kwonlyargs,
+                       kwdefaults or None, annotations)
+
+
+class _FunctionWrapper:
+    """
+    Object to wrap user's function, allowing picklability
+    """
+    def __init__(self, f, args):
+        self.f = f
+        self.args = [] if args is None else args
+
+    def __call__(self, x):
+        return self.f(x, *self.args)
+
+
+class _ScalarFunctionWrapper:
+    """
+    Object to wrap scalar user function, allowing picklability
+    """
+    def __init__(self, f, args=None):
+        self.f = f
+        self.args = [] if args is None else args
+        self.nfev = 0
+
+    def __call__(self, x):
+        # Send a copy because the user may overwrite it.
+        # The user of this class might want `x` to remain unchanged.
+        fx = self.f(np.copy(x), *self.args)
+        self.nfev += 1
+
+        # Make sure the function returns a true scalar
+        if not np.isscalar(fx):
+            try:
+                fx = np.asarray(fx).item()
+            except (TypeError, ValueError) as e:
+                raise ValueError(
+                    "The user-provided objective function "
+                    "must return a scalar value."
+                ) from e
+        return fx
+
+class MapWrapper:
+    """
+    Parallelisation wrapper for working with map-like callables, such as
+    `multiprocessing.Pool.map`.
+
+    Parameters
+    ----------
+    pool : int or map-like callable
+        If `pool` is an integer, then it specifies the number of threads to
+        use for parallelization. If ``int(pool) == 1``, then no parallel
+        processing is used and the map builtin is used.
+        If ``pool == -1``, then the pool will utilize all available CPUs.
+        If `pool` is a map-like callable that follows the same
+        calling sequence as the built-in map function, then this callable is
+        used for parallelization.
+    """
+    def __init__(self, pool=1):
+        self.pool = None
+        self._mapfunc = map
+        self._own_pool = False
+
+        if callable(pool):
+            self.pool = pool
+            self._mapfunc = self.pool
+        else:
+            from multiprocessing import get_context, get_start_method
+
+            method = get_start_method(allow_none=True)
+
+            if method is None and os.name=='posix' and sys.version_info < (3, 14):
+                # Python 3.13 and older used "fork" on posix, which can lead to
+                # deadlocks. This backports that fix to older Python versions.
+                method = 'forkserver'
+
+            # user supplies a number
+            if int(pool) == -1:
+                # use as many processors as possible
+                self.pool = get_context(method=method).Pool()
+                self._mapfunc = self.pool.map
+                self._own_pool = True
+            elif int(pool) == 1:
+                pass
+            elif int(pool) > 1:
+                # use the number of processors requested
+                self.pool = get_context(method=method).Pool(processes=int(pool))
+                self._mapfunc = self.pool.map
+                self._own_pool = True
+            else:
+                raise RuntimeError("Number of workers specified must be -1,"
+                                   " an int >= 1, or an object with a 'map' "
+                                   "method")
+
+    def __enter__(self):
+        return self
+
+    def terminate(self):
+        if self._own_pool:
+            self.pool.terminate()
+
+    def join(self):
+        if self._own_pool:
+            self.pool.join()
+
+    def close(self):
+        if self._own_pool:
+            self.pool.close()
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        if self._own_pool:
+            self.pool.close()
+            self.pool.terminate()
+
+    def __call__(self, func, iterable):
+        # only accept one iterable because that's all Pool.map accepts
+        try:
+            return self._mapfunc(func, iterable)
+        except TypeError as e:
+            # wrong number of arguments
+            raise TypeError("The map-like callable must be of the"
+                            " form f(func, iterable)") from e
+
+
+def _workers_wrapper(func):
+    """
+    Wrapper to deal with setup-cleanup of workers outside a user function via a
+    ContextManager. It saves having to do the setup/tear down with within that
+    function, which can be messy.
+    """
+    @functools.wraps(func)
+    def inner(*args, **kwds):
+        kwargs = kwds.copy()
+        if 'workers' not in kwargs:
+            _workers = map
+        elif 'workers' in kwargs and kwargs['workers'] is None:
+            _workers = map
+        else:
+            _workers = kwargs['workers']
+
+        with MapWrapper(_workers) as mf:
+            kwargs['workers'] = mf
+            return func(*args, **kwargs)
+
+    return inner
+
+
+def rng_integers(gen, low, high=None, size=None, dtype='int64',
+                 endpoint=False):
+    """
+    Return random integers from low (inclusive) to high (exclusive), or if
+    endpoint=True, low (inclusive) to high (inclusive). Replaces
+    `RandomState.randint` (with endpoint=False) and
+    `RandomState.random_integers` (with endpoint=True).
+
+    Return random integers from the "discrete uniform" distribution of the
+    specified dtype. If high is None (the default), then results are from
+    0 to low.
+
+    Parameters
+    ----------
+    gen : {None, np.random.RandomState, np.random.Generator}
+        Random number generator. If None, then the np.random.RandomState
+        singleton is used.
+    low : int or array-like of ints
+        Lowest (signed) integers to be drawn from the distribution (unless
+        high=None, in which case this parameter is 0 and this value is used
+        for high).
+    high : int or array-like of ints
+        If provided, one above the largest (signed) integer to be drawn from
+        the distribution (see above for behavior if high=None). If array-like,
+        must contain integer values.
+    size : array-like of ints, optional
+        Output shape. If the given shape is, e.g., (m, n, k), then m * n * k
+        samples are drawn. Default is None, in which case a single value is
+        returned.
+    dtype : {str, dtype}, optional
+        Desired dtype of the result. All dtypes are determined by their name,
+        i.e., 'int64', 'int', etc, so byteorder is not available and a specific
+        precision may have different C types depending on the platform.
+        The default value is 'int64'.
+    endpoint : bool, optional
+        If True, sample from the interval [low, high] instead of the default
+        [low, high) Defaults to False.
+
+    Returns
+    -------
+    out: int or ndarray of ints
+        size-shaped array of random integers from the appropriate distribution,
+        or a single such random int if size not provided.
+    """
+    if isinstance(gen, np.random.Generator):
+        return gen.integers(low, high=high, size=size, dtype=dtype,
+                            endpoint=endpoint)
+    else:
+        if gen is None:
+            # default is RandomState singleton used by np.random.
+            gen = np.random.mtrand._rand
+        if endpoint:
+            # inclusive of endpoint
+            # remember that low and high can be arrays, so don't modify in
+            # place
+            if high is None:
+                return gen.randint(low + 1, size=size, dtype=dtype)
+            if high is not None:
+                return gen.randint(low, high=high + 1, size=size, dtype=dtype)
+
+        # exclusive
+        return gen.randint(low, high=high, size=size, dtype=dtype)
+
+
+@contextmanager
+def _fixed_default_rng(seed=1638083107694713882823079058616272161):
+    """Context with a fixed np.random.default_rng seed."""
+    orig_fun = np.random.default_rng
+    np.random.default_rng = lambda seed=seed: orig_fun(seed)
+    try:
+        yield
+    finally:
+        np.random.default_rng = orig_fun
+
+
+@contextmanager
+def ignore_warns(expected_warning, *, match=None):
+    with warnings.catch_warnings():
+        warnings.filterwarnings("ignore", match, expected_warning)
+        yield
+
+
+def _rng_html_rewrite(func):
+    """Rewrite the HTML rendering of ``np.random.default_rng``.
+
+    This is intended to decorate
+    ``numpydoc.docscrape_sphinx.SphinxDocString._str_examples``.
+
+    Examples are only run by Sphinx when there are plot involved. Even so,
+    it does not change the result values getting printed.
+    """
+    # hexadecimal or number seed, case-insensitive
+    pattern = re.compile(r'np.random.default_rng\((0x[0-9A-F]+|\d+)\)', re.I)
+
+    def _wrapped(*args, **kwargs):
+        res = func(*args, **kwargs)
+        lines = [
+            re.sub(pattern, 'np.random.default_rng()', line)
+            for line in res
+        ]
+        return lines
+
+    return _wrapped
+
+
+def _argmin(a, keepdims=False, axis=None):
+    """
+    argmin with a `keepdims` parameter.
+
+    See https://github.com/numpy/numpy/issues/8710
+
+    If axis is not None, a.shape[axis] must be greater than 0.
+    """
+    res = np.argmin(a, axis=axis)
+    if keepdims and axis is not None:
+        res = np.expand_dims(res, axis=axis)
+    return res
+
+
+def _contains_nan(
+    a: Array,
+    nan_policy: Literal["propagate", "raise", "omit"] = "propagate",
+    *,
+    xp_omit_okay: bool = False,
+    xp: ModuleType | None = None,
+) -> Array | bool:
+    # Regarding `xp_omit_okay`: Temporarily, while `_axis_nan_policy` does not
+    # handle non-NumPy arrays, most functions that call `_contains_nan` want
+    # it to raise an error if `nan_policy='omit'` and `xp` is not `np`.
+    # Some functions support `nan_policy='omit'` natively, so setting this to
+    # `True` prevents the error from being raised.
+    policies = {"propagate", "raise", "omit"}
+    if nan_policy not in policies:
+        msg = f"nan_policy must be one of {policies}."
+        raise ValueError(msg)
+
+    if xp_size(a) == 0:
+        return False
+
+    if xp is None:
+        xp = array_namespace(a)
+
+    if xp.isdtype(a.dtype, "real floating"):
+        # Faster and less memory-intensive than xp.any(xp.isnan(a)), and unlike other
+        # reductions, `max`/`min` won't return NaN unless there is a NaN in the data.
+        contains_nan = xp.isnan(xp.max(a))
+    elif xp.isdtype(a.dtype, "complex floating"):
+        # Typically `real` and `imag` produce views; otherwise, `xp.any(xp.isnan(a))`
+        # would be more efficient.
+        contains_nan = xp.isnan(xp.max(xp.real(a))) | xp.isnan(xp.max(xp.imag(a)))
+    elif is_numpy(xp) and np.issubdtype(a.dtype, object):
+        contains_nan = False
+        for el in a.ravel():
+            # isnan doesn't work on non-numeric elements
+            if np.issubdtype(type(el), np.number) and np.isnan(el):
+                contains_nan = True
+                break
+    else:
+        # Only `object` and `inexact` arrays can have NaNs
+        return False
+
+    # The implicit call to bool(contains_nan) must happen after testing
+    # nan_policy to prevent lazy and device-bound xps from raising in the
+    # default policy='propagate' case.
+    if nan_policy == 'raise':
+        if is_lazy_array(a):
+            msg = "nan_policy='raise' is not supported for lazy arrays."
+            raise TypeError(msg)
+        if contains_nan:
+            msg = "The input contains nan values"
+            raise ValueError(msg)
+    elif nan_policy == 'omit' and not xp_omit_okay and not is_numpy(xp):
+        if is_lazy_array(a):
+            msg = "nan_policy='omit' is not supported for lazy arrays."
+            raise TypeError(msg)
+
+    return contains_nan
+
+
+def _rename_parameter(old_name, new_name, dep_version=None):
+    """
+    Generate decorator for backward-compatible keyword renaming.
+
+    Apply the decorator generated by `_rename_parameter` to functions with a
+    recently renamed parameter to maintain backward-compatibility.
+
+    After decoration, the function behaves as follows:
+    If only the new parameter is passed into the function, behave as usual.
+    If only the old parameter is passed into the function (as a keyword), raise
+    a DeprecationWarning if `dep_version` is provided, and behave as usual
+    otherwise.
+    If both old and new parameters are passed into the function, raise a
+    DeprecationWarning if `dep_version` is provided, and raise the appropriate
+    TypeError (function got multiple values for argument).
+
+    Parameters
+    ----------
+    old_name : str
+        Old name of parameter
+    new_name : str
+        New name of parameter
+    dep_version : str, optional
+        Version of SciPy in which old parameter was deprecated in the format
+        'X.Y.Z'. If supplied, the deprecation message will indicate that
+        support for the old parameter will be removed in version 'X.Y+2.Z'
+
+    Notes
+    -----
+    Untested with functions that accept *args. Probably won't work as written.
+
+    """
+    def decorator(fun):
+        @functools.wraps(fun)
+        def wrapper(*args, **kwargs):
+            if old_name in kwargs:
+                if dep_version:
+                    end_version = dep_version.split('.')
+                    end_version[1] = str(int(end_version[1]) + 2)
+                    end_version = '.'.join(end_version)
+                    message = (f"Use of keyword argument `{old_name}` is "
+                               f"deprecated and replaced by `{new_name}`.  "
+                               f"Support for `{old_name}` will be removed "
+                               f"in SciPy {end_version}.")
+                    warnings.warn(message, DeprecationWarning, stacklevel=2)
+                if new_name in kwargs:
+                    message = (f"{fun.__name__}() got multiple values for "
+                               f"argument now known as `{new_name}`")
+                    raise TypeError(message)
+                kwargs[new_name] = kwargs.pop(old_name)
+            return fun(*args, **kwargs)
+        return wrapper
+    return decorator
+
+
+def _rng_spawn(rng, n_children):
+    # spawns independent RNGs from a parent RNG
+    bg = rng._bit_generator
+    ss = bg._seed_seq
+    child_rngs = [np.random.Generator(type(bg)(child_ss))
+                  for child_ss in ss.spawn(n_children)]
+    return child_rngs
+
+
+def _get_nan(*data, shape=(), xp=None):
+    xp = array_namespace(*data) if xp is None else xp
+    # Get NaN of appropriate dtype for data
+    dtype = xp_result_type(*data, force_floating=True, xp=xp)
+    device = xp_result_device(*data)
+    res = xp.full(shape, xp.nan, dtype=dtype, device=device)
+    if not shape:
+        res = res[()]
+    # whenever mdhaber/marray#89 is resolved, could just return `res`
+    return res.data if is_marray(xp) else res
+
+
+def normalize_axis_index(axis, ndim):
+    # Check if `axis` is in the correct range and normalize it
+    if axis < -ndim or axis >= ndim:
+        msg = f"axis {axis} is out of bounds for array of dimension {ndim}"
+        raise AxisError(msg)
+
+    if axis < 0:
+        axis = axis + ndim
+    return axis
+
+
+def _call_callback_maybe_halt(callback, res):
+    """Call wrapped callback; return True if algorithm should stop.
+
+    Parameters
+    ----------
+    callback : callable or None
+        A user-provided callback wrapped with `_wrap_callback`
+    res : OptimizeResult
+        Information about the current iterate
+
+    Returns
+    -------
+    halt : bool
+        True if minimization should stop
+
+    """
+    if callback is None:
+        return False
+    try:
+        callback(res)
+        return False
+    except StopIteration:
+        callback.stop_iteration = True
+        return True
+
+
+class _RichResult(dict):
+    """ Container for multiple outputs with pretty-printing """
+    def __getattr__(self, name):
+        try:
+            return self[name]
+        except KeyError as e:
+            raise AttributeError(name) from e
+
+    __setattr__ = dict.__setitem__  # type: ignore[assignment]
+    __delattr__ = dict.__delitem__  # type: ignore[assignment]
+
+    def __repr__(self):
+        order_keys = ['message', 'success', 'status', 'fun', 'funl', 'x', 'xl',
+                      'col_ind', 'nit', 'lower', 'upper', 'eqlin', 'ineqlin',
+                      'converged', 'flag', 'function_calls', 'iterations',
+                      'root']
+        order_keys = getattr(self, '_order_keys', order_keys)
+        # 'slack', 'con' are redundant with residuals
+        # 'crossover_nit' is probably not interesting to most users
+        omit_keys = {'slack', 'con', 'crossover_nit', '_order_keys'}
+
+        def key(item):
+            try:
+                return order_keys.index(item[0].lower())
+            except ValueError:  # item not in list
+                return np.inf
+
+        def omit_redundant(items):
+            for item in items:
+                if item[0] in omit_keys:
+                    continue
+                yield item
+
+        def item_sorter(d):
+            return sorted(omit_redundant(d.items()), key=key)
+
+        if self.keys():
+            return _dict_formatter(self, sorter=item_sorter)
+        else:
+            return self.__class__.__name__ + "()"
+
+    def __dir__(self):
+        return list(self.keys())
+
+
+def _indenter(s, n=0):
+    """
+    Ensures that lines after the first are indented by the specified amount
+    """
+    split = s.split("\n")
+    indent = " "*n
+    return ("\n" + indent).join(split)
+
+
+def _float_formatter_10(x):
+    """
+    Returns a string representation of a float with exactly ten characters
+    """
+    if np.isposinf(x):
+        return "       inf"
+    elif np.isneginf(x):
+        return "      -inf"
+    elif np.isnan(x):
+        return "       nan"
+    return np.format_float_scientific(x, precision=3, pad_left=2, unique=False)
+
+
+def _dict_formatter(d, n=0, mplus=1, sorter=None):
+    """
+    Pretty printer for dictionaries
+
+    `n` keeps track of the starting indentation;
+    lines are indented by this much after a line break.
+    `mplus` is additional left padding applied to keys
+    """
+    if isinstance(d, dict):
+        m = max(map(len, list(d.keys()))) + mplus  # width to print keys
+        s = '\n'.join([k.rjust(m) + ': ' +  # right justified, width m
+                       _indenter(_dict_formatter(v, m+n+2, 0, sorter), m+2)
+                       for k, v in sorter(d)])  # +2 for ': '
+    else:
+        # By default, NumPy arrays print with linewidth=76. `n` is
+        # the indent at which a line begins printing, so it is subtracted
+        # from the default to avoid exceeding 76 characters total.
+        # `edgeitems` is the number of elements to include before and after
+        # ellipses when arrays are not shown in full.
+        # `threshold` is the maximum number of elements for which an
+        # array is shown in full.
+        # These values tend to work well for use with OptimizeResult.
+        with np.printoptions(linewidth=76-n, edgeitems=2, threshold=12,
+                             formatter={'float_kind': _float_formatter_10}):
+            s = str(d)
+    return s
+
+
+_batch_note = """
+The documentation is written assuming array arguments are of specified
+"core" shapes. However, array argument(s) of this function may have additional
+"batch" dimensions prepended to the core shape. In this case, the array is treated
+as a batch of lower-dimensional slices; see :ref:`linalg_batch` for details.
+Note that calls with zero-size batches are unsupported and will raise a ``ValueError``.
+"""
+
+
+def _apply_over_batch(*argdefs):
+    """
+    Factory for decorator that applies a function over batched arguments.
+
+    Array arguments may have any number of core dimensions (typically 0,
+    1, or 2) and any broadcastable batch shapes. There may be any
+    number of array outputs of any number of dimensions. Assumptions
+    right now - which are satisfied by all functions of interest in `linalg` -
+    are that all array inputs are consecutive keyword or positional arguments,
+    and that the wrapped function returns either a single array or a tuple of
+    arrays. It's only as general as it needs to be right now - it can be extended.
+
+    Parameters
+    ----------
+    *argdefs : tuple of (str, int)
+        Definitions of array arguments: the keyword name of the argument, and
+        the number of core dimensions.
+
+    Example:
+    --------
+    `linalg.eig` accepts two matrices as the first two arguments `a` and `b`, where
+    `b` is optional, and returns one array or a tuple of arrays, depending on the
+    values of other positional or keyword arguments. To generate a wrapper that applies
+    the function over batches of `a` and optionally `b` :
+
+    >>> _apply_over_batch(('a', 2), ('b', 2))
+    """
+    names, ndims = list(zip(*argdefs))
+    n_arrays = len(names)
+
+    def decorator(f):
+        @functools.wraps(f)
+        def wrapper(*args, **kwargs):
+            args = list(args)
+
+            # Ensure all arrays in `arrays`, other arguments in `other_args`/`kwargs`
+            arrays, other_args = args[:n_arrays], args[n_arrays:]
+            for i, name in enumerate(names):
+                if name in kwargs:
+                    if i + 1 <= len(args):
+                        raise ValueError(f'{f.__name__}() got multiple values '
+                                         f'for argument `{name}`.')
+                    else:
+                        arrays.append(kwargs.pop(name))
+
+            xp = array_namespace(*arrays)
+
+            # Determine core and batch shapes
+            batch_shapes = []
+            core_shapes = []
+            for i, (array, ndim) in enumerate(zip(arrays, ndims)):
+                array = None if array is None else xp.asarray(array)
+                shape = () if array is None else array.shape
+
+                if ndim == "1|2":  # special case for `solve`, etc.
+                    ndim = 2 if array.ndim >= 2 else 1
+
+                arrays[i] = array
+                batch_shapes.append(shape[:-ndim] if ndim > 0 else shape)
+                core_shapes.append(shape[-ndim:] if ndim > 0 else ())
+
+            # Early exit if call is not batched
+            if not any(batch_shapes):
+                return f(*arrays, *other_args, **kwargs)
+
+            # Determine broadcasted batch shape
+            batch_shape = np.broadcast_shapes(*batch_shapes)  # Gives OK error message
+
+            # We can't support zero-size batches right now because without data with
+            # which to call the function, the decorator doesn't even know the *number*
+            # of outputs, let alone their core shapes or dtypes.
+            if math.prod(batch_shape) == 0:
+                message = f'`{f.__name__}` does not support zero-size batches.'
+                raise ValueError(message)
+
+            # Broadcast arrays to appropriate shape
+            for i, (array, core_shape) in enumerate(zip(arrays, core_shapes)):
+                if array is None:
+                    continue
+                arrays[i] = xp.broadcast_to(array, batch_shape + core_shape)
+
+            # Main loop
+            results = []
+            for index in np.ndindex(batch_shape):
+                result = f(*((array[index] if array is not None else None)
+                             for array in arrays), *other_args, **kwargs)
+                # Assume `result` is either a tuple or single array. This is easily
+                # generalized by allowing the contributor to pass an `unpack_result`
+                # callable to the decorator factory.
+                result = (result,) if not isinstance(result, tuple) else result
+                results.append(result)
+            results = list(zip(*results))
+
+            # Reshape results
+            for i, result in enumerate(results):
+                result = xp.stack(result)
+                core_shape = result.shape[1:]
+                results[i] = xp.reshape(result, batch_shape + core_shape)
+
+            # Assume `result` should be a single array if there is only one element or
+            # a `tuple` otherwise. This is easily generalized by allowing the
+            # contributor to pass an `pack_result` callable to the decorator factory.
+            return results[0] if len(results) == 1 else results
+
+        doc = FunctionDoc(wrapper)
+        doc['Extended Summary'].append(_batch_note.rstrip())
+        wrapper.__doc__ = str(doc).split("\n", 1)[1].lstrip(" \n")  # remove signature
+
+        return wrapper
+    return decorator
+
+
+def np_vecdot(x1, x2, /, *, axis=-1):
+    # `np.vecdot` has advantages (e.g. see gh-22462), so let's use it when
+    # available. As functions are translated to Array API, `np_vecdot` can be
+    # replaced with `xp.vecdot`.
+    if np.__version__ > "2.0":
+        return np.vecdot(x1, x2, axis=axis)
+    else:
+        # of course there are other fancy ways of doing this (e.g. `einsum`)
+        # but let's keep it simple since it's temporary
+        return np.sum(x1 * x2, axis=axis)
+
+
+def _dedent_for_py313(s):
+    """Apply textwrap.dedent to s for Python versions 3.13 or later."""
+    return s if sys.version_info < (3, 13) else textwrap.dedent(s)
+
+
+def broadcastable(shape_a: tuple[int, ...], shape_b: tuple[int, ...]) -> bool:
+    """Check if two shapes are broadcastable."""
+    return all(
+        (m == n) or (m == 1) or (n == 1) for m, n in zip(shape_a[::-1], shape_b[::-1])
+    )
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/__init__.py
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index 0000000000000000000000000000000000000000..4abca400a24f71dd59876488e4cf9fde89de9489
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/__init__.py
@@ -0,0 +1,22 @@
+"""
+NumPy Array API compatibility library
+
+This is a small wrapper around NumPy, CuPy, JAX, sparse and others that are
+compatible with the Array API standard https://data-apis.org/array-api/latest/.
+See also NEP 47 https://numpy.org/neps/nep-0047-array-api-standard.html.
+
+Unlike array_api_strict, this is not a strict minimal implementation of the
+Array API, but rather just an extension of the main NumPy namespace with
+changes needed to be compliant with the Array API. See
+https://numpy.org/doc/stable/reference/array_api.html for a full list of
+changes. In particular, unlike array_api_strict, this package does not use a
+separate Array object, but rather just uses numpy.ndarray directly.
+
+Library authors using the Array API may wish to test against array_api_strict
+to ensure they are not using functionality outside of the standard, but prefer
+this implementation for the default when working with NumPy arrays.
+
+"""
+__version__ = '1.13.0'
+
+from .common import *  # noqa: F401, F403
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/_internal.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/_internal.py
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index 0000000000000000000000000000000000000000..baa39ded8decf2837540837ebc7b49c7b6971b82
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/_internal.py
@@ -0,0 +1,77 @@
+"""
+Internal helpers
+"""
+
+import importlib
+from collections.abc import Callable
+from functools import wraps
+from inspect import signature
+from types import ModuleType
+from typing import TypeVar
+
+_T = TypeVar("_T")
+
+
+def get_xp(xp: ModuleType) -> Callable[[Callable[..., _T]], Callable[..., _T]]:
+    """
+    Decorator to automatically replace xp with the corresponding array module.
+
+    Use like
+
+    import numpy as np
+
+    @get_xp(np)
+    def func(x, /, xp, kwarg=None):
+        return xp.func(x, kwarg=kwarg)
+
+    Note that xp must be a keyword argument and come after all non-keyword
+    arguments.
+
+    """
+
+    def inner(f: Callable[..., _T], /) -> Callable[..., _T]:
+        @wraps(f)
+        def wrapped_f(*args: object, **kwargs: object) -> object:
+            return f(*args, xp=xp, **kwargs)
+
+        sig = signature(f)
+        new_sig = sig.replace(
+            parameters=[par for i, par in sig.parameters.items() if i != "xp"]
+        )
+
+        if wrapped_f.__doc__ is None:
+            wrapped_f.__doc__ = f"""\
+Array API compatibility wrapper for {f.__name__}.
+
+See the corresponding documentation in NumPy/CuPy and/or the array API
+specification for more details.
+
+"""
+        wrapped_f.__signature__ = new_sig  # type: ignore[attr-defined] # pyright: ignore[reportAttributeAccessIssue]
+        return wrapped_f  # type: ignore[return-value] # pyright: ignore[reportReturnType]
+
+    return inner
+
+
+def clone_module(mod_name: str, globals_: dict[str, object]) -> list[str]:
+    """Import everything from module, updating globals().
+    Returns __all__.
+    """
+    mod = importlib.import_module(mod_name)
+    # Neither of these two methods is sufficient by itself,
+    # depending on various idiosyncrasies of the libraries we're wrapping.
+    objs = {}
+    exec(f"from {mod.__name__} import *", objs)
+
+    for n in dir(mod):
+        if not n.startswith("_") and hasattr(mod, n):
+            objs[n] = getattr(mod, n)
+
+    globals_.update(objs)
+    return list(objs)
+
+
+__all__ = ["get_xp", "clone_module"]
+
+def __dir__() -> list[str]:
+    return __all__
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/__init__.py
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index 0000000000000000000000000000000000000000..8236080738175f0fb7d1f47fcc52522306b43050
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/__init__.py
@@ -0,0 +1 @@
+from ._helpers import *  # noqa: F403
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_aliases.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_aliases.py
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index 0000000000000000000000000000000000000000..3587ef16fa18b22081770ecbd13335a4fed5ac0c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_aliases.py
@@ -0,0 +1,702 @@
+"""
+These are functions that are just aliases of existing functions in NumPy.
+"""
+
+from __future__ import annotations
+
+import inspect
+from collections.abc import Sequence
+from typing import TYPE_CHECKING, Any, NamedTuple, cast
+
+from ._helpers import _check_device, array_namespace
+from ._helpers import device as _get_device
+from ._helpers import is_cupy_namespace
+from ._typing import Array, Device, DType, Namespace
+
+if TYPE_CHECKING:
+    # TODO: import from typing (requires Python >=3.13)
+    from typing_extensions import TypeIs
+
+# These functions are modified from the NumPy versions.
+
+# Creation functions add the device keyword (which does nothing for NumPy and Dask)
+
+
+def arange(
+    start: float,
+    /,
+    stop: float | None = None,
+    step: float = 1,
+    *,
+    xp: Namespace,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.arange(start, stop=stop, step=step, dtype=dtype, **kwargs)
+
+
+def empty(
+    shape: int | tuple[int, ...],
+    xp: Namespace,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.empty(shape, dtype=dtype, **kwargs)
+
+
+def empty_like(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.empty_like(x, dtype=dtype, **kwargs)
+
+
+def eye(
+    n_rows: int,
+    n_cols: int | None = None,
+    /,
+    *,
+    xp: Namespace,
+    k: int = 0,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.eye(n_rows, M=n_cols, k=k, dtype=dtype, **kwargs)
+
+
+def full(
+    shape: int | tuple[int, ...],
+    fill_value: complex,
+    xp: Namespace,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.full(shape, fill_value, dtype=dtype, **kwargs)
+
+
+def full_like(
+    x: Array,
+    /,
+    fill_value: complex,
+    *,
+    xp: Namespace,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.full_like(x, fill_value, dtype=dtype, **kwargs)
+
+
+def linspace(
+    start: float,
+    stop: float,
+    /,
+    num: int,
+    *,
+    xp: Namespace,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    endpoint: bool = True,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.linspace(start, stop, num, dtype=dtype, endpoint=endpoint, **kwargs)
+
+
+def ones(
+    shape: int | tuple[int, ...],
+    xp: Namespace,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.ones(shape, dtype=dtype, **kwargs)
+
+
+def ones_like(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.ones_like(x, dtype=dtype, **kwargs)
+
+
+def zeros(
+    shape: int | tuple[int, ...],
+    xp: Namespace,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.zeros(shape, dtype=dtype, **kwargs)
+
+
+def zeros_like(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    _check_device(xp, device)
+    return xp.zeros_like(x, dtype=dtype, **kwargs)
+
+
+# np.unique() is split into four functions in the array API:
+# unique_all, unique_counts, unique_inverse, and unique_values (this is done
+# to remove polymorphic return types).
+
+# The functions here return namedtuples (np.unique() returns a normal
+# tuple).
+
+
+# Note that these named tuples aren't actually part of the standard namespace,
+# but I don't see any issue with exporting the names here regardless.
+class UniqueAllResult(NamedTuple):
+    values: Array
+    indices: Array
+    inverse_indices: Array
+    counts: Array
+
+
+class UniqueCountsResult(NamedTuple):
+    values: Array
+    counts: Array
+
+
+class UniqueInverseResult(NamedTuple):
+    values: Array
+    inverse_indices: Array
+
+
+def _unique_kwargs(xp: Namespace) -> dict[str, bool]:
+    # Older versions of NumPy and CuPy do not have equal_nan. Rather than
+    # trying to parse version numbers, just check if equal_nan is in the
+    # signature.
+    s = inspect.signature(xp.unique)
+    if "equal_nan" in s.parameters:
+        return {"equal_nan": False}
+    return {}
+
+
+def unique_all(x: Array, /, xp: Namespace) -> UniqueAllResult:
+    kwargs = _unique_kwargs(xp)
+    values, indices, inverse_indices, counts = xp.unique(
+        x,
+        return_counts=True,
+        return_index=True,
+        return_inverse=True,
+        **kwargs,
+    )
+    # np.unique() flattens inverse indices, but they need to share x's shape
+    # See https://github.com/numpy/numpy/issues/20638
+    inverse_indices = inverse_indices.reshape(x.shape)
+    return UniqueAllResult(
+        values,
+        indices,
+        inverse_indices,
+        counts,
+    )
+
+
+def unique_counts(x: Array, /, xp: Namespace) -> UniqueCountsResult:
+    kwargs = _unique_kwargs(xp)
+    res = xp.unique(
+        x, return_counts=True, return_index=False, return_inverse=False, **kwargs
+    )
+
+    return UniqueCountsResult(*res)
+
+
+def unique_inverse(x: Array, /, xp: Namespace) -> UniqueInverseResult:
+    kwargs = _unique_kwargs(xp)
+    values, inverse_indices = xp.unique(
+        x,
+        return_counts=False,
+        return_index=False,
+        return_inverse=True,
+        **kwargs,
+    )
+    # xp.unique() flattens inverse indices, but they need to share x's shape
+    # See https://github.com/numpy/numpy/issues/20638
+    inverse_indices = inverse_indices.reshape(x.shape)
+    return UniqueInverseResult(values, inverse_indices)
+
+
+def unique_values(x: Array, /, xp: Namespace) -> Array:
+    kwargs = _unique_kwargs(xp)
+    return xp.unique(
+        x,
+        return_counts=False,
+        return_index=False,
+        return_inverse=False,
+        **kwargs,
+    )
+
+
+# These functions have different keyword argument names
+
+
+def std(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    axis: int | tuple[int, ...] | None = None,
+    correction: float = 0.0,  # correction instead of ddof
+    keepdims: bool = False,
+    **kwargs: object,
+) -> Array:
+    return xp.std(x, axis=axis, ddof=correction, keepdims=keepdims, **kwargs)
+
+
+def var(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    axis: int | tuple[int, ...] | None = None,
+    correction: float = 0.0,  # correction instead of ddof
+    keepdims: bool = False,
+    **kwargs: object,
+) -> Array:
+    return xp.var(x, axis=axis, ddof=correction, keepdims=keepdims, **kwargs)
+
+
+# cumulative_sum is renamed from cumsum, and adds the include_initial keyword
+# argument
+
+
+def cumulative_sum(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    axis: int | None = None,
+    dtype: DType | None = None,
+    include_initial: bool = False,
+    **kwargs: object,
+) -> Array:
+    wrapped_xp = array_namespace(x)
+
+    # TODO: The standard is not clear about what should happen when x.ndim == 0.
+    if axis is None:
+        if x.ndim > 1:
+            raise ValueError(
+                "axis must be specified in cumulative_sum for more than one dimension"
+            )
+        axis = 0
+
+    res = xp.cumsum(x, axis=axis, dtype=dtype, **kwargs)
+
+    # np.cumsum does not support include_initial
+    if include_initial:
+        initial_shape = list(x.shape)
+        initial_shape[axis] = 1
+        res = xp.concatenate(
+            [
+                wrapped_xp.zeros(
+                    shape=initial_shape, dtype=res.dtype, device=_get_device(res)
+                ),
+                res,
+            ],
+            axis=axis,
+        )
+    return res
+
+
+def cumulative_prod(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    axis: int | None = None,
+    dtype: DType | None = None,
+    include_initial: bool = False,
+    **kwargs: object,
+) -> Array:
+    wrapped_xp = array_namespace(x)
+
+    if axis is None:
+        if x.ndim > 1:
+            raise ValueError(
+                "axis must be specified in cumulative_prod for more than one dimension"
+            )
+        axis = 0
+
+    res = xp.cumprod(x, axis=axis, dtype=dtype, **kwargs)
+
+    # np.cumprod does not support include_initial
+    if include_initial:
+        initial_shape = list(x.shape)
+        initial_shape[axis] = 1
+        res = xp.concatenate(
+            [
+                wrapped_xp.ones(
+                    shape=initial_shape, dtype=res.dtype, device=_get_device(res)
+                ),
+                res,
+            ],
+            axis=axis,
+        )
+    return res
+
+
+# The min and max argument names in clip are different and not optional in numpy, and type
+# promotion behavior is different.
+def clip(
+    x: Array,
+    /,
+    min: float | Array | None = None,
+    max: float | Array | None = None,
+    *,
+    xp: Namespace,
+    # TODO: np.clip has other ufunc kwargs
+    out: Array | None = None,
+) -> Array:
+    def _isscalar(a: object) -> TypeIs[float | None]:
+        return isinstance(a, int | float) or a is None
+
+    min_shape = () if _isscalar(min) else min.shape
+    max_shape = () if _isscalar(max) else max.shape
+
+    wrapped_xp = array_namespace(x)
+
+    result_shape = xp.broadcast_shapes(x.shape, min_shape, max_shape)
+
+    # np.clip does type promotion but the array API clip requires that the
+    # output have the same dtype as x. We do this instead of just downcasting
+    # the result of xp.clip() to handle some corner cases better (e.g.,
+    # avoiding uint64 -> float64 promotion).
+
+    # Note: cases where min or max overflow (integer) or round (float) in the
+    # wrong direction when downcasting to x.dtype are unspecified. This code
+    # just does whatever NumPy does when it downcasts in the assignment, but
+    # other behavior could be preferred, especially for integers. For example,
+    # this code produces:
+
+    # >>> clip(asarray(0, dtype=int8), asarray(128, dtype=int16), None)
+    # -128
+
+    # but an answer of 0 might be preferred. See
+    # https://github.com/numpy/numpy/issues/24976 for more discussion on this issue.
+
+    # At least handle the case of Python integers correctly (see
+    # https://github.com/numpy/numpy/pull/26892).
+    if wrapped_xp.isdtype(x.dtype, "integral"):
+        if type(min) is int and min <= wrapped_xp.iinfo(x.dtype).min:
+            min = None
+        if type(max) is int and max >= wrapped_xp.iinfo(x.dtype).max:
+            max = None
+
+    dev = _get_device(x)
+    if out is None:
+        out = wrapped_xp.empty(result_shape, dtype=x.dtype, device=dev)
+    assert out is not None  # workaround for a type-narrowing issue in pyright
+    out[()] = x
+
+    if min is not None:
+        a = wrapped_xp.asarray(min, dtype=x.dtype, device=dev)
+        a = xp.broadcast_to(a, result_shape)
+        ia = (out < a) | xp.isnan(a)
+        out[ia] = a[ia]
+
+    if max is not None:
+        b = wrapped_xp.asarray(max, dtype=x.dtype, device=dev)
+        b = xp.broadcast_to(b, result_shape)
+        ib = (out > b) | xp.isnan(b)
+        out[ib] = b[ib]
+
+    # Return a scalar for 0-D
+    return out[()]
+
+
+# Unlike transpose(), the axes argument to permute_dims() is required.
+def permute_dims(x: Array, /, axes: tuple[int, ...], xp: Namespace) -> Array:
+    return xp.transpose(x, axes)
+
+
+# np.reshape calls the keyword argument 'newshape' instead of 'shape'
+def reshape(
+    x: Array,
+    /,
+    shape: tuple[int, ...],
+    xp: Namespace,
+    *,
+    copy: bool | None = None,
+    **kwargs: object,
+) -> Array:
+    if copy is True:
+        x = x.copy()
+    elif copy is False:
+        y = x.view()
+        y.shape = shape
+        return y
+    return xp.reshape(x, shape, **kwargs)
+
+
+# The descending keyword is new in sort and argsort, and 'kind' replaced with
+# 'stable'
+def argsort(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    axis: int = -1,
+    descending: bool = False,
+    stable: bool = True,
+    **kwargs: object,
+) -> Array:
+    # Note: this keyword argument is different, and the default is different.
+    # We set it in kwargs like this because numpy.sort uses kind='quicksort'
+    # as the default whereas cupy.sort uses kind=None.
+    if stable:
+        kwargs["kind"] = "stable"
+    if not descending:
+        res = xp.argsort(x, axis=axis, **kwargs)
+    else:
+        # As NumPy has no native descending sort, we imitate it here. Note that
+        # simply flipping the results of xp.argsort(x, ...) would not
+        # respect the relative order like it would in native descending sorts.
+        res = xp.flip(
+            xp.argsort(xp.flip(x, axis=axis), axis=axis, **kwargs),
+            axis=axis,
+        )
+        # Rely on flip()/argsort() to validate axis
+        normalised_axis = axis if axis >= 0 else x.ndim + axis
+        max_i = x.shape[normalised_axis] - 1
+        res = max_i - res
+    return res
+
+
+def sort(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    axis: int = -1,
+    descending: bool = False,
+    stable: bool = True,
+    **kwargs: object,
+) -> Array:
+    # Note: this keyword argument is different, and the default is different.
+    # We set it in kwargs like this because numpy.sort uses kind='quicksort'
+    # as the default whereas cupy.sort uses kind=None.
+    if stable:
+        kwargs["kind"] = "stable"
+    res = xp.sort(x, axis=axis, **kwargs)
+    if descending:
+        res = xp.flip(res, axis=axis)
+    return res
+
+
+# nonzero should error for zero-dimensional arrays
+def nonzero(x: Array, /, xp: Namespace, **kwargs: object) -> tuple[Array, ...]:
+    if x.ndim == 0:
+        raise ValueError("nonzero() does not support zero-dimensional arrays")
+    return xp.nonzero(x, **kwargs)
+
+
+# linear algebra functions
+
+
+def matmul(x1: Array, x2: Array, /, xp: Namespace, **kwargs: object) -> Array:
+    return xp.matmul(x1, x2, **kwargs)
+
+
+# Unlike transpose, matrix_transpose only transposes the last two axes.
+def matrix_transpose(x: Array, /, xp: Namespace) -> Array:
+    if x.ndim < 2:
+        raise ValueError("x must be at least 2-dimensional for matrix_transpose")
+    return xp.swapaxes(x, -1, -2)
+
+
+def tensordot(
+    x1: Array,
+    x2: Array,
+    /,
+    xp: Namespace,
+    *,
+    axes: int | tuple[Sequence[int], Sequence[int]] = 2,
+    **kwargs: object,
+) -> Array:
+    return xp.tensordot(x1, x2, axes=axes, **kwargs)
+
+
+def vecdot(x1: Array, x2: Array, /, xp: Namespace, *, axis: int = -1) -> Array:
+    if x1.shape[axis] != x2.shape[axis]:
+        raise ValueError("x1 and x2 must have the same size along the given axis")
+
+    if hasattr(xp, "broadcast_tensors"):
+        _broadcast = xp.broadcast_tensors
+    else:
+        _broadcast = xp.broadcast_arrays
+
+    x1_ = xp.moveaxis(x1, axis, -1)
+    x2_ = xp.moveaxis(x2, axis, -1)
+    x1_, x2_ = _broadcast(x1_, x2_)
+
+    res = xp.conj(x1_[..., None, :]) @ x2_[..., None]
+    return res[..., 0, 0]
+
+
+# isdtype is a new function in the 2022.12 array API specification.
+
+
+def isdtype(
+    dtype: DType,
+    kind: DType | str | tuple[DType | str, ...],
+    xp: Namespace,
+    *,
+    _tuple: bool = True,  # Disallow nested tuples
+) -> bool:
+    """
+    Returns a boolean indicating whether a provided dtype is of a specified data type ``kind``.
+
+    Note that outside of this function, this compat library does not yet fully
+    support complex numbers.
+
+    See
+    https://data-apis.org/array-api/latest/API_specification/generated/array_api.isdtype.html
+    for more details
+    """
+    if isinstance(kind, tuple) and _tuple:
+        return any(
+            isdtype(dtype, k, xp, _tuple=False)
+            for k in cast("tuple[DType | str, ...]", kind)
+        )
+    elif isinstance(kind, str):
+        if kind == "bool":
+            return dtype == xp.bool_
+        elif kind == "signed integer":
+            return xp.issubdtype(dtype, xp.signedinteger)
+        elif kind == "unsigned integer":
+            return xp.issubdtype(dtype, xp.unsignedinteger)
+        elif kind == "integral":
+            return xp.issubdtype(dtype, xp.integer)
+        elif kind == "real floating":
+            return xp.issubdtype(dtype, xp.floating)
+        elif kind == "complex floating":
+            return xp.issubdtype(dtype, xp.complexfloating)
+        elif kind == "numeric":
+            return xp.issubdtype(dtype, xp.number)
+        else:
+            raise ValueError(f"Unrecognized data type kind: {kind!r}")
+    else:
+        # This will allow things that aren't required by the spec, like
+        # isdtype(np.float64, float) or isdtype(np.int64, 'l'). Should we be
+        # more strict here to match the type annotation? Note that the
+        # array_api_strict implementation will be very strict.
+        return dtype == kind
+
+
+# unstack is a new function in the 2023.12 array API standard
+def unstack(x: Array, /, xp: Namespace, *, axis: int = 0) -> tuple[Array, ...]:
+    if x.ndim == 0:
+        raise ValueError("Input array must be at least 1-d.")
+    return tuple(xp.moveaxis(x, axis, 0))
+
+
+# numpy 1.26 does not use the standard definition for sign on complex numbers
+
+
+def sign(x: Array, /, xp: Namespace, **kwargs: object) -> Array:
+    if isdtype(x.dtype, "complex floating", xp=xp):
+        out = (x / xp.abs(x, **kwargs))[...]
+        # sign(0) = 0 but the above formula would give nan
+        out[x == 0j] = 0j
+    else:
+        out = xp.sign(x, **kwargs)
+    # CuPy sign() does not propagate nans. See
+    # https://github.com/data-apis/array-api-compat/issues/136
+    if is_cupy_namespace(xp) and isdtype(x.dtype, "real floating", xp=xp):
+        out[xp.isnan(x)] = xp.nan
+    return out[()]
+
+
+def finfo(type_: DType | Array, /, xp: Namespace) -> Any:
+    # It is surprisingly difficult to recognize a dtype apart from an array.
+    # np.int64 is not the same as np.asarray(1).dtype!
+    try:
+        return xp.finfo(type_)
+    except (ValueError, TypeError):
+        return xp.finfo(type_.dtype)
+
+
+def iinfo(type_: DType | Array, /, xp: Namespace) -> Any:
+    try:
+        return xp.iinfo(type_)
+    except (ValueError, TypeError):
+        return xp.iinfo(type_.dtype)
+
+
+__all__ = [
+    "arange",
+    "empty",
+    "empty_like",
+    "eye",
+    "full",
+    "full_like",
+    "linspace",
+    "ones",
+    "ones_like",
+    "zeros",
+    "zeros_like",
+    "UniqueAllResult",
+    "UniqueCountsResult",
+    "UniqueInverseResult",
+    "unique_all",
+    "unique_counts",
+    "unique_inverse",
+    "unique_values",
+    "std",
+    "var",
+    "cumulative_sum",
+    "cumulative_prod",
+    "clip",
+    "permute_dims",
+    "reshape",
+    "argsort",
+    "sort",
+    "nonzero",
+    "matmul",
+    "matrix_transpose",
+    "tensordot",
+    "vecdot",
+    "isdtype",
+    "unstack",
+    "sign",
+    "finfo",
+    "iinfo",
+]
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_fft.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_fft.py
new file mode 100644
index 0000000000000000000000000000000000000000..18839d37f84949ec2bf851b548c2e13b5179e04e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_fft.py
@@ -0,0 +1,213 @@
+from __future__ import annotations
+
+from collections.abc import Sequence
+from typing import Literal, TypeAlias
+
+from ._typing import Array, Device, DType, Namespace
+
+_Norm: TypeAlias = Literal["backward", "ortho", "forward"]
+
+# Note: NumPy fft functions improperly upcast float32 and complex64 to
+# complex128, which is why we require wrapping them all here.
+
+def fft(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    n: int | None = None,
+    axis: int = -1,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.fft(x, n=n, axis=axis, norm=norm)
+    if x.dtype in [xp.float32, xp.complex64]:
+        return res.astype(xp.complex64)
+    return res
+
+def ifft(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    n: int | None = None,
+    axis: int = -1,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.ifft(x, n=n, axis=axis, norm=norm)
+    if x.dtype in [xp.float32, xp.complex64]:
+        return res.astype(xp.complex64)
+    return res
+
+def fftn(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    s: Sequence[int] | None = None,
+    axes: Sequence[int] | None = None,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.fftn(x, s=s, axes=axes, norm=norm)
+    if x.dtype in [xp.float32, xp.complex64]:
+        return res.astype(xp.complex64)
+    return res
+
+def ifftn(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    s: Sequence[int] | None = None,
+    axes: Sequence[int] | None = None,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.ifftn(x, s=s, axes=axes, norm=norm)
+    if x.dtype in [xp.float32, xp.complex64]:
+        return res.astype(xp.complex64)
+    return res
+
+def rfft(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    n: int | None = None,
+    axis: int = -1,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.rfft(x, n=n, axis=axis, norm=norm)
+    if x.dtype == xp.float32:
+        return res.astype(xp.complex64)
+    return res
+
+def irfft(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    n: int | None = None,
+    axis: int = -1,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.irfft(x, n=n, axis=axis, norm=norm)
+    if x.dtype == xp.complex64:
+        return res.astype(xp.float32)
+    return res
+
+def rfftn(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    s: Sequence[int] | None = None,
+    axes: Sequence[int] | None = None,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.rfftn(x, s=s, axes=axes, norm=norm)
+    if x.dtype == xp.float32:
+        return res.astype(xp.complex64)
+    return res
+
+def irfftn(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    s: Sequence[int] | None = None,
+    axes: Sequence[int] | None = None,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.irfftn(x, s=s, axes=axes, norm=norm)
+    if x.dtype == xp.complex64:
+        return res.astype(xp.float32)
+    return res
+
+def hfft(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    n: int | None = None,
+    axis: int = -1,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.hfft(x, n=n, axis=axis, norm=norm)
+    if x.dtype in [xp.float32, xp.complex64]:
+        return res.astype(xp.float32)
+    return res
+
+def ihfft(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    n: int | None = None,
+    axis: int = -1,
+    norm: _Norm = "backward",
+) -> Array:
+    res = xp.fft.ihfft(x, n=n, axis=axis, norm=norm)
+    if x.dtype in [xp.float32, xp.complex64]:
+        return res.astype(xp.complex64)
+    return res
+
+def fftfreq(
+    n: int,
+    /,
+    xp: Namespace,
+    *,
+    d: float = 1.0,
+    dtype: DType | None = None,
+    device: Device | None = None,
+) -> Array:
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    res = xp.fft.fftfreq(n, d=d)
+    if dtype is not None:
+        return res.astype(dtype)
+    return res
+
+def rfftfreq(
+    n: int,
+    /,
+    xp: Namespace,
+    *,
+    d: float = 1.0,
+    dtype: DType | None = None,
+    device: Device | None = None,
+) -> Array:
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    res = xp.fft.rfftfreq(n, d=d)
+    if dtype is not None:
+        return res.astype(dtype)
+    return res
+
+def fftshift(
+    x: Array, /, xp: Namespace, *, axes: int | Sequence[int] | None = None
+) -> Array:
+    return xp.fft.fftshift(x, axes=axes)
+
+def ifftshift(
+    x: Array, /, xp: Namespace, *, axes: int | Sequence[int] | None = None
+) -> Array:
+    return xp.fft.ifftshift(x, axes=axes)
+
+__all__ = [
+    "fft",
+    "ifft",
+    "fftn",
+    "ifftn",
+    "rfft",
+    "irfft",
+    "rfftn",
+    "irfftn",
+    "hfft",
+    "ihfft",
+    "fftfreq",
+    "rfftfreq",
+    "fftshift",
+    "ifftshift",
+]
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_helpers.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_helpers.py
new file mode 100644
index 0000000000000000000000000000000000000000..8194a083db92fc2c09f93062d4b13d23ed0b611f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_helpers.py
@@ -0,0 +1,1079 @@
+"""
+Various helper functions which are not part of the spec.
+
+Functions which start with an underscore are for internal use only but helpers
+that are in __all__ are intended as additional helper functions for use by end
+users of the compat library.
+"""
+
+from __future__ import annotations
+
+import enum
+import inspect
+import math
+import sys
+import warnings
+from collections.abc import Collection, Hashable
+from functools import lru_cache
+from typing import (
+    TYPE_CHECKING,
+    Any,
+    Final,
+    Literal,
+    SupportsIndex,
+    TypeAlias,
+    TypeGuard,
+    cast,
+    overload,
+)
+
+from ._typing import Array, Device, HasShape, Namespace, SupportsArrayNamespace
+
+if TYPE_CHECKING:
+    import cupy as cp
+    import dask.array as da
+    import jax
+    import ndonnx as ndx
+    import numpy as np
+    import numpy.typing as npt
+    import sparse
+    import torch
+
+    # TODO: import from typing (requires Python >=3.13)
+    from typing_extensions import TypeIs
+
+    _ZeroGradientArray: TypeAlias = npt.NDArray[np.void]
+
+    _ArrayApiObj: TypeAlias = (
+        npt.NDArray[Any]
+        | cp.ndarray
+        | da.Array
+        | jax.Array
+        | ndx.Array
+        | sparse.SparseArray
+        | torch.Tensor
+        | SupportsArrayNamespace[Any]
+    )
+
+_API_VERSIONS_OLD: Final = frozenset({"2021.12", "2022.12", "2023.12"})
+_API_VERSIONS: Final = _API_VERSIONS_OLD | frozenset({"2024.12"})
+
+
+@lru_cache(100)
+def _issubclass_fast(cls: type, modname: str, clsname: str) -> bool:
+    try:
+        mod = sys.modules[modname]
+    except KeyError:
+        return False
+    parent_cls = getattr(mod, clsname)
+    return issubclass(cls, parent_cls)
+
+
+def _is_jax_zero_gradient_array(x: object) -> TypeGuard[_ZeroGradientArray]:
+    """Return True if `x` is a zero-gradient array.
+
+    These arrays are a design quirk of Jax that may one day be removed.
+    See https://github.com/google/jax/issues/20620.
+    """
+    # Fast exit
+    try:
+        dtype = x.dtype  # type: ignore[attr-defined]
+    except AttributeError:
+        return False
+    cls = cast(Hashable, type(dtype))
+    if not _issubclass_fast(cls, "numpy.dtypes", "VoidDType"):
+        return False
+
+    if "jax" not in sys.modules:
+        return False
+
+    import jax
+    # jax.float0 is a np.dtype([('float0', 'V')])
+    return dtype == jax.float0
+
+
+def is_numpy_array(x: object) -> TypeIs[npt.NDArray[Any]]:
+    """
+    Return True if `x` is a NumPy array.
+
+    This function does not import NumPy if it has not already been imported
+    and is therefore cheap to use.
+
+    This also returns True for `ndarray` subclasses and NumPy scalar objects.
+
+    See Also
+    --------
+
+    array_namespace
+    is_array_api_obj
+    is_cupy_array
+    is_torch_array
+    is_ndonnx_array
+    is_dask_array
+    is_jax_array
+    is_pydata_sparse_array
+    """
+    # TODO: Should we reject ndarray subclasses?
+    cls = cast(Hashable, type(x))
+    return (
+        _issubclass_fast(cls, "numpy", "ndarray") 
+        or _issubclass_fast(cls, "numpy", "generic")
+    ) and not _is_jax_zero_gradient_array(x)
+
+
+def is_cupy_array(x: object) -> bool:
+    """
+    Return True if `x` is a CuPy array.
+
+    This function does not import CuPy if it has not already been imported
+    and is therefore cheap to use.
+
+    This also returns True for `cupy.ndarray` subclasses and CuPy scalar objects.
+
+    See Also
+    --------
+
+    array_namespace
+    is_array_api_obj
+    is_numpy_array
+    is_torch_array
+    is_ndonnx_array
+    is_dask_array
+    is_jax_array
+    is_pydata_sparse_array
+    """
+    cls = cast(Hashable, type(x))
+    return _issubclass_fast(cls, "cupy", "ndarray")
+
+
+def is_torch_array(x: object) -> TypeIs[torch.Tensor]:
+    """
+    Return True if `x` is a PyTorch tensor.
+
+    This function does not import PyTorch if it has not already been imported
+    and is therefore cheap to use.
+
+    See Also
+    --------
+
+    array_namespace
+    is_array_api_obj
+    is_numpy_array
+    is_cupy_array
+    is_dask_array
+    is_jax_array
+    is_pydata_sparse_array
+    """
+    cls = cast(Hashable, type(x))
+    return _issubclass_fast(cls, "torch", "Tensor")
+
+
+def is_ndonnx_array(x: object) -> TypeIs[ndx.Array]:
+    """
+    Return True if `x` is a ndonnx Array.
+
+    This function does not import ndonnx if it has not already been imported
+    and is therefore cheap to use.
+
+    See Also
+    --------
+
+    array_namespace
+    is_array_api_obj
+    is_numpy_array
+    is_cupy_array
+    is_ndonnx_array
+    is_dask_array
+    is_jax_array
+    is_pydata_sparse_array
+    """
+    cls = cast(Hashable, type(x))
+    return _issubclass_fast(cls, "ndonnx", "Array")
+
+
+def is_dask_array(x: object) -> TypeIs[da.Array]:
+    """
+    Return True if `x` is a dask.array Array.
+
+    This function does not import dask if it has not already been imported
+    and is therefore cheap to use.
+
+    See Also
+    --------
+
+    array_namespace
+    is_array_api_obj
+    is_numpy_array
+    is_cupy_array
+    is_torch_array
+    is_ndonnx_array
+    is_jax_array
+    is_pydata_sparse_array
+    """
+    cls = cast(Hashable, type(x))
+    return _issubclass_fast(cls, "dask.array", "Array")
+
+
+def is_jax_array(x: object) -> TypeIs[jax.Array]:
+    """
+    Return True if `x` is a JAX array.
+
+    This function does not import JAX if it has not already been imported
+    and is therefore cheap to use.
+
+
+    See Also
+    --------
+
+    array_namespace
+    is_array_api_obj
+    is_numpy_array
+    is_cupy_array
+    is_torch_array
+    is_ndonnx_array
+    is_dask_array
+    is_pydata_sparse_array
+    """
+    cls = cast(Hashable, type(x))
+    # We test for jax.core.Tracer here to identify jax arrays during jit tracing. From jax 0.8.2 on,
+    # tracers are not a subclass of jax.Array anymore. Note that tracers can also represent
+    # non-array values and a fully correct implementation would need to use isinstance checks. Since
+    # we use hash-based caching with type names as keys, we cannot use instance checks without
+    # losing performance here. For more information, see
+    # https://github.com/data-apis/array-api-compat/pull/369 and the corresponding issue.
+    return (
+        _issubclass_fast(cls, "jax", "Array")
+        or _issubclass_fast(cls, "jax.core", "Tracer")
+        or _is_jax_zero_gradient_array(x)
+    )
+
+
+def is_pydata_sparse_array(x: object) -> TypeIs[sparse.SparseArray]:
+    """
+    Return True if `x` is an array from the `sparse` package.
+
+    This function does not import `sparse` if it has not already been imported
+    and is therefore cheap to use.
+
+
+    See Also
+    --------
+
+    array_namespace
+    is_array_api_obj
+    is_numpy_array
+    is_cupy_array
+    is_torch_array
+    is_ndonnx_array
+    is_dask_array
+    is_jax_array
+    """
+    # TODO: Account for other backends.
+    cls = cast(Hashable, type(x))
+    return _issubclass_fast(cls, "sparse", "SparseArray")
+
+
+def is_array_api_obj(x: object) -> TypeGuard[_ArrayApiObj]:
+    """
+    Return True if `x` is an array API compatible array object.
+
+    See Also
+    --------
+
+    array_namespace
+    is_numpy_array
+    is_cupy_array
+    is_torch_array
+    is_ndonnx_array
+    is_dask_array
+    is_jax_array
+    """
+    return (
+        hasattr(x, '__array_namespace__') 
+        or _is_array_api_cls(cast(Hashable, type(x)))
+    )
+
+
+@lru_cache(100)
+def _is_array_api_cls(cls: type) -> bool:
+    return (
+        # TODO: drop support for numpy<2 which didn't have __array_namespace__
+        _issubclass_fast(cls, "numpy", "ndarray")
+        or _issubclass_fast(cls, "numpy", "generic")
+        or _issubclass_fast(cls, "cupy", "ndarray")
+        or _issubclass_fast(cls, "torch", "Tensor")
+        or _issubclass_fast(cls, "dask.array", "Array")
+        or _issubclass_fast(cls, "sparse", "SparseArray")
+        # TODO: drop support for jax<0.4.32 which didn't have __array_namespace__
+        or _issubclass_fast(cls, "jax", "Array")
+        or _issubclass_fast(cls, "jax.core", "Tracer")  # see is_jax_array for limitations
+    )
+
+
+def _compat_module_name() -> str:
+    assert __name__.endswith(".common._helpers")
+    return __name__.removesuffix(".common._helpers")
+
+
+@lru_cache(100)
+def is_numpy_namespace(xp: Namespace) -> bool:
+    """
+    Returns True if `xp` is a NumPy namespace.
+
+    This includes both NumPy itself and the version wrapped by array-api-compat.
+
+    See Also
+    --------
+
+    array_namespace
+    is_cupy_namespace
+    is_torch_namespace
+    is_ndonnx_namespace
+    is_dask_namespace
+    is_jax_namespace
+    is_pydata_sparse_namespace
+    is_array_api_strict_namespace
+    """
+    return xp.__name__ in {"numpy", _compat_module_name() + ".numpy"}
+
+
+@lru_cache(100)
+def is_cupy_namespace(xp: Namespace) -> bool:
+    """
+    Returns True if `xp` is a CuPy namespace.
+
+    This includes both CuPy itself and the version wrapped by array-api-compat.
+
+    See Also
+    --------
+
+    array_namespace
+    is_numpy_namespace
+    is_torch_namespace
+    is_ndonnx_namespace
+    is_dask_namespace
+    is_jax_namespace
+    is_pydata_sparse_namespace
+    is_array_api_strict_namespace
+    """
+    return xp.__name__ in {"cupy", _compat_module_name() + ".cupy"}
+
+
+@lru_cache(100)
+def is_torch_namespace(xp: Namespace) -> bool:
+    """
+    Returns True if `xp` is a PyTorch namespace.
+
+    This includes both PyTorch itself and the version wrapped by array-api-compat.
+
+    See Also
+    --------
+
+    array_namespace
+    is_numpy_namespace
+    is_cupy_namespace
+    is_ndonnx_namespace
+    is_dask_namespace
+    is_jax_namespace
+    is_pydata_sparse_namespace
+    is_array_api_strict_namespace
+    """
+    return xp.__name__ in {"torch", _compat_module_name() + ".torch"}
+
+
+def is_ndonnx_namespace(xp: Namespace) -> bool:
+    """
+    Returns True if `xp` is an NDONNX namespace.
+
+    See Also
+    --------
+
+    array_namespace
+    is_numpy_namespace
+    is_cupy_namespace
+    is_torch_namespace
+    is_dask_namespace
+    is_jax_namespace
+    is_pydata_sparse_namespace
+    is_array_api_strict_namespace
+    """
+    return xp.__name__ == "ndonnx"
+
+
+@lru_cache(100)
+def is_dask_namespace(xp: Namespace) -> bool:
+    """
+    Returns True if `xp` is a Dask namespace.
+
+    This includes both ``dask.array`` itself and the version wrapped by array-api-compat.
+
+    See Also
+    --------
+
+    array_namespace
+    is_numpy_namespace
+    is_cupy_namespace
+    is_torch_namespace
+    is_ndonnx_namespace
+    is_jax_namespace
+    is_pydata_sparse_namespace
+    is_array_api_strict_namespace
+    """
+    return xp.__name__ in {"dask.array", _compat_module_name() + ".dask.array"}
+
+
+def is_jax_namespace(xp: Namespace) -> bool:
+    """
+    Returns True if `xp` is a JAX namespace.
+
+    This includes ``jax.numpy`` and ``jax.experimental.array_api`` which existed in
+    older versions of JAX.
+
+    See Also
+    --------
+
+    array_namespace
+    is_numpy_namespace
+    is_cupy_namespace
+    is_torch_namespace
+    is_ndonnx_namespace
+    is_dask_namespace
+    is_pydata_sparse_namespace
+    is_array_api_strict_namespace
+    """
+    return xp.__name__ in {"jax.numpy", "jax.experimental.array_api"}
+
+
+def is_pydata_sparse_namespace(xp: Namespace) -> bool:
+    """
+    Returns True if `xp` is a pydata/sparse namespace.
+
+    See Also
+    --------
+
+    array_namespace
+    is_numpy_namespace
+    is_cupy_namespace
+    is_torch_namespace
+    is_ndonnx_namespace
+    is_dask_namespace
+    is_jax_namespace
+    is_array_api_strict_namespace
+    """
+    return xp.__name__ == "sparse"
+
+
+def is_array_api_strict_namespace(xp: Namespace) -> bool:
+    """
+    Returns True if `xp` is an array-api-strict namespace.
+
+    See Also
+    --------
+
+    array_namespace
+    is_numpy_namespace
+    is_cupy_namespace
+    is_torch_namespace
+    is_ndonnx_namespace
+    is_dask_namespace
+    is_jax_namespace
+    is_pydata_sparse_namespace
+    """
+    return xp.__name__ == "array_api_strict"
+
+
+def _check_api_version(api_version: str | None) -> None:
+    if api_version in _API_VERSIONS_OLD:
+        warnings.warn(
+            f"The {api_version} version of the array API specification was requested but the returned namespace is actually version 2024.12"
+        )
+    elif api_version is not None and api_version not in _API_VERSIONS:
+        raise ValueError(
+            "Only the 2024.12 version of the array API specification is currently supported"
+        )
+
+
+class _ClsToXPInfo(enum.Enum):
+    SCALAR = 0
+    MAYBE_JAX_ZERO_GRADIENT = 1
+
+
+@lru_cache(100)
+def _cls_to_namespace(
+    cls: type,
+    api_version: str | None,
+    use_compat: bool | None,
+) -> tuple[Namespace | None, _ClsToXPInfo | None]:
+    if use_compat not in (None, True, False):
+        raise ValueError("use_compat must be None, True, or False")
+    _use_compat = use_compat in (None, True)
+    cls_ = cast(Hashable, cls)  # Make mypy happy
+
+    if (
+        _issubclass_fast(cls_, "numpy", "ndarray") 
+        or _issubclass_fast(cls_, "numpy", "generic")
+    ):
+        if use_compat is True:
+            _check_api_version(api_version)
+            from .. import numpy as xp
+        elif use_compat is False:
+            import numpy as xp  # type: ignore[no-redef]
+        else:
+            # NumPy 2.0+ have __array_namespace__; however they are not
+            # yet fully array API compatible.
+            from .. import numpy as xp  # type: ignore[no-redef]
+        return xp, _ClsToXPInfo.MAYBE_JAX_ZERO_GRADIENT
+
+    # Note: this must happen _after_ the test for np.generic,
+    # because np.float64 and np.complex128 are subclasses of float and complex.
+    if issubclass(cls, int | float | complex | type(None)):
+        return None, _ClsToXPInfo.SCALAR
+
+    if _issubclass_fast(cls_, "cupy", "ndarray"):
+        if _use_compat:
+            _check_api_version(api_version)
+            from .. import cupy as xp  # type: ignore[no-redef]
+        else:
+            import cupy as xp  # type: ignore[no-redef]
+        return xp, None
+
+    if _issubclass_fast(cls_, "torch", "Tensor"):
+        if _use_compat:
+            _check_api_version(api_version)
+            from .. import torch as xp  # type: ignore[no-redef]
+        else:
+            import torch as xp  # type: ignore[no-redef]
+        return xp, None
+
+    if _issubclass_fast(cls_, "dask.array", "Array"):
+        if _use_compat:
+            _check_api_version(api_version)
+            from ..dask import array as xp  # type: ignore[no-redef]
+        else:
+            import dask.array as xp  # type: ignore[no-redef]
+        return xp, None
+
+    # Backwards compatibility for jax<0.4.32
+    if _issubclass_fast(cls_, "jax", "Array"):
+        return _jax_namespace(api_version, use_compat), None
+
+    return None, None
+
+
+def _jax_namespace(api_version: str | None, use_compat: bool | None) -> Namespace:
+    if use_compat:
+        raise ValueError("JAX does not have an array-api-compat wrapper")
+    import jax.numpy as jnp
+    if not hasattr(jnp, "__array_namespace_info__"):
+        # JAX v0.4.32 and newer implements the array API directly in jax.numpy.
+        # For older JAX versions, it is available via jax.experimental.array_api.
+        # jnp.Array objects gain the __array_namespace__ method.
+        import jax.experimental.array_api  # noqa: F401
+    # Test api_version
+    return jnp.empty(0).__array_namespace__(api_version=api_version)
+
+
+def array_namespace(
+    *xs: Array | complex | None,
+    api_version: str | None = None,
+    use_compat: bool | None = None,
+) -> Namespace:
+    """
+    Get the array API compatible namespace for the arrays `xs`.
+
+    Parameters
+    ----------
+    xs: arrays
+        one or more arrays. xs can also be Python scalars (bool, int, float,
+        complex, or None), which are ignored.
+
+    api_version: str
+        The newest version of the spec that you need support for (currently
+        the compat library wrapped APIs support v2024.12).
+
+    use_compat: bool or None
+        If None (the default), the native namespace will be returned if it is
+        already array API compatible, otherwise a compat wrapper is used. If
+        True, the compat library wrapped library will be returned. If False,
+        the native library namespace is returned.
+
+    Returns
+    -------
+
+    out: namespace
+        The array API compatible namespace corresponding to the arrays in `xs`.
+
+    Raises
+    ------
+    TypeError
+        If `xs` contains arrays from different array libraries or contains a
+        non-array.
+
+
+    Typical usage is to pass the arguments of a function to
+    `array_namespace()` at the top of a function to get the corresponding
+    array API namespace:
+
+    .. code:: python
+
+       def your_function(x, y):
+           xp = array_api_compat.array_namespace(x, y)
+           # Now use xp as the array library namespace
+           return xp.mean(x, axis=0) + 2*xp.std(y, axis=0)
+
+
+    Wrapped array namespaces can also be imported directly. For example,
+    `array_namespace(np.array(...))` will return `array_api_compat.numpy`.
+    This function will also work for any array library not wrapped by
+    array-api-compat if it explicitly defines `__array_namespace__
+    `__
+    (the wrapped namespace is always preferred if it exists).
+
+    See Also
+    --------
+
+    is_array_api_obj
+    is_numpy_array
+    is_cupy_array
+    is_torch_array
+    is_dask_array
+    is_jax_array
+    is_pydata_sparse_array
+
+    """
+    namespaces: set[Namespace] = set()
+    for x in xs:
+        xp, info = _cls_to_namespace(cast(Hashable, type(x)), api_version, use_compat)
+        if info is _ClsToXPInfo.SCALAR:
+            continue
+
+        if (
+            info is _ClsToXPInfo.MAYBE_JAX_ZERO_GRADIENT
+            and _is_jax_zero_gradient_array(x)
+        ):
+            xp = _jax_namespace(api_version, use_compat)
+
+        if xp is None:
+            get_ns = getattr(x, "__array_namespace__", None)
+            if get_ns is None:
+                raise TypeError(f"{type(x).__name__} is not a supported array type")
+            if use_compat:
+                raise ValueError(
+                    "The given array does not have an array-api-compat wrapper"
+                )
+            xp = get_ns(api_version=api_version)
+
+        namespaces.add(xp)
+
+    try:
+        (xp,) = namespaces
+        return xp
+    except ValueError:
+        if not namespaces:
+            raise TypeError(
+                "array_namespace requires at least one non-scalar array input"
+            )
+        raise TypeError(f"Multiple namespaces for array inputs: {namespaces}")
+
+
+# backwards compatibility alias
+get_namespace = array_namespace
+
+
+def _check_device(bare_xp: Namespace, device: Device) -> None:  # pyright: ignore[reportUnusedFunction]
+    """
+    Validate dummy device on device-less array backends.
+
+    Notes
+    -----
+    This function is also invoked by CuPy, which does have multiple devices
+    if there are multiple GPUs available.
+    However, CuPy multi-device support is currently impossible
+    without using the global device or a context manager:
+
+    https://github.com/data-apis/array-api-compat/pull/293
+    """
+    if bare_xp is sys.modules.get("numpy"):
+        if device not in ("cpu", None):
+            raise ValueError(f"Unsupported device for NumPy: {device!r}")
+
+    elif bare_xp is sys.modules.get("dask.array"):
+        if device not in ("cpu", _DASK_DEVICE, None):
+            raise ValueError(f"Unsupported device for Dask: {device!r}")
+
+
+# Placeholder object to represent the dask device
+# when the array backend is not the CPU.
+# (since it is not easy to tell which device a dask array is on)
+class _dask_device:
+    def __repr__(self) -> Literal["DASK_DEVICE"]:
+        return "DASK_DEVICE"
+
+
+_DASK_DEVICE = _dask_device()
+
+
+# device() is not on numpy.ndarray or dask.array and to_device() is not on numpy.ndarray
+# or cupy.ndarray. They are not included in array objects of this library
+# because this library just reuses the respective ndarray classes without
+# wrapping or subclassing them. These helper functions can be used instead of
+# the wrapper functions for libraries that need to support both NumPy/CuPy and
+# other libraries that use devices.
+def device(x: _ArrayApiObj, /) -> Device:
+    """
+    Hardware device the array data resides on.
+
+    This is equivalent to `x.device` according to the `standard
+    `__.
+    This helper is included because some array libraries either do not have
+    the `device` attribute or include it with an incompatible API.
+
+    Parameters
+    ----------
+    x: array
+        array instance from an array API compatible library.
+
+    Returns
+    -------
+    out: device
+        a ``device`` object (see the `Device Support `__
+        section of the array API specification).
+
+    Notes
+    -----
+
+    For NumPy the device is always `"cpu"`. For Dask, the device is always a
+    special `DASK_DEVICE` object.
+
+    See Also
+    --------
+
+    to_device : Move array data to a different device.
+
+    """
+    if is_numpy_array(x):
+        return "cpu"
+    elif is_dask_array(x):
+        # Peek at the metadata of the Dask array to determine type
+        if is_numpy_array(x._meta):
+            # Must be on CPU since backed by numpy
+            return "cpu"
+        return _DASK_DEVICE
+    elif is_jax_array(x):
+        # FIXME Jitted JAX arrays do not have a device attribute
+        #       https://github.com/jax-ml/jax/issues/26000
+        #       Return None in this case. Note that this workaround breaks
+        #       the standard and will result in new arrays being created on the
+        #       default device instead of the same device as the input array(s).
+        x_device = getattr(x, "device", None)
+        # Older JAX releases had .device() as a method, which has been replaced
+        # with a property in accordance with the standard.
+        if inspect.ismethod(x_device):
+            return x_device()
+        else:
+            return x_device
+    elif is_pydata_sparse_array(x):
+        # `sparse` will gain `.device`, so check for this first.
+        x_device = getattr(x, "device", None)
+        if x_device is not None:
+            return x_device
+        # Everything but DOK has this attr.
+        try:
+            inner = x.data  # pyright: ignore
+        except AttributeError:
+            return "cpu"
+        # Return the device of the constituent array
+        return device(inner)  # pyright: ignore
+    return x.device  # type: ignore  # pyright: ignore
+
+
+# Prevent shadowing, used below
+_device = device
+
+
+# Based on cupy.array_api.Array.to_device
+def _cupy_to_device(
+    x: cp.ndarray,
+    device: Device,
+    /,
+    stream: int | Any | None = None,
+) -> cp.ndarray:
+    import cupy as cp
+
+    if device == "cpu":
+        # allowing us to use `to_device(x, "cpu")`
+        # is useful for portable test swapping between
+        # host and device backends
+        return x.get()
+    if not isinstance(device, cp.cuda.Device):
+        raise TypeError(f"Unsupported device type {device!r}")
+
+    if stream is None:
+        with device:
+            return cp.asarray(x)
+
+    # stream can be an int as specified in __dlpack__, or a CuPy stream
+    if isinstance(stream, int):
+        stream = cp.cuda.ExternalStream(stream)
+    elif not isinstance(stream, cp.cuda.Stream):
+        raise TypeError(f"Unsupported stream type {stream!r}")
+
+    with device, stream:
+        return cp.asarray(x)
+
+
+def _torch_to_device(
+    x: torch.Tensor,
+    device: torch.device | str | int,
+    /,
+    stream: int | Any | None = None,
+) -> torch.Tensor:
+    if stream is not None:
+        raise NotImplementedError
+    return x.to(device)
+
+
+def to_device(x: Array, device: Device, /, *, stream: int | Any | None = None) -> Array:
+    """
+    Copy the array from the device on which it currently resides to the specified ``device``.
+
+    This is equivalent to `x.to_device(device, stream=stream)` according to
+    the `standard
+    `__.
+    This helper is included because some array libraries do not have the
+    `to_device` method.
+
+    Parameters
+    ----------
+
+    x: array
+        array instance from an array API compatible library.
+
+    device: device
+        a ``device`` object (see the `Device Support `__
+        section of the array API specification).
+
+    stream: int | Any | None
+        stream object to use during copy. In addition to the types supported
+        in ``array.__dlpack__``, implementations may choose to support any
+        library-specific stream object with the caveat that any code using
+        such an object would not be portable.
+
+    Returns
+    -------
+
+    out: array
+        an array with the same data and data type as ``x`` and located on the
+        specified ``device``.
+
+    Notes
+    -----
+
+    For NumPy, this function effectively does nothing since the only supported
+    device is the CPU. For CuPy, this method supports CuPy CUDA
+    :external+cupy:class:`Device ` and
+    :external+cupy:class:`Stream ` objects. For PyTorch,
+    this is the same as :external+torch:meth:`x.to(device) `
+    (the ``stream`` argument is not supported in PyTorch).
+
+    See Also
+    --------
+
+    device : Hardware device the array data resides on.
+
+    """
+    if is_numpy_array(x):
+        if stream is not None:
+            raise ValueError("The stream argument to to_device() is not supported")
+        if device == "cpu":
+            return x
+        raise ValueError(f"Unsupported device {device!r}")
+    elif is_cupy_array(x):
+        # cupy does not yet have to_device
+        return _cupy_to_device(x, device, stream=stream)
+    elif is_torch_array(x):
+        return _torch_to_device(x, device, stream=stream)
+    elif is_dask_array(x):
+        if stream is not None:
+            raise ValueError("The stream argument to to_device() is not supported")
+        # TODO: What if our array is on the GPU already?
+        if device == "cpu":
+            return x
+        raise ValueError(f"Unsupported device {device!r}")
+    elif is_jax_array(x):
+        if not hasattr(x, "__array_namespace__"):
+            # In JAX v0.4.31 and older, this import adds to_device method to x...
+            import jax.experimental.array_api  # noqa: F401  # pyright: ignore
+
+            # ... but only on eager JAX. It won't work inside jax.jit.
+            if not hasattr(x, "to_device"):
+                return x
+        return x.to_device(device, stream=stream)
+    elif is_pydata_sparse_array(x) and device == _device(x):
+        # Perform trivial check to return the same array if
+        # device is same instead of err-ing.
+        return x
+    return x.to_device(device, stream=stream)  # pyright: ignore
+
+
+@overload
+def size(x: HasShape[Collection[SupportsIndex]]) -> int: ...
+@overload
+def size(x: HasShape[Collection[SupportsIndex | None]]) -> int | None: ...
+def size(x: HasShape[Collection[SupportsIndex | None]]) -> int | None:
+    """
+    Return the total number of elements of x.
+
+    This is equivalent to `x.size` according to the `standard
+    `__.
+
+    This helper is included because PyTorch defines `size` in an
+    :external+torch:meth:`incompatible way `.
+    It also fixes dask.array's behaviour which returns nan for unknown sizes, whereas
+    the standard requires None.
+    """
+    # Lazy API compliant arrays, such as ndonnx, can contain None in their shape
+    if None in x.shape:
+        return None
+    out = math.prod(cast("Collection[SupportsIndex]", x.shape))
+    # dask.array.Array.shape can contain NaN
+    return None if math.isnan(out) else out
+
+
+@lru_cache(100)
+def _is_writeable_cls(cls: type) -> bool | None:
+    if (
+        _issubclass_fast(cls, "numpy", "generic")
+        or _issubclass_fast(cls, "jax", "Array")
+        or _issubclass_fast(cls, "jax.core", "Tracer")  # see is_jax_array for limitations
+        or _issubclass_fast(cls, "sparse", "SparseArray")
+    ):
+        return False
+    if _is_array_api_cls(cls):
+        return True
+    return None
+
+
+def is_writeable_array(x: object) -> TypeGuard[_ArrayApiObj]:
+    """
+    Return False if ``x.__setitem__`` is expected to raise; True otherwise.
+    Return False if `x` is not an array API compatible object.
+
+    Warning
+    -------
+    As there is no standard way to check if an array is writeable without actually
+    writing to it, this function blindly returns True for all unknown array types.
+    """
+    cls = cast(Hashable, type(x))
+    if _issubclass_fast(cls, "numpy", "ndarray"):
+        return cast("npt.NDArray", x).flags.writeable
+    res = _is_writeable_cls(cls)
+    if res is not None:
+        return res
+    return hasattr(x, '__array_namespace__')
+
+
+@lru_cache(100)
+def _is_lazy_cls(cls: type) -> bool | None:
+    if (
+        _issubclass_fast(cls, "numpy", "ndarray")
+        or _issubclass_fast(cls, "numpy", "generic")
+        or _issubclass_fast(cls, "cupy", "ndarray")
+        or _issubclass_fast(cls, "torch", "Tensor")
+        or _issubclass_fast(cls, "sparse", "SparseArray")
+    ):
+        return False
+    if (
+        _issubclass_fast(cls, "jax", "Array")
+        or _issubclass_fast(cls, "jax.core", "Tracer")  # see is_jax_array for limitations
+        or _issubclass_fast(cls, "dask.array", "Array")
+        or _issubclass_fast(cls, "ndonnx", "Array")
+    ):
+        return True
+    return  None
+
+
+def is_lazy_array(x: object) -> TypeGuard[_ArrayApiObj]:
+    """Return True if x is potentially a future or it may be otherwise impossible or
+    expensive to eagerly read its contents, regardless of their size, e.g. by
+    calling ``bool(x)`` or ``float(x)``.
+
+    Return False otherwise; e.g. ``bool(x)`` etc. is guaranteed to succeed and to be
+    cheap as long as the array has the right dtype and size.
+
+    Note
+    ----
+    This function errs on the side of caution for array types that may or may not be
+    lazy, e.g. JAX arrays, by always returning True for them.
+    """
+    # **JAX note:** while it is possible to determine if you're inside or outside
+    # jax.jit by testing the subclass of a jax.Array object, as well as testing bool()
+    # as we do below for unknown arrays, this is not recommended by JAX best practices.
+
+    # **Dask note:** Dask eagerly computes the graph on __bool__, __float__, and so on.
+    # This behaviour, while impossible to change without breaking backwards
+    # compatibility, is highly detrimental to performance as the whole graph will end
+    # up being computed multiple times.
+
+    # Note: skipping reclassification of JAX zero gradient arrays, as one will
+    # exclusively get them once they leave a jax.grad JIT context.
+    cls = cast(Hashable, type(x))
+    res = _is_lazy_cls(cls)
+    if res is not None:
+        return res
+
+    if not hasattr(x, "__array_namespace__"):
+        return False
+
+    # Unknown Array API compatible object. Note that this test may have dire consequences
+    # in terms of performance, e.g. for a lazy object that eagerly computes the graph
+    # on __bool__ (dask is one such example, which however is special-cased above).
+
+    # Select a single point of the array
+    s = size(cast("HasShape[Collection[SupportsIndex | None]]", x))
+    if s is None:
+        return True
+    xp = array_namespace(x)
+    if s > 1:
+        x = xp.reshape(x, (-1,))[0]
+    # Cast to dtype=bool and deal with size 0 arrays
+    x = xp.any(x)
+
+    try:
+        bool(x)
+        return False
+    # The Array API standard dictactes that __bool__ should raise TypeError if the
+    # output cannot be defined.
+    # Here we allow for it to raise arbitrary exceptions, e.g. like Dask does.
+    except Exception:
+        return True
+
+
+__all__ = [
+    "array_namespace",
+    "device",
+    "get_namespace",
+    "is_array_api_obj",
+    "is_array_api_strict_namespace",
+    "is_cupy_array",
+    "is_cupy_namespace",
+    "is_dask_array",
+    "is_dask_namespace",
+    "is_jax_array",
+    "is_jax_namespace",
+    "is_numpy_array",
+    "is_numpy_namespace",
+    "is_torch_array",
+    "is_torch_namespace",
+    "is_ndonnx_array",
+    "is_ndonnx_namespace",
+    "is_pydata_sparse_array",
+    "is_pydata_sparse_namespace",
+    "is_writeable_array",
+    "is_lazy_array",
+    "size",
+    "to_device",
+]
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_linalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..69672af768d065a3a7507e0a5ea84d6238ff174d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_linalg.py
@@ -0,0 +1,230 @@
+from __future__ import annotations
+
+import math
+from typing import Literal, NamedTuple, cast
+
+import numpy as np
+
+if np.__version__[0] == "2":
+    from numpy.lib.array_utils import normalize_axis_tuple
+else:
+    from numpy.core.numeric import normalize_axis_tuple  # type: ignore[no-redef]
+
+from .._internal import get_xp
+from ._aliases import isdtype, matmul, matrix_transpose, tensordot, vecdot
+from ._typing import Array, DType, JustFloat, JustInt, Namespace
+
+
+# These are in the main NumPy namespace but not in numpy.linalg
+def cross(
+    x1: Array,
+    x2: Array,
+    /,
+    xp: Namespace,
+    *,
+    axis: int = -1,
+    **kwargs: object,
+) -> Array:
+    return xp.cross(x1, x2, axis=axis, **kwargs)
+
+def outer(x1: Array, x2: Array, /, xp: Namespace, **kwargs: object) -> Array:
+    return xp.outer(x1, x2, **kwargs)
+
+class EighResult(NamedTuple):
+    eigenvalues: Array
+    eigenvectors: Array
+
+class QRResult(NamedTuple):
+    Q: Array
+    R: Array
+
+class SlogdetResult(NamedTuple):
+    sign: Array
+    logabsdet: Array
+
+class SVDResult(NamedTuple):
+    U: Array
+    S: Array
+    Vh: Array
+
+# These functions are the same as their NumPy counterparts except they return
+# a namedtuple.
+def eigh(x: Array, /, xp: Namespace, **kwargs: object) -> EighResult:
+    return EighResult(*xp.linalg.eigh(x, **kwargs))
+
+def qr(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    mode: Literal["reduced", "complete"] = "reduced",
+    **kwargs: object,
+) -> QRResult:
+    return QRResult(*xp.linalg.qr(x, mode=mode, **kwargs))
+
+def slogdet(x: Array, /, xp: Namespace, **kwargs: object) -> SlogdetResult:
+    return SlogdetResult(*xp.linalg.slogdet(x, **kwargs))
+
+def svd(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    full_matrices: bool = True,
+    **kwargs: object,
+) -> SVDResult:
+    return SVDResult(*xp.linalg.svd(x, full_matrices=full_matrices, **kwargs))
+
+# These functions have additional keyword arguments
+
+# The upper keyword argument is new from NumPy
+def cholesky(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    upper: bool = False,
+    **kwargs: object,
+) -> Array:
+    L = xp.linalg.cholesky(x, **kwargs)
+    if upper:
+        U = get_xp(xp)(matrix_transpose)(L)
+        if get_xp(xp)(isdtype)(U.dtype, 'complex floating'):
+            U = xp.conj(U)  # pyright: ignore[reportConstantRedefinition]
+        return U
+    return L
+
+# The rtol keyword argument of matrix_rank() and pinv() is new from NumPy.
+# Note that it has a different semantic meaning from tol and rcond.
+def matrix_rank(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    rtol: float | Array | None = None,
+    **kwargs: object,
+) -> Array:
+    # this is different from xp.linalg.matrix_rank, which supports 1
+    # dimensional arrays.
+    if x.ndim < 2:
+        raise xp.linalg.LinAlgError("1-dimensional array given. Array must be at least two-dimensional")
+    S: Array = get_xp(xp)(svdvals)(x, **kwargs)
+    if rtol is None:
+        tol = S.max(axis=-1, keepdims=True) * max(x.shape[-2:]) * xp.finfo(S.dtype).eps
+    else:
+        # this is different from xp.linalg.matrix_rank, which does not
+        # multiply the tolerance by the largest singular value.
+        tol = S.max(axis=-1, keepdims=True)*xp.asarray(rtol)[..., xp.newaxis]
+    return xp.count_nonzero(S > tol, axis=-1)
+
+def pinv(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    rtol: float | Array | None = None,
+    **kwargs: object,
+) -> Array:
+    # this is different from xp.linalg.pinv, which does not multiply the
+    # default tolerance by max(M, N).
+    if rtol is None:
+        rtol = max(x.shape[-2:]) * xp.finfo(x.dtype).eps
+    return xp.linalg.pinv(x, rcond=rtol, **kwargs)
+
+# These functions are new in the array API spec
+
+def matrix_norm(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    keepdims: bool = False,
+    ord: Literal[1, 2, -1, -2] | JustFloat | Literal["fro", "nuc"] | None = "fro",
+) -> Array:
+    return xp.linalg.norm(x, axis=(-2, -1), keepdims=keepdims, ord=ord)
+
+# svdvals is not in NumPy (but it is in SciPy). It is equivalent to
+# xp.linalg.svd(compute_uv=False).
+def svdvals(x: Array, /, xp: Namespace) -> Array | tuple[Array, ...]:
+    return xp.linalg.svd(x, compute_uv=False)
+
+def vector_norm(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    axis: int | tuple[int, ...] | None = None,
+    keepdims: bool = False,
+    ord: JustInt | JustFloat = 2,
+) -> Array:
+    # xp.linalg.norm tries to do a matrix norm whenever axis is a 2-tuple or
+    # when axis=None and the input is 2-D, so to force a vector norm, we make
+    # it so the input is 1-D (for axis=None), or reshape so that norm is done
+    # on a single dimension.
+    if axis is None:
+        # Note: xp.linalg.norm() doesn't handle 0-D arrays
+        _x = x.ravel()
+        _axis = 0
+    elif isinstance(axis, tuple):
+        # Note: The axis argument supports any number of axes, whereas
+        # xp.linalg.norm() only supports a single axis for vector norm.
+        normalized_axis = cast(
+            "tuple[int, ...]",
+            normalize_axis_tuple(axis, x.ndim),  # pyright: ignore[reportCallIssue]
+        )
+        rest = tuple(i for i in range(x.ndim) if i not in normalized_axis)
+        newshape = axis + rest
+        _x = xp.transpose(x, newshape).reshape(
+            (math.prod([x.shape[i] for i in axis]), *[x.shape[i] for i in rest]))
+        _axis = 0
+    else:
+        _x = x
+        _axis = axis
+
+    res = xp.linalg.norm(_x, axis=_axis, ord=ord)
+
+    if keepdims:
+        # We can't reuse xp.linalg.norm(keepdims) because of the reshape hacks
+        # above to avoid matrix norm logic.
+        shape = list(x.shape)
+        axes = cast(
+            "tuple[int, ...]",
+            normalize_axis_tuple(  # pyright: ignore[reportCallIssue]
+                range(x.ndim) if axis is None else axis,
+                x.ndim,
+            ),
+        )
+        for i in axes:
+            shape[i] = 1
+        res = xp.reshape(res, tuple(shape))
+
+    return res
+
+# xp.diagonal and xp.trace operate on the first two axes whereas these
+# operates on the last two
+
+def diagonal(x: Array, /, xp: Namespace, *, offset: int = 0, **kwargs: object) -> Array:
+    return xp.diagonal(x, offset=offset, axis1=-2, axis2=-1, **kwargs)
+
+def trace(
+    x: Array,
+    /,
+    xp: Namespace,
+    *,
+    offset: int = 0,
+    dtype: DType | None = None,
+    **kwargs: object,
+) -> Array:
+    return xp.asarray(
+        xp.trace(x, offset=offset, dtype=dtype, axis1=-2, axis2=-1, **kwargs)
+    )
+
+__all__ = ['cross', 'matmul', 'outer', 'tensordot', 'EighResult',
+           'QRResult', 'SlogdetResult', 'SVDResult', 'eigh', 'qr', 'slogdet',
+           'svd', 'cholesky', 'matrix_rank', 'pinv', 'matrix_norm',
+           'matrix_transpose', 'svdvals', 'vecdot', 'vector_norm', 'diagonal',
+           'trace']
+
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_typing.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_typing.py
new file mode 100644
index 0000000000000000000000000000000000000000..11b00bd10395f43bf71e008d09aad5dffaf2f98a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/common/_typing.py
@@ -0,0 +1,189 @@
+from __future__ import annotations
+
+from collections.abc import Mapping
+from types import ModuleType as Namespace
+from typing import (
+    TYPE_CHECKING,
+    Literal,
+    Protocol,
+    TypeAlias,
+    TypedDict,
+    TypeVar,
+    final,
+)
+
+if TYPE_CHECKING:
+    from _typeshed import Incomplete
+
+    SupportsBufferProtocol: TypeAlias = Incomplete
+    Array: TypeAlias = Incomplete
+    Device: TypeAlias = Incomplete
+    DType: TypeAlias = Incomplete
+else:
+    SupportsBufferProtocol = object
+    Array = object
+    Device = object
+    DType = object
+
+
+_T_co = TypeVar("_T_co", covariant=True)
+
+
+# These "Just" types are equivalent to the `Just` type from the `optype` library,
+# apart from them not being `@runtime_checkable`.
+# - docs: https://github.com/jorenham/optype/blob/master/README.md#just
+# - code: https://github.com/jorenham/optype/blob/master/optype/_core/_just.py
+@final
+class JustInt(Protocol):  # type: ignore[misc]
+    @property  # type: ignore[override]
+    def __class__(self, /) -> type[int]: ...
+    @__class__.setter
+    def __class__(self, value: type[int], /) -> None: ...  # pyright: ignore[reportIncompatibleMethodOverride]
+
+
+@final
+class JustFloat(Protocol):  # type: ignore[misc]
+    @property  # type: ignore[override]
+    def __class__(self, /) -> type[float]: ...
+    @__class__.setter
+    def __class__(self, value: type[float], /) -> None: ...  # pyright: ignore[reportIncompatibleMethodOverride]
+
+
+@final
+class JustComplex(Protocol):  # type: ignore[misc]
+    @property  # type: ignore[override]
+    def __class__(self, /) -> type[complex]: ...
+    @__class__.setter
+    def __class__(self, value: type[complex], /) -> None: ...  # pyright: ignore[reportIncompatibleMethodOverride]
+
+
+class NestedSequence(Protocol[_T_co]):
+    def __getitem__(self, key: int, /) -> _T_co | NestedSequence[_T_co]: ...
+    def __len__(self, /) -> int: ...
+
+
+class SupportsArrayNamespace(Protocol[_T_co]):
+    def __array_namespace__(self, /, *, api_version: str | None) -> _T_co: ...
+
+
+class HasShape(Protocol[_T_co]):
+    @property
+    def shape(self, /) -> _T_co: ...
+
+
+# Return type of `__array_namespace_info__.default_dtypes`
+Capabilities = TypedDict(
+    "Capabilities",
+    {
+        "boolean indexing": bool,
+        "data-dependent shapes": bool,
+        "max dimensions": int,
+    },
+)
+
+# Return type of `__array_namespace_info__.default_dtypes`
+DefaultDTypes = TypedDict(
+    "DefaultDTypes",
+    {
+        "real floating": DType,
+        "complex floating": DType,
+        "integral": DType,
+        "indexing": DType,
+    },
+)
+
+
+_DTypeKind: TypeAlias = Literal[
+    "bool",
+    "signed integer",
+    "unsigned integer",
+    "integral",
+    "real floating",
+    "complex floating",
+    "numeric",
+]
+# Type of the `kind` parameter in `__array_namespace_info__.dtypes`
+DTypeKind: TypeAlias = _DTypeKind | tuple[_DTypeKind, ...]
+
+
+# `__array_namespace_info__.dtypes(kind="bool")`
+class DTypesBool(TypedDict):
+    bool: DType
+
+
+# `__array_namespace_info__.dtypes(kind="signed integer")`
+class DTypesSigned(TypedDict):
+    int8: DType
+    int16: DType
+    int32: DType
+    int64: DType
+
+
+# `__array_namespace_info__.dtypes(kind="unsigned integer")`
+class DTypesUnsigned(TypedDict):
+    uint8: DType
+    uint16: DType
+    uint32: DType
+    uint64: DType
+
+
+# `__array_namespace_info__.dtypes(kind="integral")`
+class DTypesIntegral(DTypesSigned, DTypesUnsigned):
+    pass
+
+
+# `__array_namespace_info__.dtypes(kind="real floating")`
+class DTypesReal(TypedDict):
+    float32: DType
+    float64: DType
+
+
+# `__array_namespace_info__.dtypes(kind="complex floating")`
+class DTypesComplex(TypedDict):
+    complex64: DType
+    complex128: DType
+
+
+# `__array_namespace_info__.dtypes(kind="numeric")`
+class DTypesNumeric(DTypesIntegral, DTypesReal, DTypesComplex):
+    pass
+
+
+# `__array_namespace_info__.dtypes(kind=None)` (default)
+class DTypesAll(DTypesBool, DTypesNumeric):
+    pass
+
+
+# `__array_namespace_info__.dtypes(kind=?)` (fallback)
+DTypesAny: TypeAlias = Mapping[str, DType]
+
+
+__all__ = [
+    "Array",
+    "Capabilities",
+    "DType",
+    "DTypeKind",
+    "DTypesAny",
+    "DTypesAll",
+    "DTypesBool",
+    "DTypesNumeric",
+    "DTypesIntegral",
+    "DTypesSigned",
+    "DTypesUnsigned",
+    "DTypesReal",
+    "DTypesComplex",
+    "DefaultDTypes",
+    "Device",
+    "HasShape",
+    "Namespace",
+    "JustInt",
+    "JustFloat",
+    "JustComplex",
+    "NestedSequence",
+    "SupportsArrayNamespace",
+    "SupportsBufferProtocol",
+]
+
+
+def __dir__() -> list[str]:
+    return __all__
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/._linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/._linalg.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..af003c5adaa52992bb673259d882098a499753e9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/__init__.py
@@ -0,0 +1,24 @@
+from typing import Final
+from cupy import * # noqa: F403
+
+# from cupy import * doesn't overwrite these builtin names
+from cupy import abs, max, min, round # noqa: F401
+
+# These imports may overwrite names from the import * above.
+from ._aliases import * # noqa: F403
+from ._info import __array_namespace_info__  # noqa: F401
+
+# See the comment in the numpy __init__.py
+__import__(__package__ + '.linalg')
+__import__(__package__ + '.fft')
+
+__array_api_version__: Final = '2024.12'
+
+__all__ = sorted(
+    {name for name in globals() if not name.startswith("__")}
+    - {"Final", "_aliases", "_info", "_typing"}
+    | {"__array_api_version__", "__array_namespace_info__", "linalg", "fft"}
+)
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/_aliases.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/_aliases.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e512fc896399bae466f3b9a7803ce280c06f551
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/_aliases.py
@@ -0,0 +1,168 @@
+from __future__ import annotations
+
+from builtins import bool as py_bool
+
+import cupy as cp
+
+from ..common import _aliases, _helpers
+from ..common._typing import NestedSequence, SupportsBufferProtocol
+from .._internal import get_xp
+from ._typing import Array, Device, DType
+
+bool = cp.bool_
+
+# Basic renames
+acos = cp.arccos
+acosh = cp.arccosh
+asin = cp.arcsin
+asinh = cp.arcsinh
+atan = cp.arctan
+atan2 = cp.arctan2
+atanh = cp.arctanh
+bitwise_left_shift = cp.left_shift
+bitwise_invert = cp.invert
+bitwise_right_shift = cp.right_shift
+concat = cp.concatenate
+pow = cp.power
+
+arange = get_xp(cp)(_aliases.arange)
+empty = get_xp(cp)(_aliases.empty)
+empty_like = get_xp(cp)(_aliases.empty_like)
+eye = get_xp(cp)(_aliases.eye)
+full = get_xp(cp)(_aliases.full)
+full_like = get_xp(cp)(_aliases.full_like)
+linspace = get_xp(cp)(_aliases.linspace)
+ones = get_xp(cp)(_aliases.ones)
+ones_like = get_xp(cp)(_aliases.ones_like)
+zeros = get_xp(cp)(_aliases.zeros)
+zeros_like = get_xp(cp)(_aliases.zeros_like)
+UniqueAllResult = get_xp(cp)(_aliases.UniqueAllResult)
+UniqueCountsResult = get_xp(cp)(_aliases.UniqueCountsResult)
+UniqueInverseResult = get_xp(cp)(_aliases.UniqueInverseResult)
+unique_all = get_xp(cp)(_aliases.unique_all)
+unique_counts = get_xp(cp)(_aliases.unique_counts)
+unique_inverse = get_xp(cp)(_aliases.unique_inverse)
+unique_values = get_xp(cp)(_aliases.unique_values)
+std = get_xp(cp)(_aliases.std)
+var = get_xp(cp)(_aliases.var)
+cumulative_sum = get_xp(cp)(_aliases.cumulative_sum)
+cumulative_prod = get_xp(cp)(_aliases.cumulative_prod)
+clip = get_xp(cp)(_aliases.clip)
+permute_dims = get_xp(cp)(_aliases.permute_dims)
+reshape = get_xp(cp)(_aliases.reshape)
+argsort = get_xp(cp)(_aliases.argsort)
+sort = get_xp(cp)(_aliases.sort)
+nonzero = get_xp(cp)(_aliases.nonzero)
+matmul = get_xp(cp)(_aliases.matmul)
+matrix_transpose = get_xp(cp)(_aliases.matrix_transpose)
+tensordot = get_xp(cp)(_aliases.tensordot)
+sign = get_xp(cp)(_aliases.sign)
+finfo = get_xp(cp)(_aliases.finfo)
+iinfo = get_xp(cp)(_aliases.iinfo)
+
+
+# asarray also adds the copy keyword, which is not present in numpy 1.0.
+def asarray(
+    obj: Array | complex | NestedSequence[complex] | SupportsBufferProtocol,
+    /,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    copy: py_bool | None = None,
+    **kwargs: object,
+) -> Array:
+    """
+    Array API compatibility wrapper for asarray().
+
+    See the corresponding documentation in the array library and/or the array API
+    specification for more details.
+    """
+    with cp.cuda.Device(device):
+        if copy is None:
+            return cp.asarray(obj, dtype=dtype, **kwargs)
+        else:
+            res = cp.array(obj, dtype=dtype, copy=copy, **kwargs)
+            if not copy and res is not obj:
+                raise ValueError("Unable to avoid copy while creating an array as requested")
+            return res
+
+
+def astype(
+    x: Array,
+    dtype: DType,
+    /,
+    *,
+    copy: py_bool = True,
+    device: Device | None = None,
+) -> Array:
+    if device is None:
+        return x.astype(dtype=dtype, copy=copy)
+    out = _helpers.to_device(x.astype(dtype=dtype, copy=False), device)
+    return out.copy() if copy and out is x else out
+
+
+# cupy.count_nonzero does not have keepdims
+def count_nonzero(
+    x: Array,
+    axis: int | tuple[int, ...] | None = None,
+    keepdims: py_bool = False,
+) -> Array:
+   result = cp.count_nonzero(x, axis)
+   if keepdims:
+       if axis is None:
+            return cp.reshape(result, [1]*x.ndim)
+       return cp.expand_dims(result, axis)
+   return result
+
+# ceil, floor, and trunc return integers for integer inputs
+
+def ceil(x: Array, /) -> Array:
+    if cp.issubdtype(x.dtype, cp.integer):
+        return x.copy()
+    return cp.ceil(x)
+
+
+def floor(x: Array, /) -> Array:
+    if cp.issubdtype(x.dtype, cp.integer):
+        return x.copy()
+    return cp.floor(x)
+
+
+def trunc(x: Array, /) -> Array:
+    if cp.issubdtype(x.dtype, cp.integer):
+        return x.copy()
+    return cp.trunc(x)
+
+
+# take_along_axis: axis defaults to -1 but in cupy (and numpy) axis is a required arg
+def take_along_axis(x: Array, indices: Array, /, *, axis: int = -1) -> Array:
+    return cp.take_along_axis(x, indices, axis=axis)
+
+
+# These functions are completely new here. If the library already has them
+# (i.e., numpy 2.0), use the library version instead of our wrapper.
+if hasattr(cp, 'vecdot'):
+    vecdot = cp.vecdot
+else:
+    vecdot = get_xp(cp)(_aliases.vecdot)
+
+if hasattr(cp, 'isdtype'):
+    isdtype = cp.isdtype
+else:
+    isdtype = get_xp(cp)(_aliases.isdtype)
+
+if hasattr(cp, 'unstack'):
+    unstack = cp.unstack
+else:
+    unstack = get_xp(cp)(_aliases.unstack)
+
+__all__ = _aliases.__all__ + ['asarray', 'astype',
+                              'acos', 'acosh', 'asin', 'asinh', 'atan',
+                              'atan2', 'atanh', 'bitwise_left_shift',
+                              'bitwise_invert', 'bitwise_right_shift',
+                              'bool', 'concat', 'count_nonzero', 'pow', 'sign',
+                              'ceil', 'floor', 'trunc', 'take_along_axis']
+
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/_info.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..78e48a3358cf547a9a77c5ebdc95fa81c3d4e144
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/_info.py
@@ -0,0 +1,336 @@
+"""
+Array API Inspection namespace
+
+This is the namespace for inspection functions as defined by the array API
+standard. See
+https://data-apis.org/array-api/latest/API_specification/inspection.html for
+more details.
+
+"""
+from cupy import (
+    dtype,
+    cuda,
+    bool_ as bool,
+    intp,
+    int8,
+    int16,
+    int32,
+    int64,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+    float32,
+    float64,
+    complex64,
+    complex128,
+)
+
+
+class __array_namespace_info__:
+    """
+    Get the array API inspection namespace for CuPy.
+
+    The array API inspection namespace defines the following functions:
+
+    - capabilities()
+    - default_device()
+    - default_dtypes()
+    - dtypes()
+    - devices()
+
+    See
+    https://data-apis.org/array-api/latest/API_specification/inspection.html
+    for more details.
+
+    Returns
+    -------
+    info : ModuleType
+        The array API inspection namespace for CuPy.
+
+    Examples
+    --------
+    >>> info = xp.__array_namespace_info__()
+    >>> info.default_dtypes()
+    {'real floating': cupy.float64,
+     'complex floating': cupy.complex128,
+     'integral': cupy.int64,
+     'indexing': cupy.int64}
+
+    """
+
+    __module__ = 'cupy'
+
+    def capabilities(self):
+        """
+        Return a dictionary of array API library capabilities.
+
+        The resulting dictionary has the following keys:
+
+        - **"boolean indexing"**: boolean indicating whether an array library
+          supports boolean indexing. Always ``True`` for CuPy.
+
+        - **"data-dependent shapes"**: boolean indicating whether an array
+          library supports data-dependent output shapes. Always ``True`` for
+          CuPy.
+
+        See
+        https://data-apis.org/array-api/latest/API_specification/generated/array_api.info.capabilities.html
+        for more details.
+
+        See Also
+        --------
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Returns
+        -------
+        capabilities : dict
+            A dictionary of array API library capabilities.
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.capabilities()
+        {'boolean indexing': True,
+         'data-dependent shapes': True,
+         'max dimensions': 64}
+
+        """
+        return {
+            "boolean indexing": True,
+            "data-dependent shapes": True,
+            "max dimensions": 64,
+        }
+
+    def default_device(self):
+        """
+        The default device used for new CuPy arrays.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Returns
+        -------
+        device : Device
+            The default device used for new CuPy arrays.
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.default_device()
+        Device(0)
+
+        Notes
+        -----
+        This method returns the static default device when CuPy is initialized.
+        However, the *current* device used by creation functions (``empty`` etc.)
+        can be changed globally or with a context manager.
+
+        See Also
+        --------
+        https://github.com/data-apis/array-api/issues/835
+        """
+        return cuda.Device(0)
+
+    def default_dtypes(self, *, device=None):
+        """
+        The default data types used for new CuPy arrays.
+
+        For CuPy, this always returns the following dictionary:
+
+        - **"real floating"**: ``cupy.float64``
+        - **"complex floating"**: ``cupy.complex128``
+        - **"integral"**: ``cupy.intp``
+        - **"indexing"**: ``cupy.intp``
+
+        Parameters
+        ----------
+        device : str, optional
+            The device to get the default data types for.
+
+        Returns
+        -------
+        dtypes : dict
+            A dictionary describing the default data types used for new CuPy
+            arrays.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.default_dtypes()
+        {'real floating': cupy.float64,
+         'complex floating': cupy.complex128,
+         'integral': cupy.int64,
+         'indexing': cupy.int64}
+
+        """
+        # TODO: Does this depend on device?
+        return {
+            "real floating": dtype(float64),
+            "complex floating": dtype(complex128),
+            "integral": dtype(intp),
+            "indexing": dtype(intp),
+        }
+
+    def dtypes(self, *, device=None, kind=None):
+        """
+        The array API data types supported by CuPy.
+
+        Note that this function only returns data types that are defined by
+        the array API.
+
+        Parameters
+        ----------
+        device : str, optional
+            The device to get the data types for.
+        kind : str or tuple of str, optional
+            The kind of data types to return. If ``None``, all data types are
+            returned. If a string, only data types of that kind are returned.
+            If a tuple, a dictionary containing the union of the given kinds
+            is returned. The following kinds are supported:
+
+            - ``'bool'``: boolean data types (i.e., ``bool``).
+            - ``'signed integer'``: signed integer data types (i.e., ``int8``,
+              ``int16``, ``int32``, ``int64``).
+            - ``'unsigned integer'``: unsigned integer data types (i.e.,
+              ``uint8``, ``uint16``, ``uint32``, ``uint64``).
+            - ``'integral'``: integer data types. Shorthand for ``('signed
+              integer', 'unsigned integer')``.
+            - ``'real floating'``: real-valued floating-point data types
+              (i.e., ``float32``, ``float64``).
+            - ``'complex floating'``: complex floating-point data types (i.e.,
+              ``complex64``, ``complex128``).
+            - ``'numeric'``: numeric data types. Shorthand for ``('integral',
+              'real floating', 'complex floating')``.
+
+        Returns
+        -------
+        dtypes : dict
+            A dictionary mapping the names of data types to the corresponding
+            CuPy data types.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.devices
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.dtypes(kind='signed integer')
+        {'int8': cupy.int8,
+         'int16': cupy.int16,
+         'int32': cupy.int32,
+         'int64': cupy.int64}
+
+        """
+        # TODO: Does this depend on device?
+        if kind is None:
+            return {
+                "bool": dtype(bool),
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+                "float32": dtype(float32),
+                "float64": dtype(float64),
+                "complex64": dtype(complex64),
+                "complex128": dtype(complex128),
+            }
+        if kind == "bool":
+            return {"bool": bool}
+        if kind == "signed integer":
+            return {
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+            }
+        if kind == "unsigned integer":
+            return {
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+            }
+        if kind == "integral":
+            return {
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+            }
+        if kind == "real floating":
+            return {
+                "float32": dtype(float32),
+                "float64": dtype(float64),
+            }
+        if kind == "complex floating":
+            return {
+                "complex64": dtype(complex64),
+                "complex128": dtype(complex128),
+            }
+        if kind == "numeric":
+            return {
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+                "float32": dtype(float32),
+                "float64": dtype(float64),
+                "complex64": dtype(complex64),
+                "complex128": dtype(complex128),
+            }
+        if isinstance(kind, tuple):
+            res = {}
+            for k in kind:
+                res.update(self.dtypes(kind=k))
+            return res
+        raise ValueError(f"unsupported kind: {kind!r}")
+
+    def devices(self):
+        """
+        The devices supported by CuPy.
+
+        Returns
+        -------
+        devices : list[Device]
+            The devices supported by CuPy.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes
+
+        """
+        return [cuda.Device(i) for i in range(cuda.runtime.getDeviceCount())]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/_typing.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/_typing.py
new file mode 100644
index 0000000000000000000000000000000000000000..e5c202dc53e097936671115943072ad58dd8d389
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/_typing.py
@@ -0,0 +1,30 @@
+from __future__ import annotations
+
+__all__ = ["Array", "DType", "Device"]
+
+from typing import TYPE_CHECKING
+
+import cupy as cp
+from cupy import ndarray as Array
+from cupy.cuda.device import Device
+
+if TYPE_CHECKING:
+    # NumPy 1.x on Python 3.10 fails to parse np.dtype[]
+    DType = cp.dtype[
+        cp.intp
+        | cp.int8
+        | cp.int16
+        | cp.int32
+        | cp.int64
+        | cp.uint8
+        | cp.uint16
+        | cp.uint32
+        | cp.uint64
+        | cp.float32
+        | cp.float64
+        | cp.complex64
+        | cp.complex128
+        | cp.bool_
+    ]
+else:
+    DType = cp.dtype
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/fft.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/fft.py
new file mode 100644
index 0000000000000000000000000000000000000000..53a9a45438651bc2adc7bc19884fe9361ef99580
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/fft.py
@@ -0,0 +1,36 @@
+from cupy.fft import *  # noqa: F403
+
+# cupy.fft doesn't have __all__. If it is added, replace this with
+#
+# from cupy.fft import __all__ as linalg_all
+_n: dict[str, object] = {}
+exec("from cupy.fft import *", _n)
+del _n["__builtins__"]
+fft_all = list(_n)
+del _n
+
+from ..common import _fft
+from .._internal import get_xp
+
+import cupy as cp
+
+fft = get_xp(cp)(_fft.fft)
+ifft = get_xp(cp)(_fft.ifft)
+fftn = get_xp(cp)(_fft.fftn)
+ifftn = get_xp(cp)(_fft.ifftn)
+rfft = get_xp(cp)(_fft.rfft)
+irfft = get_xp(cp)(_fft.irfft)
+rfftn = get_xp(cp)(_fft.rfftn)
+irfftn = get_xp(cp)(_fft.irfftn)
+hfft = get_xp(cp)(_fft.hfft)
+ihfft = get_xp(cp)(_fft.ihfft)
+fftfreq = get_xp(cp)(_fft.fftfreq)
+rfftfreq = get_xp(cp)(_fft.rfftfreq)
+fftshift = get_xp(cp)(_fft.fftshift)
+ifftshift = get_xp(cp)(_fft.ifftshift)
+
+__all__ = fft_all + _fft.__all__
+
+def __dir__() -> list[str]:
+    return __all__
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/linalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..da301574728a70665dbb6728488ac2ce75e619e0
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/cupy/linalg.py
@@ -0,0 +1,47 @@
+from cupy.linalg import * # noqa: F403
+# cupy.linalg doesn't have __all__. If it is added, replace this with
+#
+# from cupy.linalg import __all__ as linalg_all
+_n: dict[str, object] = {}
+exec('from cupy.linalg import *', _n)
+del _n['__builtins__']
+linalg_all = list(_n)
+del _n
+
+from ..common import _linalg
+from .._internal import get_xp
+
+import cupy as cp
+
+# These functions are in both the main and linalg namespaces
+from ._aliases import matmul, matrix_transpose, tensordot, vecdot # noqa: F401
+
+cross = get_xp(cp)(_linalg.cross)
+outer = get_xp(cp)(_linalg.outer)
+EighResult = _linalg.EighResult
+QRResult = _linalg.QRResult
+SlogdetResult = _linalg.SlogdetResult
+SVDResult = _linalg.SVDResult
+eigh = get_xp(cp)(_linalg.eigh)
+qr = get_xp(cp)(_linalg.qr)
+slogdet = get_xp(cp)(_linalg.slogdet)
+svd = get_xp(cp)(_linalg.svd)
+cholesky = get_xp(cp)(_linalg.cholesky)
+matrix_rank = get_xp(cp)(_linalg.matrix_rank)
+pinv = get_xp(cp)(_linalg.pinv)
+matrix_norm = get_xp(cp)(_linalg.matrix_norm)
+svdvals = get_xp(cp)(_linalg.svdvals)
+diagonal = get_xp(cp)(_linalg.diagonal)
+trace = get_xp(cp)(_linalg.trace)
+
+# These functions are completely new here. If the library already has them
+# (i.e., numpy 2.0), use the library version instead of our wrapper.
+if hasattr(cp.linalg, 'vector_norm'):
+    vector_norm = cp.linalg.vector_norm
+else:
+    vector_norm = get_xp(cp)(_linalg.vector_norm)
+
+__all__ = linalg_all + _linalg.__all__
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/._fft.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/._fft.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/._linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/._linalg.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..f78aa8b378444aa486519b06f6d81daa45cb8f67
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/__init__.py
@@ -0,0 +1,26 @@
+from typing import Final
+
+from ..._internal import clone_module
+
+__all__ = clone_module("dask.array", globals())
+
+# These imports may overwrite names from the import * above.
+from . import _aliases
+from ._aliases import *  # type: ignore[assignment] # noqa: F403
+from ._info import __array_namespace_info__  # noqa: F401
+
+__array_api_version__: Final = "2024.12"
+del Final
+
+# See the comment in the numpy __init__.py
+__import__(__package__ + '.linalg')
+__import__(__package__ + '.fft')
+
+__all__ = sorted(
+    set(__all__)
+    | set(_aliases.__all__)
+    | {"__array_api_version__", "__array_namespace_info__", "linalg", "fft"}
+)
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/_aliases.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/_aliases.py
new file mode 100644
index 0000000000000000000000000000000000000000..54d323b2a5b6fd933ce8db39e584dff4877a2daa
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/_aliases.py
@@ -0,0 +1,369 @@
+# pyright: reportPrivateUsage=false
+# pyright: reportUnknownArgumentType=false
+# pyright: reportUnknownMemberType=false
+# pyright: reportUnknownVariableType=false
+
+from __future__ import annotations
+
+from builtins import bool as py_bool
+from collections.abc import Callable
+from typing import TYPE_CHECKING, Any
+
+if TYPE_CHECKING:
+    from typing_extensions import TypeIs
+
+import dask.array as da
+import numpy as np
+from numpy import bool_ as bool
+from numpy import (
+    can_cast,
+    complex64,
+    complex128,
+    float32,
+    float64,
+    int8,
+    int16,
+    int32,
+    int64,
+    result_type,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+)
+
+from ..._internal import get_xp
+from ...common import _aliases, _helpers, array_namespace
+from ...common._typing import (
+    Array,
+    Device,
+    DType,
+    NestedSequence,
+    SupportsBufferProtocol,
+)
+
+isdtype = get_xp(np)(_aliases.isdtype)
+unstack = get_xp(da)(_aliases.unstack)
+
+
+# da.astype doesn't respect copy=True
+def astype(
+    x: Array,
+    dtype: DType,
+    /,
+    *,
+    copy: py_bool = True,
+    device: Device | None = None,
+) -> Array:
+    """
+    Array API compatibility wrapper for astype().
+
+    See the corresponding documentation in the array library and/or the array API
+    specification for more details.
+    """
+    # TODO: respect device keyword?
+    _helpers._check_device(da, device)
+
+    if not copy and dtype == x.dtype:
+        return x
+    x = x.astype(dtype)
+    return x.copy() if copy else x
+
+
+# Common aliases
+
+
+# This arange func is modified from the common one to
+# not pass stop/step as keyword arguments, which will cause
+# an error with dask
+def arange(
+    start: float,
+    /,
+    stop: float | None = None,
+    step: float = 1,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    **kwargs: object,
+) -> Array:
+    """
+    Array API compatibility wrapper for arange().
+
+    See the corresponding documentation in the array library and/or the array API
+    specification for more details.
+    """
+    # TODO: respect device keyword?
+    _helpers._check_device(da, device)
+
+    args: list[Any] = [start]
+    if stop is not None:
+        args.append(stop)
+    else:
+        # stop is None, so start is actually stop
+        # prepend the default value for start which is 0
+        args.insert(0, 0)
+    args.append(step)
+
+    return da.arange(*args, dtype=dtype, **kwargs)
+
+
+eye = get_xp(da)(_aliases.eye)
+linspace = get_xp(da)(_aliases.linspace)
+UniqueAllResult = get_xp(da)(_aliases.UniqueAllResult)
+UniqueCountsResult = get_xp(da)(_aliases.UniqueCountsResult)
+UniqueInverseResult = get_xp(da)(_aliases.UniqueInverseResult)
+unique_all = get_xp(da)(_aliases.unique_all)
+unique_counts = get_xp(da)(_aliases.unique_counts)
+unique_inverse = get_xp(da)(_aliases.unique_inverse)
+unique_values = get_xp(da)(_aliases.unique_values)
+permute_dims = get_xp(da)(_aliases.permute_dims)
+std = get_xp(da)(_aliases.std)
+var = get_xp(da)(_aliases.var)
+cumulative_sum = get_xp(da)(_aliases.cumulative_sum)
+cumulative_prod = get_xp(da)(_aliases.cumulative_prod)
+empty = get_xp(da)(_aliases.empty)
+empty_like = get_xp(da)(_aliases.empty_like)
+full = get_xp(da)(_aliases.full)
+full_like = get_xp(da)(_aliases.full_like)
+ones = get_xp(da)(_aliases.ones)
+ones_like = get_xp(da)(_aliases.ones_like)
+zeros = get_xp(da)(_aliases.zeros)
+zeros_like = get_xp(da)(_aliases.zeros_like)
+reshape = get_xp(da)(_aliases.reshape)
+matrix_transpose = get_xp(da)(_aliases.matrix_transpose)
+vecdot = get_xp(da)(_aliases.vecdot)
+nonzero = get_xp(da)(_aliases.nonzero)
+matmul = get_xp(np)(_aliases.matmul)
+tensordot = get_xp(np)(_aliases.tensordot)
+sign = get_xp(np)(_aliases.sign)
+finfo = get_xp(np)(_aliases.finfo)
+iinfo = get_xp(np)(_aliases.iinfo)
+
+
+# asarray also adds the copy keyword, which is not present in numpy 1.0.
+def asarray(
+    obj: Array | complex | NestedSequence[complex] | SupportsBufferProtocol,
+    /,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    copy: py_bool | None = None,
+    **kwargs: object,
+) -> Array:
+    """
+    Array API compatibility wrapper for asarray().
+
+    See the corresponding documentation in the array library and/or the array API
+    specification for more details.
+    """
+    # TODO: respect device keyword?
+    _helpers._check_device(da, device)
+
+    if isinstance(obj, da.Array):
+        if dtype is not None and dtype != obj.dtype:
+            if copy is False:
+                raise ValueError("Unable to avoid copy when changing dtype")
+            obj = obj.astype(dtype)
+        return obj.copy() if copy else obj  # pyright: ignore[reportAttributeAccessIssue]
+
+    if copy is False:
+        raise ValueError(
+            "Unable to avoid copy when converting a non-dask object to dask"
+        )
+
+    # copy=None to be uniform across dask < 2024.12 and >= 2024.12
+    # see https://github.com/dask/dask/pull/11524/
+    obj = np.array(obj, dtype=dtype, copy=True)
+    return da.from_array(obj)
+
+
+# Element wise aliases
+from dask.array import arccos as acos
+from dask.array import arccosh as acosh
+from dask.array import arcsin as asin
+from dask.array import arcsinh as asinh
+from dask.array import arctan as atan
+from dask.array import arctan2 as atan2
+from dask.array import arctanh as atanh
+
+# Other
+from dask.array import concatenate as concat
+from dask.array import invert as bitwise_invert
+from dask.array import left_shift as bitwise_left_shift
+from dask.array import power as pow
+from dask.array import right_shift as bitwise_right_shift
+
+
+# dask.array.clip does not work unless all three arguments are provided.
+# Furthermore, the masking workaround in common._aliases.clip cannot work with
+# dask (meaning uint64 promoting to float64 is going to just be unfixed for
+# now).
+def clip(
+    x: Array,
+    /,
+    min: float | Array | None = None,
+    max: float | Array | None = None,
+) -> Array:
+    """
+    Array API compatibility wrapper for clip().
+
+    See the corresponding documentation in the array library and/or the array API
+    specification for more details.
+    """
+
+    def _isscalar(a: float | Array | None, /) -> TypeIs[float | None]:
+        return a is None or isinstance(a, (int, float))
+
+    min_shape = () if _isscalar(min) else min.shape
+    max_shape = () if _isscalar(max) else max.shape
+
+    # TODO: This won't handle dask unknown shapes
+    result_shape = np.broadcast_shapes(x.shape, min_shape, max_shape)
+
+    if min is not None:
+        min = da.broadcast_to(da.asarray(min), result_shape)
+    if max is not None:
+        max = da.broadcast_to(da.asarray(max), result_shape)
+
+    if min is None and max is None:
+        return da.positive(x)
+
+    if min is None:
+        return astype(da.minimum(x, max), x.dtype)
+    if max is None:
+        return astype(da.maximum(x, min), x.dtype)
+
+    return astype(da.minimum(da.maximum(x, min), max), x.dtype)
+
+
+def _ensure_single_chunk(x: Array, axis: int) -> tuple[Array, Callable[[Array], Array]]:
+    """
+    Make sure that Array is not broken into multiple chunks along axis.
+
+    Returns
+    -------
+    x : Array
+        The input Array with a single chunk along axis.
+    restore : Callable[Array, Array]
+        function to apply to the output to rechunk it back into reasonable chunks
+    """
+    if axis < 0:
+        axis += x.ndim
+    if x.numblocks[axis] < 2:
+        return x, lambda x: x
+
+    # Break chunks on other axes in an attempt to keep chunk size low
+    x = x.rechunk({i: -1 if i == axis else "auto" for i in range(x.ndim)})
+
+    # Rather than reconstructing the original chunks, which can be a
+    # very expensive affair, just break down oversized chunks without
+    # incurring in any transfers over the network.
+    # This has the downside of a risk of overchunking if the array is
+    # then used in operations against other arrays that match the
+    # original chunking pattern.
+    return x, lambda x: x.rechunk()
+
+
+def sort(
+    x: Array,
+    /,
+    *,
+    axis: int = -1,
+    descending: py_bool = False,
+    stable: py_bool = True,
+) -> Array:
+    """
+    Array API compatibility layer around the lack of sort() in Dask.
+
+    Warnings
+    --------
+    This function temporarily rechunks the array along `axis` to a single chunk.
+    This can be extremely inefficient and can lead to out-of-memory errors.
+
+    See the corresponding documentation in the array library and/or the array API
+    specification for more details.
+    """
+    x, restore = _ensure_single_chunk(x, axis)
+
+    meta_xp = array_namespace(x._meta)
+    x = da.map_blocks(
+        meta_xp.sort,
+        x,
+        axis=axis,
+        meta=x._meta,
+        dtype=x.dtype,
+        descending=descending,
+        stable=stable,
+    )
+
+    return restore(x)
+
+
+def argsort(
+    x: Array,
+    /,
+    *,
+    axis: int = -1,
+    descending: py_bool = False,
+    stable: py_bool = True,
+) -> Array:
+    """
+    Array API compatibility layer around the lack of argsort() in Dask.
+
+    See the corresponding documentation in the array library and/or the array API
+    specification for more details.
+
+    Warnings
+    --------
+    This function temporarily rechunks the array along `axis` into a single chunk.
+    This can be extremely inefficient and can lead to out-of-memory errors.
+    """
+    x, restore = _ensure_single_chunk(x, axis)
+
+    meta_xp = array_namespace(x._meta)
+    dtype = meta_xp.argsort(x._meta).dtype
+    meta = meta_xp.astype(x._meta, dtype)
+    x = da.map_blocks(
+        meta_xp.argsort,
+        x,
+        axis=axis,
+        meta=meta,
+        dtype=dtype,
+        descending=descending,
+        stable=stable,
+    )
+
+    return restore(x)
+
+
+# dask.array.count_nonzero does not have keepdims
+def count_nonzero(
+    x: Array,
+    axis: int | None = None,
+    keepdims: py_bool = False,
+) -> Array:
+    result = da.count_nonzero(x, axis)
+    if keepdims:
+        if axis is None:
+            return da.reshape(result, [1] * x.ndim)
+        return da.expand_dims(result, axis)
+    return result
+
+
+__all__ = [
+    "count_nonzero",
+    "bool",
+    "int8", "int16", "int32", "int64",
+    "uint8", "uint16", "uint32", "uint64",
+    "float32", "float64",
+    "complex64", "complex128",
+    "asarray", "astype", "can_cast", "result_type",
+    "pow",
+    "concat",
+    "acos", "acosh", "asin", "asinh", "atan", "atan2", "atanh",
+    "bitwise_left_shift", "bitwise_right_shift", "bitwise_invert",
+]  # fmt: skip
+__all__ += _aliases.__all__
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/_info.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..2f39fc4b17ef730b8063b8ff10146731924244ba
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/_info.py
@@ -0,0 +1,407 @@
+"""
+Array API Inspection namespace
+
+This is the namespace for inspection functions as defined by the array API
+standard. See
+https://data-apis.org/array-api/latest/API_specification/inspection.html for
+more details.
+
+"""
+
+# pyright: reportPrivateUsage=false
+
+from __future__ import annotations
+
+from typing import Literal, TypeAlias, overload
+
+import dask.array as da
+from numpy import bool_ as bool
+from numpy import (
+    complex64,
+    complex128,
+    dtype,
+    float32,
+    float64,
+    int8,
+    int16,
+    int32,
+    int64,
+    intp,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+)
+
+from ...common._helpers import _DASK_DEVICE, _check_device, _dask_device
+from ...common._typing import (
+    Capabilities,
+    DefaultDTypes,
+    DType,
+    DTypeKind,
+    DTypesAll,
+    DTypesAny,
+    DTypesBool,
+    DTypesComplex,
+    DTypesIntegral,
+    DTypesNumeric,
+    DTypesReal,
+    DTypesSigned,
+    DTypesUnsigned,
+)
+Device: TypeAlias = Literal["cpu"] | _dask_device
+
+
+class __array_namespace_info__:
+    """
+    Get the array API inspection namespace for Dask.
+
+    The array API inspection namespace defines the following functions:
+
+    - capabilities()
+    - default_device()
+    - default_dtypes()
+    - dtypes()
+    - devices()
+
+    See
+    https://data-apis.org/array-api/latest/API_specification/inspection.html
+    for more details.
+
+    Returns
+    -------
+    info : ModuleType
+        The array API inspection namespace for Dask.
+
+    Examples
+    --------
+    >>> info = xp.__array_namespace_info__()
+    >>> info.default_dtypes()
+    {'real floating': dask.float64,
+     'complex floating': dask.complex128,
+     'integral': dask.int64,
+     'indexing': dask.int64}
+
+    """
+
+    __module__ = "dask.array"
+
+    def capabilities(self) -> Capabilities:
+        """
+        Return a dictionary of array API library capabilities.
+
+        The resulting dictionary has the following keys:
+
+        - **"boolean indexing"**: boolean indicating whether an array library
+          supports boolean indexing.
+
+          Dask support boolean indexing as long as both the index
+          and the indexed arrays have known shapes.
+          Note however that the output .shape and .size properties
+          will contain a non-compliant math.nan instead of None.
+
+        - **"data-dependent shapes"**: boolean indicating whether an array
+          library supports data-dependent output shapes.
+
+          Dask implements unique_values et.al.
+          Note however that the output .shape and .size properties
+          will contain a non-compliant math.nan instead of None.
+
+        - **"max dimensions"**: integer indicating the maximum number of
+          dimensions supported by the array library.
+
+        See
+        https://data-apis.org/array-api/latest/API_specification/generated/array_api.info.capabilities.html
+        for more details.
+
+        See Also
+        --------
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Returns
+        -------
+        capabilities : dict
+            A dictionary of array API library capabilities.
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.capabilities()
+        {'boolean indexing': True,
+         'data-dependent shapes': True,
+         'max dimensions': 64}
+
+        """
+        return {
+            "boolean indexing": True,
+            "data-dependent shapes": True,
+            "max dimensions": 64,
+        }
+
+    def default_device(self) -> Device:
+        """
+        The default device used for new Dask arrays.
+
+        For Dask, this always returns ``'cpu'``.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Returns
+        -------
+        device : Device
+            The default device used for new Dask arrays.
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.default_device()
+        'cpu'
+
+        """
+        return "cpu"
+
+    def default_dtypes(self, /, *, device: Device | None = None) -> DefaultDTypes:
+        """
+        The default data types used for new Dask arrays.
+
+        For Dask, this always returns the following dictionary:
+
+        - **"real floating"**: ``numpy.float64``
+        - **"complex floating"**: ``numpy.complex128``
+        - **"integral"**: ``numpy.intp``
+        - **"indexing"**: ``numpy.intp``
+
+        Parameters
+        ----------
+        device : str, optional
+            The device to get the default data types for.
+
+        Returns
+        -------
+        dtypes : dict
+            A dictionary describing the default data types used for new Dask
+            arrays.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.default_dtypes()
+        {'real floating': dask.float64,
+         'complex floating': dask.complex128,
+         'integral': dask.int64,
+         'indexing': dask.int64}
+
+        """
+        _check_device(da, device)
+        return {
+            "real floating": dtype(float64),
+            "complex floating": dtype(complex128),
+            "integral": dtype(intp),
+            "indexing": dtype(intp),
+        }
+
+    @overload
+    def dtypes(
+        self, /, *, device: Device | None = None, kind: None = None
+    ) -> DTypesAll: ...
+    @overload
+    def dtypes(
+        self, /, *, device: Device | None = None, kind: Literal["bool"]
+    ) -> DTypesBool: ...
+    @overload
+    def dtypes(
+        self, /, *, device: Device | None = None, kind: Literal["signed integer"]
+    ) -> DTypesSigned: ...
+    @overload
+    def dtypes(
+        self, /, *, device: Device | None = None, kind: Literal["unsigned integer"]
+    ) -> DTypesUnsigned: ...
+    @overload
+    def dtypes(
+        self, /, *, device: Device | None = None, kind: Literal["integral"]
+    ) -> DTypesIntegral: ...
+    @overload
+    def dtypes(
+        self, /, *, device: Device | None = None, kind: Literal["real floating"]
+    ) -> DTypesReal: ...
+    @overload
+    def dtypes(
+        self, /, *, device: Device | None = None, kind: Literal["complex floating"]
+    ) -> DTypesComplex: ...
+    @overload
+    def dtypes(
+        self, /, *, device: Device | None = None, kind: Literal["numeric"]
+    ) -> DTypesNumeric: ...
+    def dtypes(
+        self, /, *, device: Device | None = None, kind: DTypeKind | None = None
+    ) -> DTypesAny:
+        """
+        The array API data types supported by Dask.
+
+        Note that this function only returns data types that are defined by
+        the array API.
+
+        Parameters
+        ----------
+        device : str, optional
+            The device to get the data types for.
+        kind : str or tuple of str, optional
+            The kind of data types to return. If ``None``, all data types are
+            returned. If a string, only data types of that kind are returned.
+            If a tuple, a dictionary containing the union of the given kinds
+            is returned. The following kinds are supported:
+
+            - ``'bool'``: boolean data types (i.e., ``bool``).
+            - ``'signed integer'``: signed integer data types (i.e., ``int8``,
+              ``int16``, ``int32``, ``int64``).
+            - ``'unsigned integer'``: unsigned integer data types (i.e.,
+              ``uint8``, ``uint16``, ``uint32``, ``uint64``).
+            - ``'integral'``: integer data types. Shorthand for ``('signed
+              integer', 'unsigned integer')``.
+            - ``'real floating'``: real-valued floating-point data types
+              (i.e., ``float32``, ``float64``).
+            - ``'complex floating'``: complex floating-point data types (i.e.,
+              ``complex64``, ``complex128``).
+            - ``'numeric'``: numeric data types. Shorthand for ``('integral',
+              'real floating', 'complex floating')``.
+
+        Returns
+        -------
+        dtypes : dict
+            A dictionary mapping the names of data types to the corresponding
+            Dask data types.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.devices
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.dtypes(kind='signed integer')
+        {'int8': dask.int8,
+         'int16': dask.int16,
+         'int32': dask.int32,
+         'int64': dask.int64}
+
+        """
+        _check_device(da, device)
+        if kind is None:
+            return {
+                "bool": dtype(bool),
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+                "float32": dtype(float32),
+                "float64": dtype(float64),
+                "complex64": dtype(complex64),
+                "complex128": dtype(complex128),
+            }
+        if kind == "bool":
+            return {"bool": bool}
+        if kind == "signed integer":
+            return {
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+            }
+        if kind == "unsigned integer":
+            return {
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+            }
+        if kind == "integral":
+            return {
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+            }
+        if kind == "real floating":
+            return {
+                "float32": dtype(float32),
+                "float64": dtype(float64),
+            }
+        if kind == "complex floating":
+            return {
+                "complex64": dtype(complex64),
+                "complex128": dtype(complex128),
+            }
+        if kind == "numeric":
+            return {
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+                "float32": dtype(float32),
+                "float64": dtype(float64),
+                "complex64": dtype(complex64),
+                "complex128": dtype(complex128),
+            }
+        if isinstance(kind, tuple):
+            res: dict[str, DType] = {}
+            for k in kind:
+                res.update(self.dtypes(kind=k))
+            return res
+        raise ValueError(f"unsupported kind: {kind!r}")
+
+    def devices(self) -> list[Device]:
+        """
+        The devices supported by Dask.
+
+        For Dask, this always returns ``['cpu', DASK_DEVICE]``.
+
+        Returns
+        -------
+        devices : list[Device]
+            The devices supported by Dask.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.devices()
+        ['cpu', DASK_DEVICE]
+
+        """
+        return ["cpu", _DASK_DEVICE]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/fft.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/fft.py
new file mode 100644
index 0000000000000000000000000000000000000000..44b68e733984f1f2da11cdd3b892e84b7bd5e797
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/fft.py
@@ -0,0 +1,16 @@
+from ..._internal import clone_module
+
+__all__ = clone_module("dask.array.fft", globals())
+
+from ...common import _fft
+from ..._internal import get_xp
+
+import dask.array as da
+
+fftfreq = get_xp(da)(_fft.fftfreq)
+rfftfreq = get_xp(da)(_fft.rfftfreq)
+
+__all__ += ["fftfreq", "rfftfreq"]
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/linalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..6b3c10117b10b9a8b3bb494415f6711bd3db19d1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/dask/array/linalg.py
@@ -0,0 +1,64 @@
+from __future__ import annotations
+
+from typing import Literal
+
+import dask.array as da
+
+# The `matmul` and `tensordot` functions are in both the main and linalg namespaces
+from dask.array import matmul, outer, tensordot
+
+# Exports
+from ..._internal import clone_module, get_xp
+from ...common import _linalg
+from ...common._typing import Array
+
+__all__ = clone_module("dask.array.linalg", globals())
+
+from ._aliases import matrix_transpose, vecdot
+
+EighResult = _linalg.EighResult
+QRResult = _linalg.QRResult
+SlogdetResult = _linalg.SlogdetResult
+SVDResult = _linalg.SVDResult
+# TODO: use the QR wrapper once dask
+# supports the mode keyword on QR
+# https://github.com/dask/dask/issues/10388
+#qr = get_xp(da)(_linalg.qr)
+def qr(  # type: ignore[no-redef]
+    x: Array,
+    mode: Literal["reduced", "complete"] = "reduced",
+    **kwargs: object,
+) -> QRResult:
+    if mode != "reduced":
+        raise ValueError("dask arrays only support using mode='reduced'")
+    return QRResult(*da.linalg.qr(x, **kwargs))
+trace = get_xp(da)(_linalg.trace)
+cholesky = get_xp(da)(_linalg.cholesky)
+matrix_rank = get_xp(da)(_linalg.matrix_rank)
+matrix_norm = get_xp(da)(_linalg.matrix_norm)
+
+
+# Wrap the svd functions to not pass full_matrices to dask
+# when full_matrices=False (as that is the default behavior for dask),
+# and dask doesn't have the full_matrices keyword
+def svd(x: Array, full_matrices: bool = True, **kwargs: object) -> SVDResult:  # type: ignore[no-redef]
+    if full_matrices:
+        raise ValueError("full_matrics=True is not supported by dask.")
+    return da.linalg.svd(x, coerce_signs=False, **kwargs)
+
+def svdvals(x: Array) -> Array:
+    # TODO: can't avoid computing U or V for dask
+    _, s, _ =  svd(x)
+    return s
+
+vector_norm = get_xp(da)(_linalg.vector_norm)
+diagonal = get_xp(da)(_linalg.diagonal)
+
+__all__ += ["trace", "outer", "matmul", "tensordot",
+            "matrix_transpose", "vecdot", "EighResult",
+            "QRResult", "SlogdetResult", "SVDResult", "qr",
+            "cholesky", "matrix_rank", "matrix_norm", "svdvals",
+            "vector_norm", "diagonal"]
+
+def __dir__() -> list[str]:
+    return __all__
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/._linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/._linalg.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..23379e44db6e70eae64d4987d90d5b5bc6f8d51c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/__init__.py
@@ -0,0 +1,38 @@
+# ruff: noqa: PLC0414
+from typing import Final
+
+from .._internal import clone_module
+
+# This needs to be loaded explicitly before cloning
+import numpy.typing  # noqa: F401
+
+__all__ = clone_module("numpy", globals())
+
+# These imports may overwrite names from the import * above.
+from . import _aliases
+from ._aliases import *  # type: ignore[assignment,no-redef] # noqa: F403
+from ._info import __array_namespace_info__  # noqa: F401
+
+# Don't know why, but we have to do an absolute import to import linalg. If we
+# instead do
+#
+# from . import linalg
+#
+# It doesn't overwrite np.linalg from above. The import is generated
+# dynamically so that the library can be vendored.
+__import__(__package__ + ".linalg")
+
+__import__(__package__ + ".fft")
+
+from .linalg import matrix_transpose, vecdot  # type: ignore[no-redef]  # noqa: F401
+
+__array_api_version__: Final = "2024.12"
+
+__all__ = sorted(
+    set(__all__) 
+    | set(_aliases.__all__) 
+    | {"__array_api_version__", "__array_namespace_info__", "linalg", "fft"}
+)
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/_aliases.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/_aliases.py
new file mode 100644
index 0000000000000000000000000000000000000000..87b3c2f398af09fc8065aa05a1bfccd679e639d4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/_aliases.py
@@ -0,0 +1,191 @@
+# pyright: reportPrivateUsage=false
+from __future__ import annotations
+
+from builtins import bool as py_bool
+from typing import Any, cast
+
+import numpy as np
+
+from .._internal import get_xp
+from ..common import _aliases, _helpers
+from ..common._typing import NestedSequence, SupportsBufferProtocol
+from ._typing import Array, Device, DType
+
+bool = np.bool_
+
+# Basic renames
+acos = np.arccos
+acosh = np.arccosh
+asin = np.arcsin
+asinh = np.arcsinh
+atan = np.arctan
+atan2 = np.arctan2
+atanh = np.arctanh
+bitwise_left_shift = np.left_shift
+bitwise_invert = np.invert
+bitwise_right_shift = np.right_shift
+concat = np.concatenate
+pow = np.power
+
+arange = get_xp(np)(_aliases.arange)
+empty = get_xp(np)(_aliases.empty)
+empty_like = get_xp(np)(_aliases.empty_like)
+eye = get_xp(np)(_aliases.eye)
+full = get_xp(np)(_aliases.full)
+full_like = get_xp(np)(_aliases.full_like)
+linspace = get_xp(np)(_aliases.linspace)
+ones = get_xp(np)(_aliases.ones)
+ones_like = get_xp(np)(_aliases.ones_like)
+zeros = get_xp(np)(_aliases.zeros)
+zeros_like = get_xp(np)(_aliases.zeros_like)
+UniqueAllResult = get_xp(np)(_aliases.UniqueAllResult)
+UniqueCountsResult = get_xp(np)(_aliases.UniqueCountsResult)
+UniqueInverseResult = get_xp(np)(_aliases.UniqueInverseResult)
+unique_all = get_xp(np)(_aliases.unique_all)
+unique_counts = get_xp(np)(_aliases.unique_counts)
+unique_inverse = get_xp(np)(_aliases.unique_inverse)
+unique_values = get_xp(np)(_aliases.unique_values)
+std = get_xp(np)(_aliases.std)
+var = get_xp(np)(_aliases.var)
+cumulative_sum = get_xp(np)(_aliases.cumulative_sum)
+cumulative_prod = get_xp(np)(_aliases.cumulative_prod)
+clip = get_xp(np)(_aliases.clip)
+permute_dims = get_xp(np)(_aliases.permute_dims)
+reshape = get_xp(np)(_aliases.reshape)
+argsort = get_xp(np)(_aliases.argsort)
+sort = get_xp(np)(_aliases.sort)
+nonzero = get_xp(np)(_aliases.nonzero)
+matmul = get_xp(np)(_aliases.matmul)
+matrix_transpose = get_xp(np)(_aliases.matrix_transpose)
+tensordot = get_xp(np)(_aliases.tensordot)
+sign = get_xp(np)(_aliases.sign)
+finfo = get_xp(np)(_aliases.finfo)
+iinfo = get_xp(np)(_aliases.iinfo)
+
+
+# asarray also adds the copy keyword, which is not present in numpy 1.0.
+# asarray() is different enough between numpy, cupy, and dask, the logic
+# complicated enough that it's easier to define it separately for each module
+# rather than trying to combine everything into one function in common/
+def asarray(
+    obj: Array | complex | NestedSequence[complex] | SupportsBufferProtocol,
+    /,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    copy: py_bool | None = None,
+    **kwargs: Any,
+) -> Array:
+    """
+    Array API compatibility wrapper for asarray().
+
+    See the corresponding documentation in the array library and/or the array API
+    specification for more details.
+    """
+    _helpers._check_device(np, device)
+
+    # None is unsupported in NumPy 1.0, but we can use an internal enum
+    # False in NumPy 1.0 means None in NumPy 2.0 and in the Array API
+    if copy is None:
+        copy = np._CopyMode.IF_NEEDED  # type: ignore[assignment,attr-defined]
+    elif copy is False:
+        copy = np._CopyMode.NEVER  # type: ignore[assignment,attr-defined]
+
+    return np.array(obj, copy=copy, dtype=dtype, **kwargs)
+
+
+def astype(
+    x: Array,
+    dtype: DType,
+    /,
+    *,
+    copy: py_bool = True,
+    device: Device | None = None,
+) -> Array:
+    _helpers._check_device(np, device)
+    return x.astype(dtype=dtype, copy=copy)
+
+
+# count_nonzero returns a python int for axis=None and keepdims=False
+# https://github.com/numpy/numpy/issues/17562
+def count_nonzero(
+    x: Array,
+    axis: int | tuple[int, ...] | None = None,
+    keepdims: py_bool = False,
+) -> Array:
+    # NOTE: this is currently incorrectly typed in numpy, but will be fixed in
+    # numpy 2.2.5 and 2.3.0: https://github.com/numpy/numpy/pull/28750
+    result = cast("Any", np.count_nonzero(x, axis=axis, keepdims=keepdims))  # pyright: ignore[reportArgumentType, reportCallIssue]
+    if axis is None and not keepdims:
+        return np.asarray(result)
+    return result
+
+
+# take_along_axis: axis defaults to -1 but in numpy axis is a required arg
+def take_along_axis(x: Array, indices: Array, /, *, axis: int = -1) -> Array:
+    return np.take_along_axis(x, indices, axis=axis)
+
+
+# ceil, floor, and trunc return integers for integer inputs in NumPy < 2
+
+def ceil(x: Array, /) -> Array:
+    if np.__version__ < '2' and np.issubdtype(x.dtype, np.integer):
+        return x.copy()
+    return np.ceil(x)
+
+
+def floor(x: Array, /) -> Array:
+    if np.__version__ < '2' and np.issubdtype(x.dtype, np.integer):
+        return x.copy()
+    return np.floor(x)
+
+
+def trunc(x: Array, /) -> Array:
+    if np.__version__ < '2' and np.issubdtype(x.dtype, np.integer):
+        return x.copy()
+    return np.trunc(x)
+
+
+# These functions are completely new here. If the library already has them
+# (i.e., numpy 2.0), use the library version instead of our wrapper.
+if hasattr(np, "vecdot"):
+    vecdot = np.vecdot
+else:
+    vecdot = get_xp(np)(_aliases.vecdot)  # type: ignore[assignment]
+
+if hasattr(np, "isdtype"):
+    isdtype = np.isdtype
+else:
+    isdtype = get_xp(np)(_aliases.isdtype)
+
+if hasattr(np, "unstack"):
+    unstack = np.unstack
+else:
+    unstack = get_xp(np)(_aliases.unstack)
+
+__all__ = _aliases.__all__ + [
+    "asarray",
+    "astype",
+    "acos",
+    "acosh",
+    "asin",
+    "asinh",
+    "atan",
+    "atan2",
+    "atanh",
+    "ceil",
+    "floor",
+    "trunc",
+    "bitwise_left_shift",
+    "bitwise_invert",
+    "bitwise_right_shift",
+    "bool",
+    "concat",
+    "count_nonzero",
+    "pow",
+    "take_along_axis"
+]
+
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/_info.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..c625c13e36942286a83ee3290c93208d8818bedd
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/_info.py
@@ -0,0 +1,367 @@
+"""
+Array API Inspection namespace
+
+This is the namespace for inspection functions as defined by the array API
+standard. See
+https://data-apis.org/array-api/latest/API_specification/inspection.html for
+more details.
+
+"""
+from __future__ import annotations
+
+from numpy import bool_ as bool
+from numpy import (
+    complex64,
+    complex128,
+    dtype,
+    float32,
+    float64,
+    int8,
+    int16,
+    int32,
+    int64,
+    intp,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+)
+
+from ..common._typing import DefaultDTypes
+from ._typing import Device, DType
+
+
+class __array_namespace_info__:
+    """
+    Get the array API inspection namespace for NumPy.
+
+    The array API inspection namespace defines the following functions:
+
+    - capabilities()
+    - default_device()
+    - default_dtypes()
+    - dtypes()
+    - devices()
+
+    See
+    https://data-apis.org/array-api/latest/API_specification/inspection.html
+    for more details.
+
+    Returns
+    -------
+    info : ModuleType
+        The array API inspection namespace for NumPy.
+
+    Examples
+    --------
+    >>> info = np.__array_namespace_info__()
+    >>> info.default_dtypes()
+    {'real floating': numpy.float64,
+     'complex floating': numpy.complex128,
+     'integral': numpy.int64,
+     'indexing': numpy.int64}
+
+    """
+
+    __module__ = 'numpy'
+
+    def capabilities(self):
+        """
+        Return a dictionary of array API library capabilities.
+
+        The resulting dictionary has the following keys:
+
+        - **"boolean indexing"**: boolean indicating whether an array library
+          supports boolean indexing. Always ``True`` for NumPy.
+
+        - **"data-dependent shapes"**: boolean indicating whether an array
+          library supports data-dependent output shapes. Always ``True`` for
+          NumPy.
+
+        See
+        https://data-apis.org/array-api/latest/API_specification/generated/array_api.info.capabilities.html
+        for more details.
+
+        See Also
+        --------
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Returns
+        -------
+        capabilities : dict
+            A dictionary of array API library capabilities.
+
+        Examples
+        --------
+        >>> info = np.__array_namespace_info__()
+        >>> info.capabilities()
+        {'boolean indexing': True,
+         'data-dependent shapes': True,
+         'max dimensions': 64}
+
+        """
+        return {
+            "boolean indexing": True,
+            "data-dependent shapes": True,
+            "max dimensions": 64,
+        }
+
+    def default_device(self):
+        """
+        The default device used for new NumPy arrays.
+
+        For NumPy, this always returns ``'cpu'``.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Returns
+        -------
+        device : Device
+            The default device used for new NumPy arrays.
+
+        Examples
+        --------
+        >>> info = np.__array_namespace_info__()
+        >>> info.default_device()
+        'cpu'
+
+        """
+        return "cpu"
+
+    def default_dtypes(
+        self,
+        *,
+        device: Device | None = None,
+    ) -> DefaultDTypes:
+        """
+        The default data types used for new NumPy arrays.
+
+        For NumPy, this always returns the following dictionary:
+
+        - **"real floating"**: ``numpy.float64``
+        - **"complex floating"**: ``numpy.complex128``
+        - **"integral"**: ``numpy.intp``
+        - **"indexing"**: ``numpy.intp``
+
+        Parameters
+        ----------
+        device : str, optional
+            The device to get the default data types for. For NumPy, only
+            ``'cpu'`` is allowed.
+
+        Returns
+        -------
+        dtypes : dict
+            A dictionary describing the default data types used for new NumPy
+            arrays.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Examples
+        --------
+        >>> info = np.__array_namespace_info__()
+        >>> info.default_dtypes()
+        {'real floating': numpy.float64,
+         'complex floating': numpy.complex128,
+         'integral': numpy.int64,
+         'indexing': numpy.int64}
+
+        """
+        if device not in ["cpu", None]:
+            raise ValueError(
+                'Device not understood. Only "cpu" is allowed, but received:'
+                f' {device}'
+            )
+        return {
+            "real floating": dtype(float64),
+            "complex floating": dtype(complex128),
+            "integral": dtype(intp),
+            "indexing": dtype(intp),
+        }
+
+    def dtypes(
+        self,
+        *,
+        device: Device | None = None,
+        kind: str | tuple[str, ...] | None = None,
+    ) -> dict[str, DType]:
+        """
+        The array API data types supported by NumPy.
+
+        Note that this function only returns data types that are defined by
+        the array API.
+
+        Parameters
+        ----------
+        device : str, optional
+            The device to get the data types for. For NumPy, only ``'cpu'`` is
+            allowed.
+        kind : str or tuple of str, optional
+            The kind of data types to return. If ``None``, all data types are
+            returned. If a string, only data types of that kind are returned.
+            If a tuple, a dictionary containing the union of the given kinds
+            is returned. The following kinds are supported:
+
+            - ``'bool'``: boolean data types (i.e., ``bool``).
+            - ``'signed integer'``: signed integer data types (i.e., ``int8``,
+              ``int16``, ``int32``, ``int64``).
+            - ``'unsigned integer'``: unsigned integer data types (i.e.,
+              ``uint8``, ``uint16``, ``uint32``, ``uint64``).
+            - ``'integral'``: integer data types. Shorthand for ``('signed
+              integer', 'unsigned integer')``.
+            - ``'real floating'``: real-valued floating-point data types
+              (i.e., ``float32``, ``float64``).
+            - ``'complex floating'``: complex floating-point data types (i.e.,
+              ``complex64``, ``complex128``).
+            - ``'numeric'``: numeric data types. Shorthand for ``('integral',
+              'real floating', 'complex floating')``.
+
+        Returns
+        -------
+        dtypes : dict
+            A dictionary mapping the names of data types to the corresponding
+            NumPy data types.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.devices
+
+        Examples
+        --------
+        >>> info = np.__array_namespace_info__()
+        >>> info.dtypes(kind='signed integer')
+        {'int8': numpy.int8,
+         'int16': numpy.int16,
+         'int32': numpy.int32,
+         'int64': numpy.int64}
+
+        """
+        if device not in ["cpu", None]:
+            raise ValueError(
+                'Device not understood. Only "cpu" is allowed, but received:'
+                f' {device}'
+            )
+        if kind is None:
+            return {
+                "bool": dtype(bool),
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+                "float32": dtype(float32),
+                "float64": dtype(float64),
+                "complex64": dtype(complex64),
+                "complex128": dtype(complex128),
+            }
+        if kind == "bool":
+            return {"bool": dtype(bool)}
+        if kind == "signed integer":
+            return {
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+            }
+        if kind == "unsigned integer":
+            return {
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+            }
+        if kind == "integral":
+            return {
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+            }
+        if kind == "real floating":
+            return {
+                "float32": dtype(float32),
+                "float64": dtype(float64),
+            }
+        if kind == "complex floating":
+            return {
+                "complex64": dtype(complex64),
+                "complex128": dtype(complex128),
+            }
+        if kind == "numeric":
+            return {
+                "int8": dtype(int8),
+                "int16": dtype(int16),
+                "int32": dtype(int32),
+                "int64": dtype(int64),
+                "uint8": dtype(uint8),
+                "uint16": dtype(uint16),
+                "uint32": dtype(uint32),
+                "uint64": dtype(uint64),
+                "float32": dtype(float32),
+                "float64": dtype(float64),
+                "complex64": dtype(complex64),
+                "complex128": dtype(complex128),
+            }
+        if isinstance(kind, tuple):
+            res: dict[str, DType] = {}
+            for k in kind:
+                res.update(self.dtypes(kind=k))
+            return res
+        raise ValueError(f"unsupported kind: {kind!r}")
+
+    def devices(self) -> list[Device]:
+        """
+        The devices supported by NumPy.
+
+        For NumPy, this always returns ``['cpu']``.
+
+        Returns
+        -------
+        devices : list[Device]
+            The devices supported by NumPy.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes
+
+        Examples
+        --------
+        >>> info = np.__array_namespace_info__()
+        >>> info.devices()
+        ['cpu']
+
+        """
+        return ["cpu"]
+
+
+__all__ = ["__array_namespace_info__"]
+
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/_typing.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/_typing.py
new file mode 100644
index 0000000000000000000000000000000000000000..b5fa188c52b69c16a1fa088026720fee9390e640
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/_typing.py
@@ -0,0 +1,29 @@
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Any, Literal, TypeAlias
+
+import numpy as np
+
+Device: TypeAlias = Literal["cpu"]
+
+if TYPE_CHECKING:
+
+    # NumPy 1.x on Python 3.10 fails to parse np.dtype[]
+    DType: TypeAlias = np.dtype[
+        np.bool_
+        | np.integer[Any]
+        | np.float32
+        | np.float64
+        | np.complex64
+        | np.complex128
+    ]
+    Array: TypeAlias = np.ndarray[Any, DType]
+else:
+    DType: TypeAlias = np.dtype
+    Array: TypeAlias = np.ndarray
+
+__all__ = ["Array", "DType", "Device"]
+
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/fft.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/fft.py
new file mode 100644
index 0000000000000000000000000000000000000000..a492feb8cf69085a3a6617fbee13a8ac236701fa
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/fft.py
@@ -0,0 +1,30 @@
+import numpy as np
+
+from .._internal import clone_module
+
+__all__ = clone_module("numpy.fft", globals())
+
+from .._internal import get_xp
+from ..common import _fft
+
+fft = get_xp(np)(_fft.fft)
+ifft = get_xp(np)(_fft.ifft)
+fftn = get_xp(np)(_fft.fftn)
+ifftn = get_xp(np)(_fft.ifftn)
+rfft = get_xp(np)(_fft.rfft)
+irfft = get_xp(np)(_fft.irfft)
+rfftn = get_xp(np)(_fft.rfftn)
+irfftn = get_xp(np)(_fft.irfftn)
+hfft = get_xp(np)(_fft.hfft)
+ihfft = get_xp(np)(_fft.ihfft)
+fftfreq = get_xp(np)(_fft.fftfreq)
+rfftfreq = get_xp(np)(_fft.rfftfreq)
+fftshift = get_xp(np)(_fft.fftshift)
+ifftshift = get_xp(np)(_fft.ifftshift)
+
+
+__all__ = sorted(set(__all__) | set(_fft.__all__))
+
+def __dir__() -> list[str]:
+    return __all__
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/linalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..7168441c7517ee2d8e4b03d534531a832d292f43
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/numpy/linalg.py
@@ -0,0 +1,128 @@
+# pyright: reportAttributeAccessIssue=false
+# pyright: reportUnknownArgumentType=false
+# pyright: reportUnknownMemberType=false
+# pyright: reportUnknownVariableType=false
+
+from __future__ import annotations
+
+import numpy as np
+
+from .._internal import clone_module, get_xp
+from ..common import _linalg
+
+__all__ = clone_module("numpy.linalg", globals())
+
+# These functions are in both the main and linalg namespaces
+from ._aliases import matmul, matrix_transpose, tensordot, vecdot  # noqa: F401
+from ._typing import Array
+
+cross = get_xp(np)(_linalg.cross)
+outer = get_xp(np)(_linalg.outer)
+EighResult = _linalg.EighResult
+QRResult = _linalg.QRResult
+SlogdetResult = _linalg.SlogdetResult
+SVDResult = _linalg.SVDResult
+eigh = get_xp(np)(_linalg.eigh)
+qr = get_xp(np)(_linalg.qr)
+slogdet = get_xp(np)(_linalg.slogdet)
+svd = get_xp(np)(_linalg.svd)
+cholesky = get_xp(np)(_linalg.cholesky)
+matrix_rank = get_xp(np)(_linalg.matrix_rank)
+pinv = get_xp(np)(_linalg.pinv)
+matrix_norm = get_xp(np)(_linalg.matrix_norm)
+svdvals = get_xp(np)(_linalg.svdvals)
+diagonal = get_xp(np)(_linalg.diagonal)
+trace = get_xp(np)(_linalg.trace)
+
+# Note: unlike np.linalg.solve, the array API solve() only accepts x2 as a
+# vector when it is exactly 1-dimensional. All other cases treat x2 as a stack
+# of matrices. The np.linalg.solve behavior of allowing stacks of both
+# matrices and vectors is ambiguous c.f.
+# https://github.com/numpy/numpy/issues/15349 and
+# https://github.com/data-apis/array-api/issues/285.
+
+# To workaround this, the below is the code from np.linalg.solve except
+# only calling solve1 in the exactly 1D case.
+
+
+# This code is here instead of in common because it is numpy specific. Also
+# note that CuPy's solve() does not currently support broadcasting (see
+# https://github.com/cupy/cupy/blob/main/cupy/cublas.py#L43).
+def solve(x1: Array, x2: Array, /) -> Array:
+    try:
+        from numpy.linalg._linalg import (  # type: ignore[attr-defined]
+            _assert_stacked_2d,
+            _assert_stacked_square,
+            _commonType,
+            _makearray,
+            _raise_linalgerror_singular,
+            isComplexType,
+        )
+    except ImportError:
+        from numpy.linalg.linalg import (  # type: ignore[attr-defined]
+            _assert_stacked_2d,
+            _assert_stacked_square,
+            _commonType,
+            _makearray,
+            _raise_linalgerror_singular,
+            isComplexType,
+        )
+    from numpy.linalg import _umath_linalg
+
+    x1, _ = _makearray(x1)
+    _assert_stacked_2d(x1)
+    _assert_stacked_square(x1)
+    x2, wrap = _makearray(x2)
+    t, result_t = _commonType(x1, x2)
+
+    # This part is different from np.linalg.solve
+    gufunc: np.ufunc
+    if x2.ndim == 1:
+        gufunc = _umath_linalg.solve1
+    else:
+        gufunc = _umath_linalg.solve
+
+    # This does nothing currently but is left in because it will be relevant
+    # when complex dtype support is added to the spec in 2022.
+    signature = "DD->D" if isComplexType(t) else "dd->d"
+    with np.errstate(
+        call=_raise_linalgerror_singular,
+        invalid="call",
+        over="ignore",
+        divide="ignore",
+        under="ignore",
+    ):
+        r: Array = gufunc(x1, x2, signature=signature)
+
+    return wrap(r.astype(result_t, copy=False))
+
+
+# These functions are completely new here. If the library already has them
+# (i.e., numpy 2.0), use the library version instead of our wrapper.
+if hasattr(np.linalg, "vector_norm"):
+    vector_norm = np.linalg.vector_norm
+else:
+    vector_norm = get_xp(np)(_linalg.vector_norm)
+
+
+_all = [
+    "LinAlgError",
+    "cond",
+    "det",
+    "eig",
+    "eigvals",
+    "eigvalsh",
+    "inv",
+    "lstsq",
+    "matrix_power",
+    "multi_dot",
+    "norm",
+    "solve", 
+    "tensorinv",
+    "tensorsolve",
+    "vector_norm",
+]
+__all__ = sorted(set(__all__) | set(_linalg.__all__) | set(_all))
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/._linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/._linalg.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..6cbb6ec264869090e888e6631df86ab2e99ca36a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/__init__.py
@@ -0,0 +1,25 @@
+from typing import Final
+
+from .._internal import clone_module
+
+__all__ = clone_module("torch", globals())
+
+# These imports may overwrite names from the import * above.
+from . import _aliases
+from ._aliases import * # noqa: F403
+from ._info import __array_namespace_info__  # noqa: F401
+
+# See the comment in the numpy __init__.py
+__import__(__package__ + '.linalg')
+__import__(__package__ + '.fft')
+
+__array_api_version__: Final = '2024.12'
+
+__all__ = sorted(
+    set(__all__)
+    | set(_aliases.__all__)
+    | {"__array_api_version__", "__array_namespace_info__", "linalg", "fft"}
+)
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/_aliases.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/_aliases.py
new file mode 100644
index 0000000000000000000000000000000000000000..4e8533f95e839f7ccfce2ef83a810edf2cf9662c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/_aliases.py
@@ -0,0 +1,875 @@
+from __future__ import annotations
+
+from collections.abc import Sequence
+from functools import reduce as _reduce, wraps as _wraps
+from builtins import all as _builtin_all, any as _builtin_any
+from typing import Any, Literal
+
+import torch
+
+from .._internal import get_xp
+from ..common import _aliases
+from ..common._typing import NestedSequence, SupportsBufferProtocol
+from ._typing import Array, Device, DType
+
+_int_dtypes = {
+    torch.uint8,
+    torch.int8,
+    torch.int16,
+    torch.int32,
+    torch.int64,
+}
+try:
+    # torch >=2.3
+    _int_dtypes |= {torch.uint16, torch.uint32, torch.uint64}
+except AttributeError:
+    pass
+
+
+_array_api_dtypes = {
+    torch.bool,
+    *_int_dtypes,
+    torch.float32,
+    torch.float64,
+    torch.complex64,
+    torch.complex128,
+}
+
+_promotion_table = {
+    # ints
+    (torch.int8, torch.int16): torch.int16,
+    (torch.int8, torch.int32): torch.int32,
+    (torch.int8, torch.int64): torch.int64,
+    (torch.int16, torch.int32): torch.int32,
+    (torch.int16, torch.int64): torch.int64,
+    (torch.int32, torch.int64): torch.int64,
+    # ints and uints (mixed sign)
+    (torch.uint8, torch.int8): torch.int16,
+    (torch.uint8, torch.int16): torch.int16,
+    (torch.uint8, torch.int32): torch.int32,
+    (torch.uint8, torch.int64): torch.int64,
+    # floats
+    (torch.float32, torch.float64): torch.float64,
+    # complexes
+    (torch.complex64, torch.complex128): torch.complex128,
+    # Mixed float and complex
+    (torch.float32, torch.complex64): torch.complex64,
+    (torch.float32, torch.complex128): torch.complex128,
+    (torch.float64, torch.complex64): torch.complex128,
+    (torch.float64, torch.complex128): torch.complex128,
+}
+
+_promotion_table.update({(b, a): c for (a, b), c in _promotion_table.items()})
+_promotion_table.update({(a, a): a for a in _array_api_dtypes})
+
+
+def _two_arg(f):
+    @_wraps(f)
+    def _f(x1, x2, /, **kwargs):
+        x1, x2 = _fix_promotion(x1, x2)
+        return f(x1, x2, **kwargs)
+    if _f.__doc__ is None:
+        _f.__doc__ = f"""\
+Array API compatibility wrapper for torch.{f.__name__}.
+
+See the corresponding PyTorch documentation and/or the array API specification
+for more details.
+
+"""
+    return _f
+
+def _fix_promotion(x1, x2, only_scalar=True):
+    if not isinstance(x1, torch.Tensor) or not isinstance(x2, torch.Tensor):
+        return x1, x2
+    if x1.dtype not in _array_api_dtypes or x2.dtype not in _array_api_dtypes:
+        return x1, x2
+    # If an argument is 0-D pytorch downcasts the other argument
+    if not only_scalar or x1.shape == ():
+        dtype = result_type(x1, x2)
+        x2 = x2.to(dtype)
+    if not only_scalar or x2.shape == ():
+        dtype = result_type(x1, x2)
+        x1 = x1.to(dtype)
+    return x1, x2
+
+
+_py_scalars = (bool, int, float, complex)
+
+
+def result_type(*arrays_and_dtypes: Array | DType | complex) -> DType:
+    num = len(arrays_and_dtypes)
+
+    if num == 0:
+        raise ValueError("At least one array or dtype must be provided")
+
+    elif num == 1:
+        x = arrays_and_dtypes[0]
+        if isinstance(x, torch.dtype):
+            return x
+        return x.dtype
+
+    if num == 2:
+        x, y = arrays_and_dtypes
+        return _result_type(x, y)
+
+    else:
+        # sort scalars so that they are treated last
+        scalars, others = [], []
+        for x in arrays_and_dtypes:
+            if isinstance(x, _py_scalars):
+                scalars.append(x)
+            else:
+                others.append(x)
+        if not others:
+            raise ValueError("At least one array or dtype must be provided")
+
+        # combine left-to-right
+        return _reduce(_result_type, others + scalars)
+
+
+def _result_type(x: Array | DType | complex, y: Array | DType | complex) -> DType:
+    if not (isinstance(x, _py_scalars) or isinstance(y, _py_scalars)):
+        xdt = x if isinstance(x, torch.dtype) else x.dtype
+        ydt = y if isinstance(y, torch.dtype) else y.dtype
+
+        try:
+            return _promotion_table[xdt, ydt]
+        except KeyError:
+            pass
+
+    # This doesn't result_type(dtype, dtype) for non-array API dtypes
+    # because torch.result_type only accepts tensors. This does however, allow
+    # cross-kind promotion.
+    x = torch.tensor([], dtype=x) if isinstance(x, torch.dtype) else x
+    y = torch.tensor([], dtype=y) if isinstance(y, torch.dtype) else y
+    return torch.result_type(x, y)
+
+
+def can_cast(from_: DType | Array, to: DType, /) -> bool:
+    if not isinstance(from_, torch.dtype):
+        from_ = from_.dtype
+    return torch.can_cast(from_, to)
+
+# Basic renames
+bitwise_invert = torch.bitwise_not
+newaxis = None
+# torch.conj sets the conjugation bit, which breaks conversion to other
+# libraries. See https://github.com/data-apis/array-api-compat/issues/173
+conj = torch.conj_physical
+
+# Two-arg elementwise functions
+# These require a wrapper to do the correct type promotion on 0-D tensors
+add = _two_arg(torch.add)
+atan2 = _two_arg(torch.atan2)
+bitwise_and = _two_arg(torch.bitwise_and)
+bitwise_left_shift = _two_arg(torch.bitwise_left_shift)
+bitwise_or = _two_arg(torch.bitwise_or)
+bitwise_right_shift = _two_arg(torch.bitwise_right_shift)
+bitwise_xor = _two_arg(torch.bitwise_xor)
+copysign = _two_arg(torch.copysign)
+divide = _two_arg(torch.divide)
+# Also a rename. torch.equal does not broadcast
+equal = _two_arg(torch.eq)
+floor_divide = _two_arg(torch.floor_divide)
+greater = _two_arg(torch.greater)
+greater_equal = _two_arg(torch.greater_equal)
+hypot = _two_arg(torch.hypot)
+less = _two_arg(torch.less)
+less_equal = _two_arg(torch.less_equal)
+logaddexp = _two_arg(torch.logaddexp)
+# logical functions are not included here because they only accept bool in the
+# spec, so type promotion is irrelevant.
+maximum = _two_arg(torch.maximum)
+minimum = _two_arg(torch.minimum)
+multiply = _two_arg(torch.multiply)
+not_equal = _two_arg(torch.not_equal)
+pow = _two_arg(torch.pow)
+remainder = _two_arg(torch.remainder)
+subtract = _two_arg(torch.subtract)
+
+
+def asarray(
+    obj: Array | complex | NestedSequence[complex] | SupportsBufferProtocol,
+    /,
+    *,
+    dtype: DType | None = None,
+    device: Device | None = None,
+    copy: bool | None = None,
+    **kwargs: Any,
+) -> Array:
+    # torch.asarray does not respect input->output device propagation
+    # https://github.com/pytorch/pytorch/issues/150199
+    if device is None and isinstance(obj, torch.Tensor):
+        device = obj.device
+    return torch.asarray(obj, dtype=dtype, device=device, copy=copy, **kwargs)
+
+
+# These wrappers are mostly based on the fact that pytorch uses 'dim' instead
+# of 'axis'.
+
+# torch.min and torch.max return a tuple and don't support multiple axes https://github.com/pytorch/pytorch/issues/58745
+def max(x: Array, /, *, axis: int | tuple[int, ...] | None = None, keepdims: bool = False) -> Array:
+    # https://github.com/pytorch/pytorch/issues/29137
+    if axis == ():
+        return torch.clone(x)
+    return torch.amax(x, axis, keepdims=keepdims)
+
+def min(x: Array, /, *, axis: int | tuple[int, ...] |None = None, keepdims: bool = False) -> Array:
+    # https://github.com/pytorch/pytorch/issues/29137
+    if axis == ():
+        return torch.clone(x)
+    return torch.amin(x, axis, keepdims=keepdims)
+
+clip = get_xp(torch)(_aliases.clip)
+unstack = get_xp(torch)(_aliases.unstack)
+cumulative_sum = get_xp(torch)(_aliases.cumulative_sum)
+cumulative_prod = get_xp(torch)(_aliases.cumulative_prod)
+finfo = get_xp(torch)(_aliases.finfo)
+iinfo = get_xp(torch)(_aliases.iinfo)
+
+
+# torch.sort also returns a tuple
+# https://github.com/pytorch/pytorch/issues/70921
+def sort(
+    x: Array,
+    /,
+    *,
+    axis: int = -1,
+    descending: bool = False,
+    stable: bool = True,
+    **kwargs: object,
+) -> Array:
+    return torch.sort(x, dim=axis, descending=descending, stable=stable, **kwargs).values
+
+
+# Wrap torch.argsort to set stable=True by default
+def argsort(
+    x: Array,
+    /,
+    *,
+    axis: int = -1,
+    descending: bool = False,
+    stable: bool = True,
+    **kwargs: object,
+) -> Array:
+    return torch.argsort(x, dim=axis, descending=descending, stable=stable, **kwargs)
+
+
+def _normalize_axes(axis, ndim):
+    axes = []
+    if ndim == 0 and axis:
+        # Better error message in this case
+        raise IndexError(f"Dimension out of range: {axis[0]}")
+    lower, upper = -ndim, ndim - 1
+    for a in axis:
+        if a < lower or a > upper:
+            # Match torch error message (e.g., from sum())
+            raise IndexError(f"Dimension out of range (expected to be in range of [{lower}, {upper}], but got {a}")
+        if a < 0:
+            a = a + ndim
+        if a in axes:
+            # Use IndexError instead of RuntimeError, and "axis" instead of "dim"
+            raise IndexError(f"Axis {a} appears multiple times in the list of axes")
+        axes.append(a)
+    return sorted(axes)
+
+def _axis_none_keepdims(x, ndim, keepdims):
+    # Apply keepdims when axis=None
+    # (https://github.com/pytorch/pytorch/issues/71209)
+    # Note that this is only valid for the axis=None case.
+    if keepdims:
+        for i in range(ndim):
+            x = torch.unsqueeze(x, 0)
+    return x
+
+def _reduce_multiple_axes(f, x, axis, keepdims=False, **kwargs):
+    # Some reductions don't support multiple axes
+    # (https://github.com/pytorch/pytorch/issues/56586).
+    axes = _normalize_axes(axis, x.ndim)
+    for a in reversed(axes):
+        x = torch.movedim(x, a, -1)
+    x = torch.flatten(x, -len(axes))
+
+    out = f(x, -1, **kwargs)
+
+    if keepdims:
+        for a in axes:
+            out = torch.unsqueeze(out, a)
+    return out
+
+
+def _sum_prod_no_axis(x: Array, dtype: DType | None) -> Array:
+    """
+    Implements `sum(..., axis=())` and `prod(..., axis=())`.
+    
+    Works around https://github.com/pytorch/pytorch/issues/29137
+    """
+    if dtype is not None:
+        return x.clone() if dtype == x.dtype else x.to(dtype)
+
+    # We can't upcast uint8 according to the spec because there is no
+    # torch.uint64, so at least upcast to int64 which is what prod does
+    # when axis=None.
+    if x.dtype in (torch.uint8, torch.int8, torch.int16, torch.int32):
+        return x.to(torch.int64)
+
+    return x.clone()
+
+
+def prod(x: Array,
+         /,
+         *,
+         axis: int | tuple[int, ...] | None = None,
+         dtype: DType | None = None,
+         keepdims: bool = False,
+         **kwargs: object) -> Array:
+
+    if axis == ():
+        return _sum_prod_no_axis(x, dtype)
+    # torch.prod doesn't support multiple axes
+    # (https://github.com/pytorch/pytorch/issues/56586).
+    if isinstance(axis, tuple):
+        return _reduce_multiple_axes(torch.prod, x, axis, keepdims=keepdims, dtype=dtype, **kwargs)
+    if axis is None:
+        # torch doesn't support keepdims with axis=None
+        # (https://github.com/pytorch/pytorch/issues/71209)
+        res = torch.prod(x, dtype=dtype, **kwargs)
+        res = _axis_none_keepdims(res, x.ndim, keepdims)
+        return res
+
+    return torch.prod(x, axis, dtype=dtype, keepdims=keepdims, **kwargs)
+
+
+def sum(x: Array,
+         /,
+         *,
+         axis: int | tuple[int, ...] | None = None,
+         dtype: DType | None = None,
+         keepdims: bool = False,
+         **kwargs: object) -> Array:
+
+    if axis == ():
+        return _sum_prod_no_axis(x, dtype)
+    if axis is None:
+        # torch doesn't support keepdims with axis=None
+        # (https://github.com/pytorch/pytorch/issues/71209)
+        res = torch.sum(x, dtype=dtype, **kwargs)
+        res = _axis_none_keepdims(res, x.ndim, keepdims)
+        return res
+
+    return torch.sum(x, axis, dtype=dtype, keepdims=keepdims, **kwargs)
+
+def any(x: Array,
+        /,
+        *,
+        axis: int | tuple[int, ...] | None = None,
+        keepdims: bool = False,
+        **kwargs: object) -> Array:
+
+    if axis == ():
+        return x.to(torch.bool)
+    # torch.any doesn't support multiple axes
+    # (https://github.com/pytorch/pytorch/issues/56586).
+    if isinstance(axis, tuple):
+        res = _reduce_multiple_axes(torch.any, x, axis, keepdims=keepdims, **kwargs)
+        return res.to(torch.bool)
+    if axis is None:
+        # torch doesn't support keepdims with axis=None
+        # (https://github.com/pytorch/pytorch/issues/71209)
+        res = torch.any(x, **kwargs)
+        res = _axis_none_keepdims(res, x.ndim, keepdims)
+        return res.to(torch.bool)
+
+    # torch.any doesn't return bool for uint8
+    return torch.any(x, axis, keepdims=keepdims).to(torch.bool)
+
+def all(x: Array,
+        /,
+        *,
+        axis: int | tuple[int, ...] | None = None,
+        keepdims: bool = False,
+        **kwargs: object) -> Array:
+
+    if axis == ():
+        return x.to(torch.bool)
+    # torch.all doesn't support multiple axes
+    # (https://github.com/pytorch/pytorch/issues/56586).
+    if isinstance(axis, tuple):
+        res = _reduce_multiple_axes(torch.all, x, axis, keepdims=keepdims, **kwargs)
+        return res.to(torch.bool)
+    if axis is None:
+        # torch doesn't support keepdims with axis=None
+        # (https://github.com/pytorch/pytorch/issues/71209)
+        res = torch.all(x, **kwargs)
+        res = _axis_none_keepdims(res, x.ndim, keepdims)
+        return res.to(torch.bool)
+
+    # torch.all doesn't return bool for uint8
+    return torch.all(x, axis, keepdims=keepdims).to(torch.bool)
+
+def mean(x: Array,
+         /,
+         *,
+         axis: int | tuple[int, ...] | None = None,
+         keepdims: bool = False,
+         **kwargs: object) -> Array:
+    # https://github.com/pytorch/pytorch/issues/29137
+    if axis == ():
+        return torch.clone(x)
+    if axis is None:
+        # torch doesn't support keepdims with axis=None
+        # (https://github.com/pytorch/pytorch/issues/71209)
+        res = torch.mean(x, **kwargs)
+        res = _axis_none_keepdims(res, x.ndim, keepdims)
+        return res
+    return torch.mean(x, axis, keepdims=keepdims, **kwargs)
+
+def std(x: Array,
+        /,
+        *,
+        axis: int | tuple[int, ...] | None = None,
+        correction: float = 0.0,
+        keepdims: bool = False,
+        **kwargs: object) -> Array:
+    # Note, float correction is not supported
+    # https://github.com/pytorch/pytorch/issues/61492. We don't try to
+    # implement it here for now.
+
+    if isinstance(correction, float):
+        _correction = int(correction)
+        if correction != _correction:
+            raise NotImplementedError("float correction in torch std() is not yet supported")
+    else:
+        _correction = correction
+
+    # https://github.com/pytorch/pytorch/issues/29137
+    if axis == ():
+        return torch.zeros_like(x)
+    if isinstance(axis, int):
+        axis = (axis,)
+    if axis is None:
+        # torch doesn't support keepdims with axis=None
+        # (https://github.com/pytorch/pytorch/issues/71209)
+        res = torch.std(x, tuple(range(x.ndim)), correction=_correction, **kwargs)
+        res = _axis_none_keepdims(res, x.ndim, keepdims)
+        return res
+    return torch.std(x, axis, correction=_correction, keepdims=keepdims, **kwargs)
+
+def var(x: Array,
+        /,
+        *,
+        axis: int | tuple[int, ...] | None = None,
+        correction: float = 0.0,
+        keepdims: bool = False,
+        **kwargs: object) -> Array:
+    # Note, float correction is not supported
+    # https://github.com/pytorch/pytorch/issues/61492. We don't try to
+    # implement it here for now.
+
+    # if isinstance(correction, float):
+    #     correction = int(correction)
+
+    # https://github.com/pytorch/pytorch/issues/29137
+    if axis == ():
+        return torch.zeros_like(x)
+    if isinstance(axis, int):
+        axis = (axis,)
+    if axis is None:
+        # torch doesn't support keepdims with axis=None
+        # (https://github.com/pytorch/pytorch/issues/71209)
+        res = torch.var(x, tuple(range(x.ndim)), correction=correction, **kwargs)
+        res = _axis_none_keepdims(res, x.ndim, keepdims)
+        return res
+    return torch.var(x, axis, correction=correction, keepdims=keepdims, **kwargs)
+
+# torch.concat doesn't support dim=None
+# https://github.com/pytorch/pytorch/issues/70925
+def concat(arrays: tuple[Array, ...] | list[Array],
+           /,
+           *,
+           axis: int | None = 0,
+           **kwargs: object) -> Array:
+    if axis is None:
+        arrays = tuple(ar.flatten() for ar in arrays)
+        axis = 0
+    return torch.concat(arrays, axis, **kwargs)
+
+# torch.squeeze only accepts int dim and doesn't require it
+# https://github.com/pytorch/pytorch/issues/70924. Support for tuple dim was
+# added at https://github.com/pytorch/pytorch/pull/89017.
+def squeeze(x: Array, /, axis: int | tuple[int, ...]) -> Array:
+    if isinstance(axis, int):
+        axis = (axis,)
+    for a in axis:
+        if x.shape[a] != 1:
+            raise ValueError("squeezed dimensions must be equal to 1")
+    axes = _normalize_axes(axis, x.ndim)
+    # Remove this once pytorch 1.14 is released with the above PR #89017.
+    sequence = [a - i for i, a in enumerate(axes)]
+    for a in sequence:
+        x = torch.squeeze(x, a)
+    return x
+
+# torch.broadcast_to uses size instead of shape
+def broadcast_to(x: Array, /, shape: tuple[int, ...], **kwargs: object) -> Array:
+    return torch.broadcast_to(x, shape, **kwargs)
+
+# torch.permute uses dims instead of axes
+def permute_dims(x: Array, /, axes: tuple[int, ...]) -> Array:
+    return torch.permute(x, axes)
+
+# The axis parameter doesn't work for flip() and roll()
+# https://github.com/pytorch/pytorch/issues/71210. Also torch.flip() doesn't
+# accept axis=None
+def flip(x: Array, /, *, axis: int | tuple[int, ...] | None = None, **kwargs: object) -> Array:
+    if axis is None:
+        axis = tuple(range(x.ndim))
+    # torch.flip doesn't accept dim as an int but the method does
+    # https://github.com/pytorch/pytorch/issues/18095
+    return x.flip(axis, **kwargs)
+
+def roll(x: Array, /, shift: int | tuple[int, ...], *, axis: int | tuple[int, ...] | None = None, **kwargs: object) -> Array:
+    return torch.roll(x, shift, axis, **kwargs)
+
+def nonzero(x: Array, /, **kwargs: object) -> tuple[Array, ...]:
+    if x.ndim == 0:
+        raise ValueError("nonzero() does not support zero-dimensional arrays")
+    return torch.nonzero(x, as_tuple=True, **kwargs)
+
+
+# torch uses `dim` instead of `axis`
+def diff(
+    x: Array,
+    /,
+    *,
+    axis: int = -1,
+    n: int = 1,
+    prepend: Array | None = None,
+    append: Array | None = None,
+) -> Array:
+    return torch.diff(x, dim=axis, n=n, prepend=prepend, append=append)
+
+
+# torch uses `dim` instead of `axis`, does not have keepdims
+def count_nonzero(
+    x: Array,
+    /,
+    *,
+    axis: int | tuple[int, ...] | None = None,
+    keepdims: bool = False,
+) -> Array:
+    result = torch.count_nonzero(x, dim=axis)
+    if keepdims:
+        if isinstance(axis, int):
+            return result.unsqueeze(axis)
+        elif isinstance(axis, tuple):
+            n_axis = [x.ndim + ax if ax < 0 else ax for ax in axis]
+            sh = [1 if i in n_axis else x.shape[i] for i in range(x.ndim)]
+            return torch.reshape(result, sh)
+        return _axis_none_keepdims(result, x.ndim, keepdims)
+    else:
+        return result
+
+
+# "repeat" is torch.repeat_interleave;  also the dim argument
+def repeat(x: Array, repeats: int | Array, /, *, axis: int | None = None) -> Array:
+    return torch.repeat_interleave(x, repeats, axis)
+
+
+def where(condition: Array, x1: Array | complex, x2: Array | complex, /) -> Array:
+    x1, x2 = _fix_promotion(x1, x2)
+    return torch.where(condition, x1, x2)
+
+
+# torch.reshape doesn't have the copy keyword
+def reshape(x: Array,
+            /,
+            shape: tuple[int, ...],
+            *,
+            copy: bool | None = None,
+            **kwargs: object) -> Array:
+    if copy is not None:
+        raise NotImplementedError("torch.reshape doesn't yet support the copy keyword")
+    return torch.reshape(x, shape, **kwargs)
+
+# torch.arange doesn't support returning empty arrays
+# (https://github.com/pytorch/pytorch/issues/70915), and doesn't support some
+# keyword argument combinations
+# (https://github.com/pytorch/pytorch/issues/70914)
+def arange(start: float,
+           /,
+           stop: float | None = None,
+           step: float = 1,
+           *,
+           dtype: DType | None = None,
+           device: Device | None = None,
+           **kwargs: object) -> Array:
+    if stop is None:
+        start, stop = 0, start
+    if step > 0 and stop <= start or step < 0 and stop >= start:
+        if dtype is None:
+            if _builtin_all(isinstance(i, int) for i in [start, stop, step]):
+                dtype = torch.int64
+            else:
+                dtype = torch.float32
+        return torch.empty(0, dtype=dtype, device=device, **kwargs)
+    return torch.arange(start, stop, step, dtype=dtype, device=device, **kwargs)
+
+# torch.eye does not accept None as a default for the second argument and
+# doesn't support off-diagonals (https://github.com/pytorch/pytorch/issues/70910)
+def eye(n_rows: int,
+        n_cols: int | None = None,
+        /,
+        *,
+        k: int = 0,
+        dtype: DType | None = None,
+        device: Device | None = None,
+        **kwargs: object) -> Array:
+    if n_cols is None:
+        n_cols = n_rows
+    z = torch.zeros(n_rows, n_cols, dtype=dtype, device=device, **kwargs)
+    if abs(k) <= n_rows + n_cols:
+        z.diagonal(k).fill_(1)
+    return z
+
+# torch.linspace doesn't have the endpoint parameter
+def linspace(start: float,
+             stop: float,
+             /,
+             num: int,
+             *,
+             dtype: DType | None = None,
+             device: Device | None = None,
+             endpoint: bool = True,
+             **kwargs: object) -> Array:
+    if not endpoint:
+        return torch.linspace(start, stop, num+1, dtype=dtype, device=device, **kwargs)[:-1]
+    return torch.linspace(start, stop, num, dtype=dtype, device=device, **kwargs)
+
+# torch.full does not accept an int size
+# https://github.com/pytorch/pytorch/issues/70906
+def full(shape: int | tuple[int, ...],
+         fill_value: complex,
+         *,
+         dtype: DType | None = None,
+         device: Device | None = None,
+         **kwargs: object) -> Array:
+    if isinstance(shape, int):
+        shape = (shape,)
+
+    return torch.full(shape, fill_value, dtype=dtype, device=device, **kwargs)
+
+# ones, zeros, and empty do not accept shape as a keyword argument
+def ones(shape: int | tuple[int, ...],
+         *,
+         dtype: DType | None = None,
+         device: Device | None = None,
+         **kwargs: object) -> Array:
+    return torch.ones(shape, dtype=dtype, device=device, **kwargs)
+
+def zeros(shape: int | tuple[int, ...],
+         *,
+         dtype: DType | None = None,
+         device: Device | None = None,
+         **kwargs: object) -> Array:
+    return torch.zeros(shape, dtype=dtype, device=device, **kwargs)
+
+def empty(shape: int | tuple[int, ...],
+         *,
+         dtype: DType | None = None,
+         device: Device | None = None,
+         **kwargs: object) -> Array:
+    return torch.empty(shape, dtype=dtype, device=device, **kwargs)
+
+# tril and triu do not call the keyword argument k
+
+def tril(x: Array, /, *, k: int = 0) -> Array:
+    return torch.tril(x, k)
+
+def triu(x: Array, /, *, k: int = 0) -> Array:
+    return torch.triu(x, k)
+
+# Functions that aren't in torch https://github.com/pytorch/pytorch/issues/58742
+def expand_dims(x: Array, /, *, axis: int = 0) -> Array:
+    return torch.unsqueeze(x, axis)
+
+
+def astype(
+    x: Array,
+    dtype: DType,
+    /,
+    *,
+    copy: bool = True,
+    device: Device | None = None,
+) -> Array:
+    if device is not None:
+        return x.to(device, dtype=dtype, copy=copy)
+    return x.to(dtype=dtype, copy=copy)
+
+
+def broadcast_arrays(*arrays: Array) -> list[Array]:
+    shape = torch.broadcast_shapes(*[a.shape for a in arrays])
+    return [torch.broadcast_to(a, shape) for a in arrays]
+
+# Note that these named tuples aren't actually part of the standard namespace,
+# but I don't see any issue with exporting the names here regardless.
+from ..common._aliases import (UniqueAllResult, UniqueCountsResult,
+                               UniqueInverseResult)
+
+# https://github.com/pytorch/pytorch/issues/70920
+def unique_all(x: Array) -> UniqueAllResult:
+    # torch.unique doesn't support returning indices.
+    # https://github.com/pytorch/pytorch/issues/36748. The workaround
+    # suggested in that issue doesn't actually function correctly (it relies
+    # on non-deterministic behavior of scatter()).
+    raise NotImplementedError("unique_all() not yet implemented for pytorch (see https://github.com/pytorch/pytorch/issues/36748)")
+
+    # values, inverse_indices, counts = torch.unique(x, return_counts=True, return_inverse=True)
+    # # torch.unique incorrectly gives a 0 count for nan values.
+    # # https://github.com/pytorch/pytorch/issues/94106
+    # counts[torch.isnan(values)] = 1
+    # return UniqueAllResult(values, indices, inverse_indices, counts)
+
+def unique_counts(x: Array) -> UniqueCountsResult:
+    values, counts = torch.unique(x, return_counts=True)
+
+    # torch.unique incorrectly gives a 0 count for nan values.
+    # https://github.com/pytorch/pytorch/issues/94106
+    counts[torch.isnan(values)] = 1
+    return UniqueCountsResult(values, counts)
+
+def unique_inverse(x: Array) -> UniqueInverseResult:
+    values, inverse = torch.unique(x, return_inverse=True)
+    return UniqueInverseResult(values, inverse)
+
+def unique_values(x: Array) -> Array:
+    return torch.unique(x)
+
+def matmul(x1: Array, x2: Array, /, **kwargs: object) -> Array:
+    # torch.matmul doesn't type promote (but differently from _fix_promotion)
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+    return torch.matmul(x1, x2, **kwargs)
+
+matrix_transpose = get_xp(torch)(_aliases.matrix_transpose)
+_vecdot = get_xp(torch)(_aliases.vecdot)
+
+def vecdot(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+    return _vecdot(x1, x2, axis=axis)
+
+# torch.tensordot uses dims instead of axes
+def tensordot(
+    x1: Array,
+    x2: Array,
+    /,
+    *, 
+    axes: int | tuple[Sequence[int], Sequence[int]] = 2, 
+    **kwargs: object,
+) -> Array:
+    # Note: torch.tensordot fails with integer dtypes when there is only 1
+    # element in the axis (https://github.com/pytorch/pytorch/issues/84530).
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+    return torch.tensordot(x1, x2, dims=axes, **kwargs)
+
+
+def isdtype(
+    dtype: DType, 
+    kind: DType | str | tuple[DType | str, ...],
+    *,
+    _tuple: bool = True, # Disallow nested tuples
+) -> bool:
+    """
+    Returns a boolean indicating whether a provided dtype is of a specified data type ``kind``.
+
+    Note that outside of this function, this compat library does not yet fully
+    support complex numbers.
+
+    See
+    https://data-apis.org/array-api/latest/API_specification/generated/array_api.isdtype.html
+    for more details
+    """
+    if isinstance(kind, tuple) and _tuple:
+        return _builtin_any(isdtype(dtype, k, _tuple=False) for k in kind)
+    elif isinstance(kind, str):
+        if kind == 'bool':
+            return dtype == torch.bool
+        elif kind == 'signed integer':
+            return dtype in _int_dtypes and dtype.is_signed
+        elif kind == 'unsigned integer':
+            return dtype in _int_dtypes and not dtype.is_signed
+        elif kind == 'integral':
+            return dtype in _int_dtypes
+        elif kind == 'real floating':
+            return dtype.is_floating_point
+        elif kind == 'complex floating':
+            return dtype.is_complex
+        elif kind == 'numeric':
+            return isdtype(dtype, ('integral', 'real floating', 'complex floating'))
+        else:
+            raise ValueError(f"Unrecognized data type kind: {kind!r}")
+    else:
+        return dtype == kind
+
+def take(x: Array, indices: Array, /, *, axis: int | None = None, **kwargs: object) -> Array:
+    if axis is None:
+        if x.ndim != 1:
+            raise ValueError("axis must be specified when ndim > 1")
+        axis = 0
+    # torch does not support negative indices,
+    # see https://github.com/pytorch/pytorch/issues/146211
+    return torch.index_select(
+        x,
+        axis,
+        torch.where(indices < 0, indices + x.shape[axis], indices),
+        **kwargs
+    )
+
+
+def take_along_axis(x: Array, indices: Array, /, *, axis: int = -1) -> Array:
+    # torch does not support negative indices,
+    # see https://github.com/pytorch/pytorch/issues/146211
+    return torch.take_along_dim(
+        x,
+        torch.where(indices < 0, indices + x.shape[axis], indices),
+        dim=axis
+    )
+
+
+def sign(x: Array, /) -> Array:
+    # torch sign() does not support complex numbers and does not propagate
+    # nans. See https://github.com/data-apis/array-api-compat/issues/136
+    if x.dtype.is_complex:
+        out = x/torch.abs(x)
+        # sign(0) = 0 but the above formula would give nan
+        out[x == 0+0j] = 0+0j
+        return out
+    else:
+        out = torch.sign(x)
+        if x.dtype.is_floating_point:
+            out[torch.isnan(x)] = torch.nan
+        return out
+
+
+def meshgrid(*arrays: Array, indexing: Literal['xy', 'ij'] = 'xy') -> list[Array]:
+    # enforce the default of 'xy'
+    # TODO: is the return type a list or a tuple
+    return list(torch.meshgrid(*arrays, indexing=indexing))
+
+
+__all__ = ['asarray', 'result_type', 'can_cast',
+           'permute_dims', 'bitwise_invert', 'newaxis', 'conj', 'add',
+           'atan2', 'bitwise_and', 'bitwise_left_shift', 'bitwise_or',
+           'bitwise_right_shift', 'bitwise_xor', 'copysign', 'count_nonzero',
+           'diff', 'divide',
+           'equal', 'floor_divide', 'greater', 'greater_equal', 'hypot',
+           'less', 'less_equal', 'logaddexp', 'maximum', 'minimum',
+           'multiply', 'not_equal', 'pow', 'remainder', 'subtract', 'max',
+           'min', 'clip', 'unstack', 'cumulative_sum', 'cumulative_prod', 'sort',
+           'argsort', 'prod', 'sum', 'any', 'all', 'mean', 'std', 'var', 'concat',
+           'squeeze', 'broadcast_to', 'flip', 'roll', 'nonzero', 'where', 'reshape',
+           'arange', 'eye', 'linspace', 'full', 'ones', 'zeros', 'empty',
+           'tril', 'triu', 'expand_dims', 'astype', 'broadcast_arrays',
+           'UniqueAllResult', 'UniqueCountsResult', 'UniqueInverseResult',
+           'unique_all', 'unique_counts', 'unique_inverse', 'unique_values',
+           'matmul', 'matrix_transpose', 'vecdot', 'tensordot', 'isdtype',
+           'take', 'take_along_axis', 'sign', 'finfo', 'iinfo', 'repeat', 'meshgrid']
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/_info.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/_info.py
new file mode 100644
index 0000000000000000000000000000000000000000..818e5d3702e38281a607e1d4462a0819c8594a1e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/_info.py
@@ -0,0 +1,369 @@
+"""
+Array API Inspection namespace
+
+This is the namespace for inspection functions as defined by the array API
+standard. See
+https://data-apis.org/array-api/latest/API_specification/inspection.html for
+more details.
+
+"""
+import torch
+
+from functools import cache
+
+class __array_namespace_info__:
+    """
+    Get the array API inspection namespace for PyTorch.
+
+    The array API inspection namespace defines the following functions:
+
+    - capabilities()
+    - default_device()
+    - default_dtypes()
+    - dtypes()
+    - devices()
+
+    See
+    https://data-apis.org/array-api/latest/API_specification/inspection.html
+    for more details.
+
+    Returns
+    -------
+    info : ModuleType
+        The array API inspection namespace for PyTorch.
+
+    Examples
+    --------
+    >>> info = xp.__array_namespace_info__()
+    >>> info.default_dtypes()
+    {'real floating': numpy.float64,
+     'complex floating': numpy.complex128,
+     'integral': numpy.int64,
+     'indexing': numpy.int64}
+
+    """
+
+    __module__ = 'torch'
+
+    def capabilities(self):
+        """
+        Return a dictionary of array API library capabilities.
+
+        The resulting dictionary has the following keys:
+
+        - **"boolean indexing"**: boolean indicating whether an array library
+          supports boolean indexing. Always ``True`` for PyTorch.
+
+        - **"data-dependent shapes"**: boolean indicating whether an array
+          library supports data-dependent output shapes. Always ``True`` for
+          PyTorch.
+
+        See
+        https://data-apis.org/array-api/latest/API_specification/generated/array_api.info.capabilities.html
+        for more details.
+
+        See Also
+        --------
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Returns
+        -------
+        capabilities : dict
+            A dictionary of array API library capabilities.
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.capabilities()
+        {'boolean indexing': True,
+         'data-dependent shapes': True,
+         'max dimensions': 64}
+
+        """
+        return {
+            "boolean indexing": True,
+            "data-dependent shapes": True,
+            "max dimensions": 64,
+        }
+
+    def default_device(self):
+        """
+        The default device used for new PyTorch arrays.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Returns
+        -------
+        device : Device
+            The default device used for new PyTorch arrays.
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.default_device()
+        device(type='cpu')
+
+        Notes
+        -----
+        This method returns the static default device when PyTorch is initialized.
+        However, the *current* device used by creation functions (``empty`` etc.)
+        can be changed at runtime.
+
+        See Also
+        --------
+        https://github.com/data-apis/array-api/issues/835
+        """
+        return torch.device("cpu")
+
+    def default_dtypes(self, *, device=None):
+        """
+        The default data types used for new PyTorch arrays.
+
+        Parameters
+        ----------
+        device : Device, optional
+            The device to get the default data types for.
+            Unused for PyTorch, as all devices use the same default dtypes.
+
+        Returns
+        -------
+        dtypes : dict
+            A dictionary describing the default data types used for new PyTorch
+            arrays.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.dtypes,
+        __array_namespace_info__.devices
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.default_dtypes()
+        {'real floating': torch.float32,
+         'complex floating': torch.complex64,
+         'integral': torch.int64,
+         'indexing': torch.int64}
+
+        """
+        # Note: if the default is set to float64, the devices like MPS that
+        # don't support float64 will error. We still return the default_dtype
+        # value here because this error doesn't represent a different default
+        # per-device.
+        default_floating = torch.get_default_dtype()
+        default_complex = torch.complex64 if default_floating == torch.float32 else torch.complex128
+        default_integral = torch.int64
+        return {
+            "real floating": default_floating,
+            "complex floating": default_complex,
+            "integral": default_integral,
+            "indexing": default_integral,
+        }
+
+
+    def _dtypes(self, kind):
+        bool = torch.bool
+        int8 = torch.int8
+        int16 = torch.int16
+        int32 = torch.int32
+        int64 = torch.int64
+        uint8 = torch.uint8
+        # uint16, uint32, and uint64 are present in newer versions of pytorch,
+        # but they aren't generally supported by the array API functions, so
+        # we omit them from this function.
+        float32 = torch.float32
+        float64 = torch.float64
+        complex64 = torch.complex64
+        complex128 = torch.complex128
+
+        if kind is None:
+            return {
+                "bool": bool,
+                "int8": int8,
+                "int16": int16,
+                "int32": int32,
+                "int64": int64,
+                "uint8": uint8,
+                "float32": float32,
+                "float64": float64,
+                "complex64": complex64,
+                "complex128": complex128,
+            }
+        if kind == "bool":
+            return {"bool": bool}
+        if kind == "signed integer":
+            return {
+                "int8": int8,
+                "int16": int16,
+                "int32": int32,
+                "int64": int64,
+            }
+        if kind == "unsigned integer":
+            return {
+                "uint8": uint8,
+            }
+        if kind == "integral":
+            return {
+                "int8": int8,
+                "int16": int16,
+                "int32": int32,
+                "int64": int64,
+                "uint8": uint8,
+            }
+        if kind == "real floating":
+            return {
+                "float32": float32,
+                "float64": float64,
+            }
+        if kind == "complex floating":
+            return {
+                "complex64": complex64,
+                "complex128": complex128,
+            }
+        if kind == "numeric":
+            return {
+                "int8": int8,
+                "int16": int16,
+                "int32": int32,
+                "int64": int64,
+                "uint8": uint8,
+                "float32": float32,
+                "float64": float64,
+                "complex64": complex64,
+                "complex128": complex128,
+            }
+        if isinstance(kind, tuple):
+            res = {}
+            for k in kind:
+                res.update(self.dtypes(kind=k))
+            return res
+        raise ValueError(f"unsupported kind: {kind!r}")
+
+    @cache
+    def dtypes(self, *, device=None, kind=None):
+        """
+        The array API data types supported by PyTorch.
+
+        Note that this function only returns data types that are defined by
+        the array API.
+
+        Parameters
+        ----------
+        device : Device, optional
+            The device to get the data types for.
+            Unused for PyTorch, as all devices use the same dtypes.
+        kind : str or tuple of str, optional
+            The kind of data types to return. If ``None``, all data types are
+            returned. If a string, only data types of that kind are returned.
+            If a tuple, a dictionary containing the union of the given kinds
+            is returned. The following kinds are supported:
+
+            - ``'bool'``: boolean data types (i.e., ``bool``).
+            - ``'signed integer'``: signed integer data types (i.e., ``int8``,
+              ``int16``, ``int32``, ``int64``).
+            - ``'unsigned integer'``: unsigned integer data types (i.e.,
+              ``uint8``, ``uint16``, ``uint32``, ``uint64``).
+            - ``'integral'``: integer data types. Shorthand for ``('signed
+              integer', 'unsigned integer')``.
+            - ``'real floating'``: real-valued floating-point data types
+              (i.e., ``float32``, ``float64``).
+            - ``'complex floating'``: complex floating-point data types (i.e.,
+              ``complex64``, ``complex128``).
+            - ``'numeric'``: numeric data types. Shorthand for ``('integral',
+              'real floating', 'complex floating')``.
+
+        Returns
+        -------
+        dtypes : dict
+            A dictionary mapping the names of data types to the corresponding
+            PyTorch data types.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.devices
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.dtypes(kind='signed integer')
+        {'int8': numpy.int8,
+         'int16': numpy.int16,
+         'int32': numpy.int32,
+         'int64': numpy.int64}
+
+        """
+        res = self._dtypes(kind)
+        for k, v in res.copy().items():
+            try:
+                torch.empty((0,), dtype=v, device=device)
+            except:
+                del res[k]
+        return res
+
+    @cache
+    def devices(self):
+        """
+        The devices supported by PyTorch.
+
+        Returns
+        -------
+        devices : list[Device]
+            The devices supported by PyTorch.
+
+        See Also
+        --------
+        __array_namespace_info__.capabilities,
+        __array_namespace_info__.default_device,
+        __array_namespace_info__.default_dtypes,
+        __array_namespace_info__.dtypes
+
+        Examples
+        --------
+        >>> info = xp.__array_namespace_info__()
+        >>> info.devices()
+        [device(type='cpu'), device(type='mps', index=0), device(type='meta')]
+
+        """
+        # Torch doesn't have a straightforward way to get the list of all
+        # currently supported devices. To do this, we first parse the error
+        # message of torch.device to get the list of all possible types of
+        # device:
+        try:
+            torch.device('notadevice')
+            raise AssertionError("unreachable")  # pragma: nocover
+        except RuntimeError as e:
+            # The error message is something like:
+            # "Expected one of cpu, cuda, ipu, xpu, mkldnn, opengl, opencl, ideep, hip, ve, fpga, ort, xla, lazy, vulkan, mps, meta, hpu, mtia, privateuseone device type at start of device string: notadevice"
+            devices_names = e.args[0].split('Expected one of ')[1].split(' device type')[0].split(', ')
+
+        # Next we need to check for different indices for different devices.
+        # device(device_name, index=index) doesn't actually check if the
+        # device name or index is valid. We have to try to create a tensor
+        # with it (which is why this function is cached).
+        devices = []
+        for device_name in devices_names:
+            i = 0
+            while True:
+                try:
+                    a = torch.empty((0,), device=torch.device(device_name, index=i))
+                    if a.device in devices:
+                        break
+                    devices.append(a.device)
+                except:
+                    break
+                i += 1
+
+        return devices
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/_typing.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/_typing.py
new file mode 100644
index 0000000000000000000000000000000000000000..52670871563710d326b0a114a7a517bf87098bf0
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/_typing.py
@@ -0,0 +1,3 @@
+__all__ = ["Array", "Device", "DType"]
+
+from torch import device as Device, dtype as DType, Tensor as Array
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/fft.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/fft.py
new file mode 100644
index 0000000000000000000000000000000000000000..f11b3eb5975639150c6add018c7ac36e1205b9e8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/fft.py
@@ -0,0 +1,82 @@
+from __future__ import annotations
+
+from collections.abc import Sequence
+from typing import Literal
+
+import torch  # noqa: F401
+import torch.fft
+
+from ._typing import Array
+from .._internal import clone_module
+
+__all__ = clone_module("torch.fft", globals())
+
+# Several torch fft functions do not map axes to dim
+
+def fftn(
+    x: Array,
+    /,
+    *,
+    s: Sequence[int] = None,
+    axes: Sequence[int] = None,
+    norm: Literal["backward", "ortho", "forward"] = "backward",
+    **kwargs: object,
+) -> Array:
+    return torch.fft.fftn(x, s=s, dim=axes, norm=norm, **kwargs)
+
+def ifftn(
+    x: Array,
+    /,
+    *,
+    s: Sequence[int] = None,
+    axes: Sequence[int] = None,
+    norm: Literal["backward", "ortho", "forward"] = "backward",
+    **kwargs: object,
+) -> Array:
+    return torch.fft.ifftn(x, s=s, dim=axes, norm=norm, **kwargs)
+
+def rfftn(
+    x: Array,
+    /,
+    *,
+    s: Sequence[int] = None,
+    axes: Sequence[int] = None,
+    norm: Literal["backward", "ortho", "forward"] = "backward",
+    **kwargs: object,
+) -> Array:
+    return torch.fft.rfftn(x, s=s, dim=axes, norm=norm, **kwargs)
+
+def irfftn(
+    x: Array,
+    /,
+    *,
+    s: Sequence[int] = None,
+    axes: Sequence[int] = None,
+    norm: Literal["backward", "ortho", "forward"] = "backward",
+    **kwargs: object,
+) -> Array:
+    return torch.fft.irfftn(x, s=s, dim=axes, norm=norm, **kwargs)
+
+def fftshift(
+    x: Array,
+    /,
+    *,
+    axes: int | Sequence[int] = None,
+    **kwargs: object,
+) -> Array:
+    return torch.fft.fftshift(x, dim=axes, **kwargs)
+
+def ifftshift(
+    x: Array,
+    /,
+    *,
+    axes: int | Sequence[int] = None,
+    **kwargs: object,
+) -> Array:
+    return torch.fft.ifftshift(x, dim=axes, **kwargs)
+
+
+__all__ += ["fftn", "ifftn", "rfftn", "irfftn", "fftshift", "ifftshift"]
+
+def __dir__() -> list[str]:
+    return __all__
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/linalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..08271d226734b64212a8cd687617f9ecb3197b41
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_compat/torch/linalg.py
@@ -0,0 +1,114 @@
+from __future__ import annotations
+
+import torch
+import torch.linalg
+
+from .._internal import clone_module
+
+__all__ = clone_module("torch.linalg", globals())
+
+# outer is implemented in torch but aren't in the linalg namespace
+from torch import outer
+from ._aliases import _fix_promotion, sum
+# These functions are in both the main and linalg namespaces
+from ._aliases import matmul, matrix_transpose, tensordot
+from ._typing import Array, DType
+from ..common._typing import JustInt, JustFloat
+
+# Note: torch.linalg.cross does not default to axis=-1 (it defaults to the
+# first axis with size 3), see https://github.com/pytorch/pytorch/issues/58743
+
+# torch.cross also does not support broadcasting when it would add new
+# dimensions https://github.com/pytorch/pytorch/issues/39656
+def cross(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+    if not (-min(x1.ndim, x2.ndim) <= axis < max(x1.ndim, x2.ndim)):
+        raise ValueError(f"axis {axis} out of bounds for cross product of arrays with shapes {x1.shape} and {x2.shape}")
+    if not (x1.shape[axis] == x2.shape[axis] == 3):
+        raise ValueError(f"cross product axis must have size 3, got {x1.shape[axis]} and {x2.shape[axis]}")
+    x1, x2 = torch.broadcast_tensors(x1, x2)
+    return torch.linalg.cross(x1, x2, dim=axis)
+
+def vecdot(x1: Array, x2: Array, /, *, axis: int = -1, **kwargs: object) -> Array:
+    from ._aliases import isdtype
+
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+
+    # torch.linalg.vecdot incorrectly allows broadcasting along the contracted dimension
+    if x1.shape[axis] != x2.shape[axis]:
+        raise ValueError("x1 and x2 must have the same size along the given axis")
+
+    # torch.linalg.vecdot doesn't support integer dtypes
+    if isdtype(x1.dtype, 'integral') or isdtype(x2.dtype, 'integral'):
+        if kwargs:
+            raise RuntimeError("vecdot kwargs not supported for integral dtypes")
+
+        x1_ = torch.moveaxis(x1, axis, -1)
+        x2_ = torch.moveaxis(x2, axis, -1)
+        x1_, x2_ = torch.broadcast_tensors(x1_, x2_)
+
+        res = x1_[..., None, :] @ x2_[..., None]
+        return res[..., 0, 0]
+    return torch.linalg.vecdot(x1, x2, dim=axis, **kwargs)
+
+def solve(x1: Array, x2: Array, /, **kwargs: object) -> Array:
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+    # Torch tries to emulate NumPy 1 solve behavior by using batched 1-D solve
+    # whenever
+    # 1. x1.ndim - 1 == x2.ndim
+    # 2. x1.shape[:-1] == x2.shape
+    #
+    # See linalg_solve_is_vector_rhs in
+    # aten/src/ATen/native/LinearAlgebraUtils.h and
+    # TORCH_META_FUNC(_linalg_solve_ex) in
+    # aten/src/ATen/native/BatchLinearAlgebra.cpp in the PyTorch source code.
+    #
+    # The easiest way to work around this is to prepend a size 1 dimension to
+    # x2, since x2 is already one dimension less than x1.
+    #
+    # See https://github.com/pytorch/pytorch/issues/52915
+    if x2.ndim != 1 and x1.ndim - 1 == x2.ndim and x1.shape[:-1] == x2.shape:
+        x2 = x2[None]
+    return torch.linalg.solve(x1, x2, **kwargs)
+
+# torch.trace doesn't support the offset argument and doesn't support stacking
+def trace(x: Array, /, *, offset: int = 0, dtype: DType | None = None) -> Array:
+    # Use our wrapped sum to make sure it does upcasting correctly
+    return sum(torch.diagonal(x, offset=offset, dim1=-2, dim2=-1), axis=-1, dtype=dtype)
+
+def vector_norm(
+    x: Array,
+    /,
+    *,
+    axis: int | tuple[int, ...] | None = None,
+    keepdims: bool = False,
+    # JustFloat stands for inf | -inf, which are not valid for Literal
+    ord: JustInt | JustFloat = 2,
+    **kwargs: object,
+) -> Array:
+    # torch.vector_norm incorrectly treats axis=() the same as axis=None
+    if axis == ():
+        out = kwargs.get('out')
+        if out is None:
+            dtype = None
+            if x.dtype == torch.complex64:
+                dtype = torch.float32
+            elif x.dtype == torch.complex128:
+                dtype = torch.float64
+
+            out = torch.zeros_like(x, dtype=dtype)
+
+        # The norm of a single scalar works out to abs(x) in every case except
+        # for ord=0, which is x != 0.
+        if ord == 0:
+            out[:] = (x != 0)
+        else:
+            out[:] = torch.abs(x)
+        return out
+    return torch.linalg.vector_norm(x, ord=ord, axis=axis, keepdim=keepdims, **kwargs)
+
+__all__ += ['outer', 'matmul', 'matrix_transpose', 'tensordot',
+            'cross', 'vecdot', 'solve', 'trace', 'vector_norm']
+
+def __dir__() -> list[str]:
+    return __all__
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..649e304b23d86a85f294108366a312ff544fb4e1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/__init__.py
@@ -0,0 +1,53 @@
+"""Extra array functions built on top of the array API standard."""
+
+from ._delegation import (
+    argpartition,
+    atleast_nd,
+    cov,
+    create_diagonal,
+    expand_dims,
+    isclose,
+    isin,
+    nan_to_num,
+    one_hot,
+    pad,
+    partition,
+    setdiff1d,
+    sinc,
+)
+from ._lib._at import at
+from ._lib._funcs import (
+    apply_where,
+    broadcast_shapes,
+    default_dtype,
+    kron,
+    nunique,
+)
+from ._lib._lazy import lazy_apply
+
+__version__ = "0.9.1"
+
+# pylint: disable=duplicate-code
+__all__ = [
+    "__version__",
+    "apply_where",
+    "argpartition",
+    "at",
+    "atleast_nd",
+    "broadcast_shapes",
+    "cov",
+    "create_diagonal",
+    "default_dtype",
+    "expand_dims",
+    "isclose",
+    "isin",
+    "kron",
+    "lazy_apply",
+    "nan_to_num",
+    "nunique",
+    "one_hot",
+    "pad",
+    "partition",
+    "setdiff1d",
+    "sinc",
+]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_delegation.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_delegation.py
new file mode 100644
index 0000000000000000000000000000000000000000..cb7f21cbbf91ef7ea58017928286d692a530a61c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_delegation.py
@@ -0,0 +1,1028 @@
+"""Delegation to existing implementations for Public API Functions."""
+
+from collections.abc import Sequence
+from types import ModuleType
+from typing import Literal
+
+from ._lib import _funcs
+from ._lib._utils._compat import (
+    array_namespace,
+    is_cupy_namespace,
+    is_dask_namespace,
+    is_jax_namespace,
+    is_numpy_namespace,
+    is_pydata_sparse_namespace,
+    is_torch_namespace,
+)
+from ._lib._utils._compat import device as get_device
+from ._lib._utils._helpers import asarrays, eager_shape
+from ._lib._utils._typing import Array, DType
+
+__all__ = [
+    "atleast_nd",
+    "cov",
+    "create_diagonal",
+    "expand_dims",
+    "isclose",
+    "nan_to_num",
+    "one_hot",
+    "pad",
+    "sinc",
+]
+
+
+def atleast_nd(x: Array, /, *, ndim: int, xp: ModuleType | None = None) -> Array:
+    """
+    Recursively expand the dimension of an array to at least `ndim`.
+
+    Parameters
+    ----------
+    x : array
+        Input array.
+    ndim : int
+        The minimum number of dimensions for the result.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        An array with ``res.ndim`` >= `ndim`.
+        If ``x.ndim`` >= `ndim`, `x` is returned.
+        If ``x.ndim`` < `ndim`, `x` is expanded by prepending new axes
+        until ``res.ndim`` equals `ndim`.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> x = xp.asarray([1])
+    >>> xpx.atleast_nd(x, ndim=3, xp=xp)
+    Array([[[1]]], dtype=array_api_strict.int64)
+
+    >>> x = xp.asarray([[[1, 2],
+    ...                  [3, 4]]])
+    >>> xpx.atleast_nd(x, ndim=1, xp=xp) is x
+    True
+    """
+    if xp is None:
+        xp = array_namespace(x)
+
+    if 1 <= ndim <= 2 and (
+        is_numpy_namespace(xp)
+        or is_jax_namespace(xp)
+        or is_dask_namespace(xp)
+        or is_cupy_namespace(xp)
+        or is_torch_namespace(xp)
+    ):
+        return getattr(xp, f"atleast_{ndim}d")(x)
+
+    return _funcs.atleast_nd(x, ndim=ndim, xp=xp)
+
+
+def cov(m: Array, /, *, xp: ModuleType | None = None) -> Array:
+    """
+    Estimate a covariance matrix (or a stack of covariance matrices).
+
+    Covariance indicates the level to which two variables vary together.
+    If we examine *N*-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`,
+    each with *M* observations, then element :math:`C_{ij}` of the
+    :math:`N \times N` covariance matrix is the covariance of
+    :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance
+    of :math:`x_i`.
+
+    With the exception of supporting batch input, this provides a subset of
+    the functionality of ``numpy.cov``.
+
+    Parameters
+    ----------
+    m : array
+        An array of shape ``(..., N, M)`` whose innermost two dimensions
+        contain *M* observations of *N* variables. That is,
+        each row of `m` represents a variable, and each column a single
+        observation of all those variables.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `m`. Default: infer.
+
+    Returns
+    -------
+    array
+        An array having shape (..., N, N) whose innermost two dimensions represent
+        the covariance matrix of the variables.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+
+    Consider two variables, :math:`x_0` and :math:`x_1`, which
+    correlate perfectly, but in opposite directions:
+
+    >>> x = xp.asarray([[0, 2], [1, 1], [2, 0]]).T
+    >>> x
+    Array([[0, 1, 2],
+           [2, 1, 0]], dtype=array_api_strict.int64)
+
+    Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance
+    matrix shows this clearly:
+
+    >>> xpx.cov(x, xp=xp)
+    Array([[ 1., -1.],
+           [-1.,  1.]], dtype=array_api_strict.float64)
+
+    Note that element :math:`C_{0,1}`, which shows the correlation between
+    :math:`x_0` and :math:`x_1`, is negative.
+
+    Further, note how `x` and `y` are combined:
+
+    >>> x = xp.asarray([-2.1, -1,  4.3])
+    >>> y = xp.asarray([3,  1.1,  0.12])
+    >>> X = xp.stack((x, y), axis=0)
+    >>> xpx.cov(X, xp=xp)
+    Array([[11.71      , -4.286     ],
+           [-4.286     ,  2.14413333]], dtype=array_api_strict.float64)
+
+    >>> xpx.cov(x, xp=xp)
+    Array(11.71, dtype=array_api_strict.float64)
+
+    >>> xpx.cov(y, xp=xp)
+    Array(2.14413333, dtype=array_api_strict.float64)
+
+    Input with more than two dimensions is treated as a stack of
+    two-dimensional input.
+
+    >>> stack = xp.stack((X, 2*X))
+    >>> xpx.cov(stack)
+    Array([[[ 11.71      ,  -4.286     ],
+            [ -4.286     ,   2.14413333]],
+
+           [[ 46.84      , -17.144     ],
+            [-17.144     ,   8.57653333]]], dtype=array_api_strict.float64)
+    """
+
+    if xp is None:
+        xp = array_namespace(m)
+
+    if (
+        is_numpy_namespace(xp)
+        or is_cupy_namespace(xp)
+        or is_torch_namespace(xp)
+        or is_dask_namespace(xp)
+        or is_jax_namespace(xp)
+    ) and m.ndim <= 2:
+        return xp.cov(m)
+
+    return _funcs.cov(m, xp=xp)
+
+
+def create_diagonal(
+    x: Array, /, *, offset: int = 0, xp: ModuleType | None = None
+) -> Array:
+    """
+    Construct a diagonal array.
+
+    Parameters
+    ----------
+    x : array
+        An array having shape ``(*batch_dims, k)``.
+    offset : int, optional
+        Offset from the leading diagonal (default is ``0``).
+        Use positive ints for diagonals above the leading diagonal,
+        and negative ints for diagonals below the leading diagonal.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        An array having shape ``(*batch_dims, k+abs(offset), k+abs(offset))`` with `x`
+        on the diagonal (offset by `offset`).
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> x = xp.asarray([2, 4, 8])
+
+    >>> xpx.create_diagonal(x, xp=xp)
+    Array([[2, 0, 0],
+           [0, 4, 0],
+           [0, 0, 8]], dtype=array_api_strict.int64)
+
+    >>> xpx.create_diagonal(x, offset=-2, xp=xp)
+    Array([[0, 0, 0, 0, 0],
+           [0, 0, 0, 0, 0],
+           [2, 0, 0, 0, 0],
+           [0, 4, 0, 0, 0],
+           [0, 0, 8, 0, 0]], dtype=array_api_strict.int64)
+    """
+    if xp is None:
+        xp = array_namespace(x)
+
+    if x.ndim == 0:
+        err_msg = "`x` must be at least 1-dimensional."
+        raise ValueError(err_msg)
+
+    if is_torch_namespace(xp):
+        return xp.diag_embed(x, offset=offset, dim1=-2, dim2=-1)
+
+    if (is_dask_namespace(xp) or is_cupy_namespace(xp)) and x.ndim < 2:
+        return xp.diag(x, k=offset)
+
+    if (is_jax_namespace(xp) or is_numpy_namespace(xp)) and x.ndim < 3:
+        batch_dim, n = eager_shape(x)[:-1], eager_shape(x, -1)[0] + abs(offset)
+        return xp.reshape(xp.diag(x, k=offset), (*batch_dim, n, n))
+
+    return _funcs.create_diagonal(x, offset=offset, xp=xp)
+
+
+def expand_dims(
+    a: Array, /, *, axis: int | tuple[int, ...] = (0,), xp: ModuleType | None = None
+) -> Array:
+    """
+    Expand the shape of an array.
+
+    Insert (a) new axis/axes that will appear at the position(s) specified by
+    `axis` in the expanded array shape.
+
+    This is ``xp.expand_dims`` for `axis` an int *or a tuple of ints*.
+    Roughly equivalent to ``numpy.expand_dims`` for NumPy arrays.
+
+    Parameters
+    ----------
+    a : array
+        Array to have its shape expanded.
+    axis : int or tuple of ints, optional
+        Position(s) in the expanded axes where the new axis (or axes) is/are placed.
+        If multiple positions are provided, they should be unique (note that a position
+        given by a positive index could also be referred to by a negative index -
+        that will also result in an error).
+        Default: ``(0,)``.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `a`. Default: infer.
+
+    Returns
+    -------
+    array
+        `a` with an expanded shape.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> x = xp.asarray([1, 2])
+    >>> x.shape
+    (2,)
+
+    The following is equivalent to ``x[xp.newaxis, :]`` or ``x[xp.newaxis]``:
+
+    >>> y = xpx.expand_dims(x, axis=0, xp=xp)
+    >>> y
+    Array([[1, 2]], dtype=array_api_strict.int64)
+    >>> y.shape
+    (1, 2)
+
+    The following is equivalent to ``x[:, xp.newaxis]``:
+
+    >>> y = xpx.expand_dims(x, axis=1, xp=xp)
+    >>> y
+    Array([[1],
+           [2]], dtype=array_api_strict.int64)
+    >>> y.shape
+    (2, 1)
+
+    ``axis`` may also be a tuple:
+
+    >>> y = xpx.expand_dims(x, axis=(0, 1), xp=xp)
+    >>> y
+    Array([[[1, 2]]], dtype=array_api_strict.int64)
+
+    >>> y = xpx.expand_dims(x, axis=(2, 0), xp=xp)
+    >>> y
+    Array([[[1],
+            [2]]], dtype=array_api_strict.int64)
+    """
+    if xp is None:
+        xp = array_namespace(a)
+
+    if not isinstance(axis, tuple):
+        axis = (axis,)
+    ndim = a.ndim + len(axis)
+    if axis != () and (min(axis) < -ndim or max(axis) >= ndim):
+        err_msg = (
+            f"a provided axis position is out of bounds for array of dimension {a.ndim}"
+        )
+        raise IndexError(err_msg)
+    axis = tuple(dim % ndim for dim in axis)
+    if len(set(axis)) != len(axis):
+        err_msg = "Duplicate dimensions specified in `axis`."
+        raise ValueError(err_msg)
+
+    if is_numpy_namespace(xp) or is_dask_namespace(xp) or is_jax_namespace(xp):
+        return xp.expand_dims(a, axis=axis)
+
+    return _funcs.expand_dims(a, axis=axis, xp=xp)
+
+
+def isclose(
+    a: Array | complex,
+    b: Array | complex,
+    *,
+    rtol: float = 1e-05,
+    atol: float = 1e-08,
+    equal_nan: bool = False,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Return a boolean array where two arrays are element-wise equal within a tolerance.
+
+    The tolerance values are positive, typically very small numbers. The relative
+    difference ``(rtol * abs(b))`` and the absolute difference `atol` are added together
+    to compare against the absolute difference between `a` and `b`.
+
+    NaNs are treated as equal if they are in the same place and if ``equal_nan=True``.
+    Infs are treated as equal if they are in the same place and of the same sign in both
+    arrays.
+
+    Parameters
+    ----------
+    a, b : Array | int | float | complex | bool
+        Input objects to compare. At least one must be an array.
+    rtol : array_like, optional
+        The relative tolerance parameter (see Notes).
+    atol : array_like, optional
+        The absolute tolerance parameter (see Notes).
+    equal_nan : bool, optional
+        Whether to compare NaN's as equal. If True, NaN's in `a` will be considered
+        equal to NaN's in `b` in the output array.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `a` and `b`. Default: infer.
+
+    Returns
+    -------
+    Array
+        A boolean array of shape broadcasted from `a` and `b`, containing ``True`` where
+        `a` is close to `b`, and ``False`` otherwise.
+
+    Warnings
+    --------
+    The default `atol` is not appropriate for comparing numbers with magnitudes much
+    smaller than one (see notes).
+
+    See Also
+    --------
+    math.isclose : Similar function in stdlib for Python scalars.
+
+    Notes
+    -----
+    For finite values, `isclose` uses the following equation to test whether two
+    floating point values are equivalent::
+
+        absolute(a - b) <= (atol + rtol * absolute(b))
+
+    Unlike the built-in `math.isclose`,
+    the above equation is not symmetric in `a` and `b`,
+    so that ``isclose(a, b)`` might be different from ``isclose(b, a)`` in some rare
+    cases.
+
+    The default value of `atol` is not appropriate when the reference value `b` has
+    magnitude smaller than one. For example, it is unlikely that ``a = 1e-9`` and
+    ``b = 2e-9`` should be considered "close", yet ``isclose(1e-9, 2e-9)`` is ``True``
+    with default settings. Be sure to select `atol` for the use case at hand, especially
+    for defining the threshold below which a non-zero value in `a` will be considered
+    "close" to a very small or zero value in `b`.
+
+    The comparison of `a` and `b` uses standard broadcasting, which means that `a` and
+    `b` need not have the same shape in order for ``isclose(a, b)`` to evaluate to
+    ``True``.
+
+    `isclose` is not defined for non-numeric data types.
+    ``bool`` is considered a numeric data-type for this purpose.
+    """
+    xp = array_namespace(a, b) if xp is None else xp
+
+    if (
+        is_numpy_namespace(xp)
+        or is_cupy_namespace(xp)
+        or is_dask_namespace(xp)
+        or is_jax_namespace(xp)
+    ):
+        return xp.isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)
+
+    if is_torch_namespace(xp):
+        a, b = asarrays(a, b, xp=xp)  # Array API 2024.12 support
+        return xp.isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)
+
+    return _funcs.isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan, xp=xp)
+
+
+def nan_to_num(
+    x: Array | float | complex,
+    /,
+    *,
+    fill_value: int | float = 0.0,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Replace NaN with zero and infinity with large finite numbers (default behaviour).
+
+    If `x` is inexact, NaN is replaced by zero or by the user defined value in the
+    `fill_value` keyword, infinity is replaced by the largest finite floating
+    point value representable by ``x.dtype``, and -infinity is replaced by the
+    most negative finite floating point value representable by ``x.dtype``.
+
+    For complex dtypes, the above is applied to each of the real and
+    imaginary components of `x` separately.
+
+    Parameters
+    ----------
+    x : array | float | complex
+        Input data.
+    fill_value : int | float, optional
+        Value to be used to fill NaN values. If no value is passed
+        then NaN values will be replaced with 0.0.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        `x`, with the non-finite values replaced.
+
+    See Also
+    --------
+    array_api.isnan : Shows which elements are Not a Number (NaN).
+
+    Examples
+    --------
+    >>> import array_api_extra as xpx
+    >>> import array_api_strict as xp
+    >>> xpx.nan_to_num(xp.inf)
+    1.7976931348623157e+308
+    >>> xpx.nan_to_num(-xp.inf)
+    -1.7976931348623157e+308
+    >>> xpx.nan_to_num(xp.nan)
+    0.0
+    >>> x = xp.asarray([xp.inf, -xp.inf, xp.nan, -128, 128])
+    >>> xpx.nan_to_num(x)
+    array([ 1.79769313e+308, -1.79769313e+308,  0.00000000e+000, # may vary
+           -1.28000000e+002,  1.28000000e+002])
+    >>> y = xp.asarray([complex(xp.inf, xp.nan), xp.nan, complex(xp.nan, xp.inf)])
+    array([  1.79769313e+308,  -1.79769313e+308,   0.00000000e+000, # may vary
+         -1.28000000e+002,   1.28000000e+002])
+    >>> xpx.nan_to_num(y)
+    array([  1.79769313e+308 +0.00000000e+000j, # may vary
+             0.00000000e+000 +0.00000000e+000j,
+             0.00000000e+000 +1.79769313e+308j])
+    """
+    if isinstance(fill_value, complex):
+        msg = "Complex fill values are not supported."
+        raise TypeError(msg)
+
+    xp = array_namespace(x) if xp is None else xp
+
+    # for scalars we want to output an array
+    y = xp.asarray(x)
+
+    if (
+        is_cupy_namespace(xp)
+        or is_jax_namespace(xp)
+        or is_numpy_namespace(xp)
+        or is_torch_namespace(xp)
+    ):
+        return xp.nan_to_num(y, nan=fill_value)
+
+    return _funcs.nan_to_num(y, fill_value=fill_value, xp=xp)
+
+
+def one_hot(
+    x: Array,
+    /,
+    num_classes: int,
+    *,
+    dtype: DType | None = None,
+    axis: int = -1,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    One-hot encode the given indices.
+
+    Each index in the input `x` is encoded as a vector of zeros of length `num_classes`
+    with the element at the given index set to one.
+
+    Parameters
+    ----------
+    x : array
+        An array with integral dtype whose values are between `0` and `num_classes - 1`.
+    num_classes : int
+        Number of classes in the one-hot dimension.
+    dtype : DType, optional
+        The dtype of the return value.  Defaults to the default float dtype (usually
+        float64).
+    axis : int, optional
+        Position in the expanded axes where the new axis is placed. Default: -1.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        An array having the same shape as `x` except for a new axis at the position
+        given by `axis` having size `num_classes`.  If `axis` is unspecified, it
+        defaults to -1, which appends a new axis.
+
+        If ``x < 0`` or ``x >= num_classes``, then the result is undefined, may raise
+        an exception, or may even cause a bad state.  `x` is not checked.
+
+    Examples
+    --------
+    >>> import array_api_extra as xpx
+    >>> import array_api_strict as xp
+    >>> xpx.one_hot(xp.asarray([1, 2, 0]), 3)
+    Array([[0., 1., 0.],
+          [0., 0., 1.],
+          [1., 0., 0.]], dtype=array_api_strict.float64)
+    """
+    # Validate inputs.
+    if xp is None:
+        xp = array_namespace(x)
+    if not xp.isdtype(x.dtype, "integral"):
+        msg = "x must have an integral dtype."
+        raise TypeError(msg)
+    if dtype is None:
+        dtype = _funcs.default_dtype(xp, device=get_device(x))
+    # Delegate where possible.
+    if is_jax_namespace(xp):
+        from jax.nn import one_hot as jax_one_hot
+
+        return jax_one_hot(x, num_classes, dtype=dtype, axis=axis)
+    if is_torch_namespace(xp):
+        from torch.nn.functional import one_hot as torch_one_hot
+
+        x = xp.astype(x, xp.int64)  # PyTorch only supports int64 here.
+        try:
+            out = torch_one_hot(x, num_classes)
+        except RuntimeError as e:
+            raise IndexError from e
+    else:
+        out = _funcs.one_hot(x, num_classes, xp=xp)
+    out = xp.astype(out, dtype, copy=False)
+    if axis != -1:
+        out = xp.moveaxis(out, -1, axis)
+    return out
+
+
+def pad(
+    x: Array,
+    pad_width: int | tuple[int, int] | Sequence[tuple[int, int]],
+    mode: Literal["constant"] = "constant",
+    *,
+    constant_values: complex = 0,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Pad the input array.
+
+    Parameters
+    ----------
+    x : array
+        Input array.
+    pad_width : int or tuple of ints or sequence of pairs of ints
+        Pad the input array with this many elements from each side.
+        If a sequence of tuples, ``[(before_0, after_0), ... (before_N, after_N)]``,
+        each pair applies to the corresponding axis of ``x``.
+        A single tuple, ``(before, after)``, is equivalent to a list of ``x.ndim``
+        copies of this tuple.
+    mode : str, optional
+        Only "constant" mode is currently supported, which pads with
+        the value passed to `constant_values`.
+    constant_values : python scalar, optional
+        Use this value to pad the input. Default is zero.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        The input array,
+        padded with ``pad_width`` elements equal to ``constant_values``.
+    """
+    xp = array_namespace(x) if xp is None else xp
+
+    if mode != "constant":
+        msg = "Only `'constant'` mode is currently supported"
+        raise NotImplementedError(msg)
+
+    if (
+        is_numpy_namespace(xp)
+        or is_cupy_namespace(xp)
+        or is_jax_namespace(xp)
+        or is_pydata_sparse_namespace(xp)
+    ):
+        return xp.pad(x, pad_width, mode, constant_values=constant_values)
+
+    # https://github.com/pytorch/pytorch/blob/cf76c05b4dc629ac989d1fb8e789d4fac04a095a/torch/_numpy/_funcs_impl.py#L2045-L2056
+    if is_torch_namespace(xp):
+        pad_width = xp.asarray(pad_width)
+        pad_width = xp.broadcast_to(pad_width, (x.ndim, 2))
+        pad_width = xp.flip(pad_width, axis=(0,)).flatten()
+        return xp.nn.functional.pad(x, tuple(pad_width), value=constant_values)  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+
+    return _funcs.pad(x, pad_width, constant_values=constant_values, xp=xp)
+
+
+def setdiff1d(
+    x1: Array | complex,
+    x2: Array | complex,
+    /,
+    *,
+    assume_unique: bool = False,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Find the set difference of two arrays.
+
+    Return the unique values in `x1` that are not in `x2`.
+
+    Parameters
+    ----------
+    x1 : array | int | float | complex | bool
+        Input array.
+    x2 : array
+        Input comparison array.
+    assume_unique : bool
+        If ``True``, the input arrays are both assumed to be unique, which
+        can speed up the calculation. Default is ``False``.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x1` and `x2`. Default: infer.
+
+    Returns
+    -------
+    array
+        1D array of values in `x1` that are not in `x2`. The result
+        is sorted when `assume_unique` is ``False``, but otherwise only sorted
+        if the input is sorted.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+
+    >>> x1 = xp.asarray([1, 2, 3, 2, 4, 1])
+    >>> x2 = xp.asarray([3, 4, 5, 6])
+    >>> xpx.setdiff1d(x1, x2, xp=xp)
+    Array([1, 2], dtype=array_api_strict.int64)
+    """
+
+    if xp is None:
+        xp = array_namespace(x1, x2)
+
+    if is_numpy_namespace(xp) or is_cupy_namespace(xp) or is_jax_namespace(xp):
+        x1, x2 = asarrays(x1, x2, xp=xp)
+        return xp.setdiff1d(x1, x2, assume_unique=assume_unique)
+
+    return _funcs.setdiff1d(x1, x2, assume_unique=assume_unique, xp=xp)
+
+
+def sinc(x: Array, /, *, xp: ModuleType | None = None) -> Array:
+    r"""
+    Return the normalized sinc function.
+
+    The sinc function is equal to :math:`\sin(\pi x)/(\pi x)` for any argument
+    :math:`x\ne 0`. ``sinc(0)`` takes the limit value 1, making ``sinc`` not
+    only everywhere continuous but also infinitely differentiable.
+
+    .. note::
+
+        Note the normalization factor of ``pi`` used in the definition.
+        This is the most commonly used definition in signal processing.
+        Use ``sinc(x / xp.pi)`` to obtain the unnormalized sinc function
+        :math:`\sin(x)/x` that is more common in mathematics.
+
+    Parameters
+    ----------
+    x : array
+        Array (possibly multi-dimensional) of values for which to calculate
+        ``sinc(x)``. Must have a real floating point dtype.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        ``sinc(x)`` calculated elementwise, which has the same shape as the input.
+
+    Notes
+    -----
+    The name sinc is short for "sine cardinal" or "sinus cardinalis".
+
+    The sinc function is used in various signal processing applications,
+    including in anti-aliasing, in the construction of a Lanczos resampling
+    filter, and in interpolation.
+
+    For bandlimited interpolation of discrete-time signals, the ideal
+    interpolation kernel is proportional to the sinc function.
+
+    References
+    ----------
+    #. Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web
+       Resource. https://mathworld.wolfram.com/SincFunction.html
+    #. Wikipedia, "Sinc function",
+       https://en.wikipedia.org/wiki/Sinc_function
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> x = xp.linspace(-4, 4, 41)
+    >>> xpx.sinc(x, xp=xp)
+    Array([-3.89817183e-17, -4.92362781e-02,
+           -8.40918587e-02, -8.90384387e-02,
+           -5.84680802e-02,  3.89817183e-17,
+            6.68206631e-02,  1.16434881e-01,
+            1.26137788e-01,  8.50444803e-02,
+           -3.89817183e-17, -1.03943254e-01,
+           -1.89206682e-01, -2.16236208e-01,
+           -1.55914881e-01,  3.89817183e-17,
+            2.33872321e-01,  5.04551152e-01,
+            7.56826729e-01,  9.35489284e-01,
+            1.00000000e+00,  9.35489284e-01,
+            7.56826729e-01,  5.04551152e-01,
+            2.33872321e-01,  3.89817183e-17,
+           -1.55914881e-01, -2.16236208e-01,
+           -1.89206682e-01, -1.03943254e-01,
+           -3.89817183e-17,  8.50444803e-02,
+            1.26137788e-01,  1.16434881e-01,
+            6.68206631e-02,  3.89817183e-17,
+           -5.84680802e-02, -8.90384387e-02,
+           -8.40918587e-02, -4.92362781e-02,
+           -3.89817183e-17], dtype=array_api_strict.float64)
+    """
+
+    if xp is None:
+        xp = array_namespace(x)
+
+    if not xp.isdtype(x.dtype, "real floating"):
+        err_msg = "`x` must have a real floating data type."
+        raise ValueError(err_msg)
+
+    if (
+        is_numpy_namespace(xp)
+        or is_cupy_namespace(xp)
+        or is_jax_namespace(xp)
+        or is_torch_namespace(xp)
+        or is_dask_namespace(xp)
+    ):
+        return xp.sinc(x)
+
+    return _funcs.sinc(x, xp=xp)
+
+
+def partition(
+    a: Array,
+    kth: int,
+    /,
+    axis: int | None = -1,
+    *,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Return a partitioned copy of an array.
+
+    Creates a copy of the array and partially sorts it in such a way that the value
+    of the element in k-th position is in the position it would be in a sorted array.
+    In the output array, all elements smaller than the k-th element are located to
+    the left of this element and all equal or greater are located to its right.
+    The ordering of the elements in the two partitions on the either side of
+    the k-th element in the output array is undefined.
+
+    Parameters
+    ----------
+    a : Array
+        Input array.
+    kth : int
+        Element index to partition by.
+    axis : int, optional
+        Axis along which to partition. The default is ``-1`` (the last axis).
+        If ``None``, the flattened array is used.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    partitioned_array
+        Array of the same type and shape as `a`.
+
+    Notes
+    -----
+    If `xp` implements ``partition`` or an equivalent function
+    (e.g. ``topk`` for torch), complexity will likely be O(n).
+    If not, this function simply calls ``xp.sort`` and complexity is O(n log n).
+    """
+    # Validate inputs.
+    if xp is None:
+        xp = array_namespace(a)
+    if a.ndim < 1:
+        msg = "`a` must be at least 1-dimensional"
+        raise TypeError(msg)
+    if axis is None:
+        return partition(xp.reshape(a, (-1,)), kth, axis=0, xp=xp)
+    (size,) = eager_shape(a, axis)
+    if not (0 <= kth < size):
+        msg = f"kth(={kth}) out of bounds [0 {size})"
+        raise ValueError(msg)
+
+    # Delegate where possible.
+    if is_numpy_namespace(xp) or is_cupy_namespace(xp) or is_jax_namespace(xp):
+        return xp.partition(a, kth, axis=axis)
+
+    # Use top-k when possible:
+    if is_torch_namespace(xp):
+        if not (axis == -1 or axis == a.ndim - 1):
+            a = xp.transpose(a, axis, -1)
+
+        out = xp.empty_like(a)
+        ranks = xp.arange(a.shape[-1]).expand_as(a)
+
+        split_value, indices = xp.kthvalue(a, kth + 1, keepdim=True)
+        del indices  # indices won't be used => del ASAP to reduce peak memory usage
+
+        # fill the left-side of the partition
+        mask_src = a < split_value
+        n_left = mask_src.sum(dim=-1, keepdim=True)
+        mask_dest = ranks < n_left
+        out[mask_dest] = a[mask_src]
+
+        # fill the middle of the partition
+        mask_src = a == split_value
+        n_left += mask_src.sum(dim=-1, keepdim=True)
+        mask_dest ^= ranks < n_left
+        out[mask_dest] = a[mask_src]
+
+        # fill the right-side of the partition
+        mask_src = a > split_value
+        mask_dest = ranks >= n_left
+        out[mask_dest] = a[mask_src]
+
+        if not (axis == -1 or axis == a.ndim - 1):
+            out = xp.transpose(out, axis, -1)
+        return out
+
+    # Note: dask topk/argtopk sort the return values, so it's
+    # not much more efficient than sorting everything when
+    # kth is not small compared to x.size
+
+    return _funcs.partition(a, kth, axis=axis, xp=xp)
+
+
+def argpartition(
+    a: Array,
+    kth: int,
+    /,
+    axis: int | None = -1,
+    *,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Perform an indirect partition along the given axis.
+
+    It returns an array of indices of the same shape as `a` that
+    index data along the given axis in partitioned order.
+
+    Parameters
+    ----------
+    a : Array
+        Input array.
+    kth : int
+        Element index to partition by.
+    axis : int, optional
+        Axis along which to partition. The default is ``-1`` (the last axis).
+        If ``None``, the flattened array is used.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    index_array
+        Array of indices that partition `a` along the specified axis.
+
+    Notes
+    -----
+    If `xp` implements ``argpartition`` or an equivalent function
+    e.g. ``topk`` for torch), complexity will likely be O(n).
+    If not, this function simply calls ``xp.argsort`` and complexity is O(n log n).
+    """
+    # Validate inputs.
+    if xp is None:
+        xp = array_namespace(a)
+    if is_pydata_sparse_namespace(xp):
+        msg = "Not implemented for sparse backend: no argsort"
+        raise NotImplementedError(msg)
+    if a.ndim < 1:
+        msg = "`a` must be at least 1-dimensional"
+        raise TypeError(msg)
+    if axis is None:
+        return argpartition(xp.reshape(a, (-1,)), kth, axis=0, xp=xp)
+    (size,) = eager_shape(a, axis)
+    if not (0 <= kth < size):
+        msg = f"kth(={kth}) out of bounds [0 {size})"
+        raise ValueError(msg)
+
+    # Delegate where possible.
+    if is_numpy_namespace(xp) or is_cupy_namespace(xp) or is_jax_namespace(xp):
+        return xp.argpartition(a, kth, axis=axis)
+
+    # Use top-k when possible:
+    if is_torch_namespace(xp):
+        # see `partition` above for commented details of those steps:
+        if not (axis == -1 or axis == a.ndim - 1):
+            a = xp.transpose(a, axis, -1)
+
+        ranks = xp.arange(a.shape[-1]).expand_as(a)
+        out = xp.empty_like(ranks)
+
+        split_value, indices = xp.kthvalue(a, kth + 1, keepdim=True)
+        del indices  # indices won't be used => del ASAP to reduce peak memory usage
+
+        mask_src = a < split_value
+        n_left = mask_src.sum(dim=-1, keepdim=True)
+        mask_dest = ranks < n_left
+        out[mask_dest] = ranks[mask_src]
+
+        mask_src = a == split_value
+        n_left += mask_src.sum(dim=-1, keepdim=True)
+        mask_dest ^= ranks < n_left
+        out[mask_dest] = ranks[mask_src]
+
+        mask_src = a > split_value
+        mask_dest = ranks >= n_left
+        out[mask_dest] = ranks[mask_src]
+
+        if not (axis == -1 or axis == a.ndim - 1):
+            out = xp.transpose(out, axis, -1)
+        return out
+
+    # Note: dask topk/argtopk sort the return values, so it's
+    # not much more efficient than sorting everything when
+    # kth is not small compared to x.size
+
+    return _funcs.argpartition(a, kth, axis=axis, xp=xp)
+
+
+def isin(
+    a: Array,
+    b: Array,
+    /,
+    *,
+    assume_unique: bool = False,
+    invert: bool = False,
+    kind: str | None = None,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Determine whether each element in `a` is present in `b`.
+
+    Return a boolean array of the same shape as `a` that is True for elements
+    that are in `b` and False otherwise.
+
+    Parameters
+    ----------
+    a : array
+        Input elements.
+    b : array
+        The elements against which to test each element of `a`.
+    assume_unique : bool, optional
+        If True, the input arrays are both assumed to be unique which can speed
+        up the calculation. Default: False.
+    invert : bool, optional
+        If True, the values in the returned array are inverted. Default: False.
+    kind : str | None, optional
+        The algorithm or method to use. This will not affect the final result,
+        but will affect the speed and memory use.
+        For NumPy the options are {None, "sort", "table"}.
+        For Jax the mapped parameter is instead `method` and the options are
+        {"compare_all", "binary_search", "sort", and "auto" (default)}
+        For CuPy, Dask, Torch and the default case this parameter is not present and
+        thus ignored. Default: None.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `a` and `b`. Default: infer.
+
+    Returns
+    -------
+    array
+        An array having the same shape as that of `a` that is True for elements
+        that are in `b` and False otherwise.
+    """
+    if xp is None:
+        xp = array_namespace(a, b)
+
+    if is_numpy_namespace(xp):
+        return xp.isin(a, b, assume_unique=assume_unique, invert=invert, kind=kind)
+    if is_jax_namespace(xp):
+        if kind is None:
+            kind = "auto"
+        return xp.isin(a, b, assume_unique=assume_unique, invert=invert, method=kind)
+    if is_cupy_namespace(xp) or is_torch_namespace(xp) or is_dask_namespace(xp):
+        return xp.isin(a, b, assume_unique=assume_unique, invert=invert)
+
+    return _funcs.isin(a, b, assume_unique=assume_unique, invert=invert, xp=xp)
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/__init__.py
@@ -0,0 +1 @@
+"""Internals of array-api-extra."""
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_at.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_at.py
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_at.py
@@ -0,0 +1,463 @@
+"""Update operations for read-only arrays."""
+
+from __future__ import annotations
+
+import operator
+from collections.abc import Callable
+from enum import Enum
+from types import ModuleType
+from typing import TYPE_CHECKING, ClassVar, cast
+
+from ._utils import _compat
+from ._utils._compat import (
+    array_namespace,
+    is_dask_array,
+    is_jax_array,
+    is_torch_array,
+    is_writeable_array,
+)
+from ._utils._helpers import meta_namespace
+from ._utils._typing import Array, SetIndex
+
+if TYPE_CHECKING:  # pragma: no cover
+    # TODO import from typing (requires Python >=3.11)
+    from typing_extensions import Self
+
+
+class _AtOp(Enum):
+    """Operations for use in `xpx.at`."""
+
+    SET = "set"
+    ADD = "add"
+    SUBTRACT = "subtract"
+    MULTIPLY = "multiply"
+    DIVIDE = "divide"
+    POWER = "power"
+    MIN = "min"
+    MAX = "max"
+
+    # @override from Python 3.12
+    def __str__(self) -> str:  # pyright: ignore[reportImplicitOverride]
+        """
+        Return string representation (useful for pytest logs).
+
+        Returns
+        -------
+        str
+            The operation's name.
+        """
+        return self.value
+
+
+class Undef(Enum):
+    """Sentinel for undefined values."""
+
+    UNDEF = 0
+
+
+_undef = Undef.UNDEF
+
+
+class at:  # pylint: disable=invalid-name  # numpydoc ignore=PR02
+    """
+    Update operations for read-only arrays.
+
+    This implements ``jax.numpy.ndarray.at`` for all writeable
+    backends (those that support ``__setitem__``) and routes
+    to the ``.at[]`` method for JAX arrays.
+
+    Parameters
+    ----------
+    x : array
+        Input array.
+    idx : index, optional
+        Only `array API standard compliant indices
+        `_
+        are supported.
+
+        You may use two alternate syntaxes::
+
+          >>> import array_api_extra as xpx
+          >>> xpx.at(x, idx).set(value)  # or add(value), etc.
+          >>> xpx.at(x)[idx].set(value)
+
+    copy : bool, optional
+        None (default)
+            The array parameter *may* be modified in place if it is
+            possible and beneficial for performance.
+            You should not reuse it after calling this function.
+        True
+            Ensure that the inputs are not modified.
+        False
+            Ensure that the update operation writes back to the input.
+            Raise ``ValueError`` if a copy cannot be avoided.
+
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    Updated input array.
+
+    Warnings
+    --------
+    (a) When you omit the ``copy`` parameter, you should never reuse the parameter
+    array later on; ideally, you should reassign it immediately::
+
+        >>> import array_api_extra as xpx
+        >>> x = xpx.at(x, 0).set(2)
+
+    The above best practice pattern ensures that the behaviour won't change depending
+    on whether ``x`` is writeable or not, as the original ``x`` object is dereferenced
+    as soon as ``xpx.at`` returns; this way there is no risk to accidentally update it
+    twice.
+
+    On the reverse, the anti-pattern below must be avoided, as it will result in
+    different behaviour on read-only versus writeable arrays::
+
+        >>> x = xp.asarray([0, 0, 0])
+        >>> y = xpx.at(x, 0).set(2)
+        >>> z = xpx.at(x, 1).set(3)
+
+    In the above example, both calls to ``xpx.at`` update ``x`` in place *if possible*.
+    This causes the behaviour to diverge depending on whether ``x`` is writeable or not:
+
+    - If ``x`` is writeable, then after the snippet above you'll have
+      ``x == y == z == [2, 3, 0]``
+    - If ``x`` is read-only, then you'll end up with
+      ``x == [0, 0, 0]``, ``y == [2, 0, 0]`` and ``z == [0, 3, 0]``.
+
+    The correct pattern to use if you want diverging outputs from the same input is
+    to enforce copies::
+
+        >>> x = xp.asarray([0, 0, 0])
+        >>> y = xpx.at(x, 0).set(2, copy=True)  # Never updates x
+        >>> z = xpx.at(x, 1).set(3)  # May or may not update x in place
+        >>> del x  # avoid accidental reuse of x as we don't know its state anymore
+
+    (b) The array API standard does not support integer array indices.
+    The behaviour of update methods when the index is an array of integers is
+    undefined and will vary between backends; this is particularly true when the
+    index contains multiple occurrences of the same index, e.g.::
+
+        >>> import numpy as np
+        >>> import jax.numpy as jnp
+        >>> import array_api_extra as xpx
+        >>> xpx.at(np.asarray([123]), np.asarray([0, 0])).add(1)
+        array([124])
+        >>> xpx.at(jnp.asarray([123]), jnp.asarray([0, 0])).add(1)
+        Array([125], dtype=int32)
+
+    See Also
+    --------
+    jax.numpy.ndarray.at : Equivalent array method in JAX.
+
+    Notes
+    -----
+    `sparse `_, as well as read-only arrays from libraries
+    not explicitly covered by ``array-api-compat``, are not supported by update
+    methods.
+
+    Boolean masks are supported on Dask and jitted JAX arrays exclusively
+    when `idx` has the same shape as `x` and `y` is 0-dimensional.
+    Note that this support is not available in JAX's native
+    ``x.at[mask].set(y)``.
+
+    This pattern::
+
+        >>> mask = m(x)
+        >>> x[mask] = f(x[mask])
+
+    Can't be replaced by `at`, as it won't work on Dask and JAX inside jax.jit::
+
+        >>> mask = m(x)
+        >>> x = xpx.at(x, mask).set(f(x[mask])  # Crash on Dask and jax.jit
+
+    You should instead use::
+
+        >>> x = xp.where(m(x), f(x), x)
+
+    Examples
+    --------
+    Given either of these equivalent expressions::
+
+      >>> import array_api_extra as xpx
+      >>> x = xpx.at(x)[1].add(2)
+      >>> x = xpx.at(x, 1).add(2)
+
+    If x is a JAX array, they are the same as::
+
+      >>> x = x.at[1].add(2)
+
+    If x is a read-only NumPy array, they are the same as::
+
+      >>> x = x.copy()
+      >>> x[1] += 2
+
+    For other known backends, they are the same as::
+
+      >>> x[1] += 2
+    """
+
+    _x: Array
+    _idx: SetIndex | Undef
+    __slots__: ClassVar[tuple[str, ...]] = ("_idx", "_x")
+
+    def __init__(
+        self, x: Array, idx: SetIndex | Undef = _undef, /
+    ) -> None:  # numpydoc ignore=GL08
+        self._x = x
+        self._idx = idx
+
+    def __getitem__(self, idx: SetIndex, /) -> Self:  # numpydoc ignore=PR01,RT01
+        """
+        Allow for the alternate syntax ``at(x)[start:stop:step]``.
+
+        It looks prettier than ``at(x, slice(start, stop, step))``
+        and feels more intuitive coming from the JAX documentation.
+        """
+        if self._idx is not _undef:
+            msg = "Index has already been set"
+            raise ValueError(msg)
+        return type(self)(self._x, idx)
+
+    def _op(
+        self,
+        at_op: _AtOp,
+        in_place_op: Callable[[Array, Array | complex], Array] | None,
+        out_of_place_op: Callable[[Array, Array], Array] | None,
+        y: Array | complex,
+        /,
+        copy: bool | None,
+        xp: ModuleType | None,
+    ) -> Array:
+        """
+        Implement all update operations.
+
+        Parameters
+        ----------
+        at_op : _AtOp
+            Method of JAX's Array.at[].
+        in_place_op : Callable[[Array, Array | complex], Array] | None
+            In-place operation to apply on mutable backends::
+
+                x[idx] = in_place_op(x[idx], y)
+
+            If None::
+
+                x[idx] = y
+
+        out_of_place_op : Callable[[Array, Array], Array] | None
+            Out-of-place operation to apply when idx is a boolean mask and the backend
+            doesn't support in-place updates::
+
+                x = xp.where(idx, out_of_place_op(x, y), x)
+
+            If None::
+
+                x = xp.where(idx, y, x)
+
+        y : array or complex
+            Right-hand side of the operation.
+        copy : bool or None
+            Whether to copy the input array. See the class docstring for details.
+        xp : array_namespace, optional
+            The array namespace for the input array. Default: infer.
+
+        Returns
+        -------
+        Array
+            Updated `x`.
+        """
+        from ._funcs import apply_where  # pylint: disable=cyclic-import
+
+        x, idx = self._x, self._idx
+        xp = array_namespace(x, y) if xp is None else xp
+
+        if isinstance(idx, Undef):
+            msg = (
+                "Index has not been set.\n"
+                "Usage: either\n"
+                "    at(x, idx).set(value)\n"
+                "or\n"
+                "    at(x)[idx].set(value)\n"
+                "(same for all other methods)."
+            )
+            raise ValueError(msg)
+
+        if copy not in (True, False, None):
+            msg = f"copy must be True, False, or None; got {copy!r}"
+            raise ValueError(msg)
+
+        writeable = None if copy else is_writeable_array(x)
+
+        # JAX inside jax.jit doesn't support in-place updates with boolean
+        # masks; Dask exclusively supports __setitem__ but not iops.
+        # We can handle the common special case of 0-dimensional y
+        # with where(idx, y, x) instead.
+        if (
+            (is_dask_array(idx) or is_jax_array(idx))
+            and idx.dtype == xp.bool
+            and idx.shape == x.shape
+        ):
+            y_xp = xp.asarray(y, dtype=x.dtype, device=_compat.device(x))
+            if y_xp.ndim == 0:
+                if out_of_place_op:  # add(), subtract(), ...
+                    # suppress inf warnings on Dask
+                    out = apply_where(
+                        idx, (x, y_xp), out_of_place_op, fill_value=x, xp=xp
+                    )
+                    # Undo int->float promotion on JAX after _AtOp.DIVIDE
+                    out = xp.astype(out, x.dtype, copy=False)
+                else:  # set()
+                    out = xp.where(idx, y_xp, x)
+
+                if copy is False:
+                    x[()] = out
+                    return x
+                return out
+
+            # else: this will work on eager JAX and crash on jax.jit and Dask
+
+        if copy or (copy is None and not writeable):
+            if is_jax_array(x):
+                # Use JAX's at[]
+                func = cast(
+                    Callable[[Array | complex], Array],
+                    getattr(x.at[idx], at_op.value),  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue,reportUnknownArgumentType]
+                )
+                out = func(y)
+                # Undo int->float promotion on JAX after _AtOp.DIVIDE
+                return xp.astype(out, x.dtype, copy=False)
+
+            # Emulate at[] behaviour for non-JAX arrays
+            # with a copy followed by an update
+
+            x = xp.asarray(x, copy=True)
+            # A copy of a read-only numpy array is writeable
+            # Note: this assumes that a copy of a writeable array is writeable
+            assert not writeable
+            writeable = None
+
+        if writeable is None:
+            writeable = is_writeable_array(x)
+        if not writeable:
+            # sparse crashes here
+            msg = f"Can't update read-only array {x}"
+            raise ValueError(msg)
+
+        # Work around bug in PyTorch where __setitem__ doesn't
+        # always support mismatched dtypes
+        # https://github.com/pytorch/pytorch/issues/150017
+        if is_torch_array(y):
+            y = xp.astype(y, x.dtype, copy=False)
+
+        # Backends without boolean indexing (other than JAX) crash here
+        if in_place_op:  # add(), subtract(), ...
+            x[idx] = in_place_op(x[idx], y)
+        else:  # set()
+            x[idx] = y
+        return x
+
+    def set(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] = y`` and return the update array."""
+        return self._op(_AtOp.SET, None, None, y, copy=copy, xp=xp)
+
+    def add(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] += y`` and return the updated array."""
+
+        # Note for this and all other methods based on _iop:
+        # operator.iadd and operator.add subtly differ in behaviour, as
+        # only iadd will trigger exceptions when y has an incompatible dtype.
+        return self._op(_AtOp.ADD, operator.iadd, operator.add, y, copy=copy, xp=xp)
+
+    def subtract(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] -= y`` and return the updated array."""
+        return self._op(
+            _AtOp.SUBTRACT, operator.isub, operator.sub, y, copy=copy, xp=xp
+        )
+
+    def multiply(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] *= y`` and return the updated array."""
+        return self._op(
+            _AtOp.MULTIPLY, operator.imul, operator.mul, y, copy=copy, xp=xp
+        )
+
+    def divide(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] /= y`` and return the updated array."""
+        return self._op(
+            _AtOp.DIVIDE, operator.itruediv, operator.truediv, y, copy=copy, xp=xp
+        )
+
+    def power(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] **= y`` and return the updated array."""
+        return self._op(_AtOp.POWER, operator.ipow, operator.pow, y, copy=copy, xp=xp)
+
+    def min(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] = minimum(x[idx], y)`` and return the updated array."""
+        # On Dask, this function runs on the chunks, so we need to determine the
+        # namespace that Dask is wrapping.
+        # Note that da.minimum _incidentally_ works on NumPy, CuPy, and sparse
+        # thanks to all these meta-namespaces implementing the __array_ufunc__
+        # interface, but there's no guarantee that it will work for other
+        # wrapped libraries in the future.
+        xp = array_namespace(self._x) if xp is None else xp
+        mxp = meta_namespace(self._x, xp=xp)
+        y = xp.asarray(y)
+        return self._op(_AtOp.MIN, mxp.minimum, mxp.minimum, y, copy=copy, xp=xp)
+
+    def max(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] = maximum(x[idx], y)`` and return the updated array."""
+        # See note on min()
+        xp = array_namespace(self._x) if xp is None else xp
+        mxp = meta_namespace(self._x, xp=xp)
+        y = xp.asarray(y)
+        return self._op(_AtOp.MAX, mxp.maximum, mxp.maximum, y, copy=copy, xp=xp)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_backends.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_backends.py
new file mode 100644
index 0000000000000000000000000000000000000000..936f5dd0a88618099d66e00de7a49d97b65d159e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_backends.py
@@ -0,0 +1,72 @@
+"""Backends against which array-api-extra runs its tests."""
+
+from __future__ import annotations
+
+from enum import Enum
+from typing import Any
+
+import numpy as np
+import pytest
+
+__all__ = ["NUMPY_VERSION", "Backend"]
+
+NUMPY_VERSION = tuple(int(v) for v in np.__version__.split(".")[:3])  # pyright: ignore[reportUnknownArgumentType]
+
+
+class Backend(Enum):  # numpydoc ignore=PR02
+    """
+    All array library backends explicitly tested by array-api-extra.
+
+    Parameters
+    ----------
+    value : str
+        Tag of the backend's module, in the format ``[:]``.
+    """
+
+    # Use : to prevent Enum from deduplicating items with the same value
+    ARRAY_API_STRICT = "array_api_strict"
+    ARRAY_API_STRICTEST = "array_api_strict:strictest"
+    NUMPY = "numpy"
+    NUMPY_READONLY = "numpy:readonly"
+    CUPY = "cupy"
+    TORCH = "torch"
+    TORCH_GPU = "torch:gpu"
+    DASK = "dask.array"
+    SPARSE = "sparse"
+    JAX = "jax.numpy"
+    JAX_GPU = "jax.numpy:gpu"
+
+    @property
+    def modname(self) -> str:  # numpydoc ignore=RT01
+        """Module name to be imported."""
+        return self.value.split(":")[0]
+
+    def like(self, *others: Backend) -> bool:  # numpydoc ignore=PR01,RT01
+        """Check if this backend uses the same module as others."""
+        return any(self.modname == other.modname for other in others)
+
+    def pytest_param(self) -> Any:
+        """
+        Backend as a pytest parameter
+
+        Returns
+        -------
+        pytest.mark.ParameterSet
+        """
+        id_ = (
+            self.name.lower().replace("_gpu", ":gpu").replace("_readonly", ":readonly")
+        )
+
+        marks = []
+        if self.like(Backend.ARRAY_API_STRICT):
+            marks.append(
+                pytest.mark.skipif(
+                    NUMPY_VERSION < (1, 26),
+                    reason="array_api_strict is untested on NumPy <1.26",
+                )
+            )
+        if self.like(Backend.DASK, Backend.JAX):
+            # Monkey-patched by lazy_xp_function
+            marks.append(pytest.mark.thread_unsafe)
+
+        return pytest.param(self, id=id_, marks=marks)  # pyright: ignore[reportUnknownArgumentType]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_funcs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_funcs.py
new file mode 100644
index 0000000000000000000000000000000000000000..6e50ce95c80c83eb61f3d3b91d92e05f06186e9c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_funcs.py
@@ -0,0 +1,744 @@
+"""Array-agnostic implementations for the public API."""
+
+import math
+import warnings
+from collections.abc import Callable, Sequence
+from types import ModuleType, NoneType
+from typing import Literal, cast, overload
+
+from ._at import at
+from ._utils import _compat, _helpers
+from ._utils._compat import array_namespace, is_dask_namespace, is_jax_array
+from ._utils._helpers import (
+    asarrays,
+    capabilities,
+    eager_shape,
+    meta_namespace,
+    ndindex,
+)
+from ._utils._typing import Array, Device, DType
+
+__all__ = [
+    "apply_where",
+    "atleast_nd",
+    "broadcast_shapes",
+    "cov",
+    "create_diagonal",
+    "expand_dims",
+    "kron",
+    "nunique",
+    "pad",
+    "setdiff1d",
+    "sinc",
+]
+
+
+@overload
+def apply_where(  # numpydoc ignore=GL08
+    cond: Array,
+    args: Array | tuple[Array, ...],
+    f1: Callable[..., Array],
+    f2: Callable[..., Array],
+    /,
+    *,
+    xp: ModuleType | None = None,
+) -> Array: ...
+
+
+@overload
+def apply_where(  # numpydoc ignore=GL08
+    cond: Array,
+    args: Array | tuple[Array, ...],
+    f1: Callable[..., Array],
+    /,
+    *,
+    fill_value: Array | complex,
+    xp: ModuleType | None = None,
+) -> Array: ...
+
+
+def apply_where(  # numpydoc ignore=PR01,PR02
+    cond: Array,
+    args: Array | tuple[Array, ...],
+    f1: Callable[..., Array],
+    f2: Callable[..., Array] | None = None,
+    /,
+    *,
+    fill_value: Array | complex | None = None,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Run one of two elementwise functions depending on a condition.
+
+    Equivalent to ``f1(*args) if cond else fill_value`` performed elementwise
+    when `fill_value` is defined, otherwise to ``f1(*args) if cond else f2(*args)``.
+
+    Parameters
+    ----------
+    cond : array
+        The condition, expressed as a boolean array.
+    args : Array or tuple of Arrays
+        Argument(s) to `f1` (and `f2`). Must be broadcastable with `cond`.
+    f1 : callable
+        Elementwise function of `args`, returning a single array.
+        Where `cond` is True, output will be ``f1(arg0[cond], arg1[cond], ...)``.
+    f2 : callable, optional
+        Elementwise function of `args`, returning a single array.
+        Where `cond` is False, output will be ``f2(arg0[cond], arg1[cond], ...)``.
+        Mutually exclusive with `fill_value`.
+    fill_value : Array or scalar, optional
+        If provided, value with which to fill output array where `cond` is False.
+        It does not need to be scalar; it needs however to be broadcastable with
+        `cond` and `args`.
+        Mutually exclusive with `f2`. You must provide one or the other.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `cond` and `args`. Default: infer.
+
+    Returns
+    -------
+    Array
+        An array with elements from the output of `f1` where `cond` is True and either
+        the output of `f2` or `fill_value` where `cond` is False. The returned array has
+        data type determined by type promotion rules between the output of `f1` and
+        either `fill_value` or the output of `f2`.
+
+    Notes
+    -----
+    ``xp.where(cond, f1(*args), f2(*args))`` requires explicitly evaluating `f1` even
+    when `cond` is False, and `f2` when cond is True. This function evaluates each
+    function only for their matching condition, if the backend allows for it.
+
+    On Dask, `f1` and `f2` are applied to the individual chunks and should use functions
+    from the namespace of the chunks.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> a = xp.asarray([5, 4, 3])
+    >>> b = xp.asarray([0, 2, 2])
+    >>> def f(a, b):
+    ...     return a // b
+    >>> xpx.apply_where(b != 0, (a, b), f, fill_value=xp.nan)
+    array([ nan,  2., 1.])
+    """
+    # Parse and normalize arguments
+    if (f2 is None) == (fill_value is None):
+        msg = "Exactly one of `fill_value` or `f2` must be given."
+        raise TypeError(msg)
+    args_ = list(args) if isinstance(args, tuple) else [args]
+    del args
+
+    xp = array_namespace(cond, fill_value, *args_) if xp is None else xp
+
+    if isinstance(fill_value, int | float | complex | NoneType):
+        cond, *args_ = xp.broadcast_arrays(cond, *args_)
+    else:
+        cond, fill_value, *args_ = xp.broadcast_arrays(cond, fill_value, *args_)
+
+    if is_dask_namespace(xp):
+        meta_xp = meta_namespace(cond, fill_value, *args_, xp=xp)
+        # map_blocks doesn't descend into tuples of Arrays
+        return xp.map_blocks(_apply_where, cond, f1, f2, fill_value, *args_, xp=meta_xp)
+    return _apply_where(cond, f1, f2, fill_value, *args_, xp=xp)
+
+
+def _apply_where(  # numpydoc ignore=PR01,RT01
+    cond: Array,
+    f1: Callable[..., Array],
+    f2: Callable[..., Array] | None,
+    fill_value: Array | int | float | complex | bool | None,
+    *args: Array,
+    xp: ModuleType,
+) -> Array:
+    """Helper of `apply_where`. On Dask, this runs on a single chunk."""
+
+    if not capabilities(xp, device=_compat.device(cond))["boolean indexing"]:
+        # jax.jit does not support assignment by boolean mask
+        return xp.where(cond, f1(*args), f2(*args) if f2 is not None else fill_value)
+
+    temp1 = f1(*(arr[cond] for arr in args))
+
+    if f2 is None:
+        dtype = xp.result_type(temp1, fill_value)
+        if isinstance(fill_value, int | float | complex):
+            out = xp.full_like(cond, dtype=dtype, fill_value=fill_value)
+        else:
+            out = xp.astype(fill_value, dtype, copy=True)
+    else:
+        ncond = ~cond
+        temp2 = f2(*(arr[ncond] for arr in args))
+        dtype = xp.result_type(temp1, temp2)
+        out = xp.empty_like(cond, dtype=dtype)
+        out = at(out, ncond).set(temp2)
+
+    return at(out, cond).set(temp1)
+
+
+def atleast_nd(x: Array, /, *, ndim: int, xp: ModuleType) -> Array:
+    # numpydoc ignore=PR01,RT01
+    """See docstring in array_api_extra._delegation."""
+
+    if x.ndim < ndim:
+        x = xp.expand_dims(x, axis=0)
+        x = atleast_nd(x, ndim=ndim, xp=xp)
+    return x
+
+
+# `float` in signature to accept `math.nan` for Dask.
+# `int`s are still accepted as `float` is a superclass of `int` in typing
+def broadcast_shapes(*shapes: tuple[float | None, ...]) -> tuple[int | None, ...]:
+    """
+    Compute the shape of the broadcasted arrays.
+
+    Duplicates :func:`numpy.broadcast_shapes`, with additional support for
+    None and NaN sizes.
+
+    This is equivalent to ``xp.broadcast_arrays(arr1, arr2, ...)[0].shape``
+    without needing to worry about the backend potentially deep copying
+    the arrays.
+
+    Parameters
+    ----------
+    *shapes : tuple[int | None, ...]
+        Shapes of the arrays to broadcast.
+
+    Returns
+    -------
+    tuple[int | None, ...]
+        The shape of the broadcasted arrays.
+
+    See Also
+    --------
+    numpy.broadcast_shapes : Equivalent NumPy function.
+    array_api.broadcast_arrays : Function to broadcast actual arrays.
+
+    Notes
+    -----
+    This function accepts the Array API's ``None`` for unknown sizes,
+    as well as Dask's non-standard ``math.nan``.
+    Regardless of input, the output always contains ``None`` for unknown sizes.
+
+    Examples
+    --------
+    >>> import array_api_extra as xpx
+    >>> xpx.broadcast_shapes((2, 3), (2, 1))
+    (2, 3)
+    >>> xpx.broadcast_shapes((4, 2, 3), (2, 1), (1, 3))
+    (4, 2, 3)
+    """
+    if not shapes:
+        return ()  # Match NumPy output
+
+    ndim = max(len(shape) for shape in shapes)
+    out: list[int | None] = []
+    for axis in range(-ndim, 0):
+        sizes = {shape[axis] for shape in shapes if axis >= -len(shape)}
+        # Dask uses NaN for unknown shape, which predates the Array API spec for None
+        none_size = None in sizes or math.nan in sizes  # noqa: PLW0177
+        sizes -= {1, None, math.nan}
+        if len(sizes) > 1:
+            msg = (
+                "shape mismatch: objects cannot be broadcast to a single shape: "
+                f"{shapes}."
+            )
+            raise ValueError(msg)
+        out.append(None if none_size else cast(int, sizes.pop()) if sizes else 1)
+
+    return tuple(out)
+
+
+def cov(m: Array, /, *, xp: ModuleType) -> Array:  # numpydoc ignore=PR01,RT01
+    """See docstring in array_api_extra._delegation."""
+    m = xp.asarray(m, copy=True)
+    dtype = (
+        xp.float64 if xp.isdtype(m.dtype, "integral") else xp.result_type(m, xp.float64)
+    )
+
+    m = atleast_nd(m, ndim=2, xp=xp)
+    m = xp.astype(m, dtype)
+
+    avg = _helpers.mean(m, axis=-1, keepdims=True, xp=xp)
+
+    m_shape = eager_shape(m)
+    fact = m_shape[-1] - 1
+
+    if fact <= 0:
+        warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning, stacklevel=2)
+        fact = 0
+
+    m -= avg
+    m_transpose = xp.matrix_transpose(m)
+    if xp.isdtype(m_transpose.dtype, "complex floating"):
+        m_transpose = xp.conj(m_transpose)
+    c = xp.matmul(m, m_transpose)
+    c /= fact
+    axes = tuple(axis for axis, length in enumerate(c.shape) if length == 1)
+    return xp.squeeze(c, axis=axes)
+
+
+def one_hot(
+    x: Array,
+    /,
+    num_classes: int,
+    *,
+    xp: ModuleType,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """See docstring in `array_api_extra._delegation.py`."""
+    # TODO: Benchmark whether this is faster on the NumPy backend:
+    # if is_numpy_array(x):
+    #     out = xp.zeros((x.size, num_classes), dtype=dtype)
+    #     out[xp.arange(x.size), xp.reshape(x, (-1,))] = 1
+    #     return xp.reshape(out, (*x.shape, num_classes))
+    range_num_classes = xp.arange(num_classes, dtype=x.dtype, device=_compat.device(x))
+    return x[..., xp.newaxis] == range_num_classes
+
+
+def create_diagonal(
+    x: Array, /, *, offset: int = 0, xp: ModuleType
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """See docstring in array_api_extra._delegation."""
+    x_shape = eager_shape(x)
+    batch_dims = x_shape[:-1]
+    n = x_shape[-1] + abs(offset)
+    diag = xp.zeros((*batch_dims, n**2), dtype=x.dtype, device=_compat.device(x))
+
+    target_slice = slice(
+        offset if offset >= 0 else abs(offset) * n,
+        min(n * (n - offset), diag.shape[-1]),
+        n + 1,
+    )
+    for index in ndindex(*batch_dims):
+        diag = at(diag)[(*index, target_slice)].set(x[(*index, slice(None))])
+    return xp.reshape(diag, (*batch_dims, n, n))
+
+
+def default_dtype(
+    xp: ModuleType,
+    kind: Literal[
+        "real floating", "complex floating", "integral", "indexing"
+    ] = "real floating",
+    *,
+    device: Device | None = None,
+) -> DType:
+    """
+    Return the default dtype for the given namespace and device.
+
+    This is a convenience shorthand for
+    ``xp.__array_namespace_info__().default_dtypes(device=device)[kind]``.
+
+    Parameters
+    ----------
+    xp : array_namespace
+        The standard-compatible namespace for which to get the default dtype.
+    kind : {'real floating', 'complex floating', 'integral', 'indexing'}, optional
+        The kind of dtype to return. Default is 'real floating'.
+    device : Device, optional
+        The device for which to get the default dtype. Default: current device.
+
+    Returns
+    -------
+    dtype
+        The default dtype for the given namespace, kind, and device.
+    """
+    dtypes = xp.__array_namespace_info__().default_dtypes(device=device)
+    try:
+        return dtypes[kind]
+    except KeyError as e:
+        domain = ("real floating", "complex floating", "integral", "indexing")
+        assert set(dtypes) == set(domain), f"Non-compliant namespace: {dtypes}"
+        msg = f"Unknown kind '{kind}'. Expected one of {domain}."
+        raise ValueError(msg) from e
+
+
+def expand_dims(a: Array, /, *, axis: tuple[int, ...] = (0,), xp: ModuleType) -> Array:
+    # numpydoc ignore=PR01,RT01
+    """See docstring in array_api_extra._delegation."""
+    for i in sorted(axis):
+        a = xp.expand_dims(a, axis=i)
+    return a
+
+
+def isclose(
+    a: Array | complex,
+    b: Array | complex,
+    *,
+    rtol: float = 1e-05,
+    atol: float = 1e-08,
+    equal_nan: bool = False,
+    xp: ModuleType,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """See docstring in array_api_extra._delegation."""
+    a, b = asarrays(a, b, xp=xp)
+
+    a_inexact = xp.isdtype(a.dtype, ("real floating", "complex floating"))
+    b_inexact = xp.isdtype(b.dtype, ("real floating", "complex floating"))
+    if a_inexact or b_inexact:
+        # prevent warnings on NumPy and Dask on inf - inf
+        mxp = meta_namespace(a, b, xp=xp)
+        out = apply_where(
+            xp.isinf(a) | xp.isinf(b),
+            (a, b),
+            lambda a, b: mxp.isinf(a) & mxp.isinf(b) & (mxp.sign(a) == mxp.sign(b)),  # pyright: ignore[reportUnknownArgumentType]
+            # Note: inf <= inf is True!
+            lambda a, b: mxp.abs(a - b) <= (atol + rtol * mxp.abs(b)),  # pyright: ignore[reportUnknownArgumentType]
+            xp=xp,
+        )
+        if equal_nan:
+            out = xp.where(xp.isnan(a) & xp.isnan(b), True, out)
+        return out
+
+    if xp.isdtype(a.dtype, "bool") or xp.isdtype(b.dtype, "bool"):
+        if atol >= 1 or rtol >= 1:
+            return xp.ones_like(a == b)
+        return a == b
+
+    # integer types
+    atol = int(atol)
+    if rtol == 0:
+        return xp.abs(a - b) <= atol
+
+    # Don't rely on OverflowError, as it is not guaranteed by the Array API.
+    nrtol = int(1.0 / rtol)
+    if nrtol > xp.iinfo(b.dtype).max:
+        # rtol * max_int < 1, so it's inconsequential
+        return xp.abs(a - b) <= atol
+    return xp.abs(a - b) <= (atol + xp.abs(b) // nrtol)
+
+
+def kron(
+    a: Array | complex,
+    b: Array | complex,
+    /,
+    *,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Kronecker product of two arrays.
+
+    Computes the Kronecker product, a composite array made of blocks of the
+    second array scaled by the first.
+
+    Equivalent to ``numpy.kron`` for NumPy arrays.
+
+    Parameters
+    ----------
+    a, b : Array | int | float | complex
+        Input arrays or scalars. At least one must be an array.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `a` and `b`. Default: infer.
+
+    Returns
+    -------
+    array
+        The Kronecker product of `a` and `b`.
+
+    Notes
+    -----
+    The function assumes that the number of dimensions of `a` and `b`
+    are the same, if necessary prepending the smallest with ones.
+    If ``a.shape = (r0,r1,..,rN)`` and ``b.shape = (s0,s1,...,sN)``,
+    the Kronecker product has shape ``(r0*s0, r1*s1, ..., rN*SN)``.
+    The elements are products of elements from `a` and `b`, organized
+    explicitly by::
+
+        kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]
+
+    where::
+
+        kt = it * st + jt,  t = 0,...,N
+
+    In the common 2-D case (N=1), the block structure can be visualized::
+
+        [[ a[0,0]*b,   a[0,1]*b,  ... , a[0,-1]*b  ],
+         [  ...                              ...   ],
+         [ a[-1,0]*b,  a[-1,1]*b, ... , a[-1,-1]*b ]]
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> xpx.kron(xp.asarray([1, 10, 100]), xp.asarray([5, 6, 7]), xp=xp)
+    Array([  5,   6,   7,  50,  60,  70, 500,
+           600, 700], dtype=array_api_strict.int64)
+
+    >>> xpx.kron(xp.asarray([5, 6, 7]), xp.asarray([1, 10, 100]), xp=xp)
+    Array([  5,  50, 500,   6,  60, 600,   7,
+            70, 700], dtype=array_api_strict.int64)
+
+    >>> xpx.kron(xp.eye(2), xp.ones((2, 2)), xp=xp)
+    Array([[1., 1., 0., 0.],
+           [1., 1., 0., 0.],
+           [0., 0., 1., 1.],
+           [0., 0., 1., 1.]], dtype=array_api_strict.float64)
+
+    >>> a = xp.reshape(xp.arange(100), (2, 5, 2, 5))
+    >>> b = xp.reshape(xp.arange(24), (2, 3, 4))
+    >>> c = xpx.kron(a, b, xp=xp)
+    >>> c.shape
+    (2, 10, 6, 20)
+    >>> I = (1, 3, 0, 2)
+    >>> J = (0, 2, 1)
+    >>> J1 = (0,) + J             # extend to ndim=4
+    >>> S1 = (1,) + b.shape
+    >>> K = tuple(xp.asarray(I) * xp.asarray(S1) + xp.asarray(J1))
+    >>> c[K] == a[I]*b[J]
+    Array(True, dtype=array_api_strict.bool)
+    """
+    if xp is None:
+        xp = array_namespace(a, b)
+    a, b = asarrays(a, b, xp=xp)
+
+    singletons = (1,) * (b.ndim - a.ndim)
+    a = cast(Array, xp.broadcast_to(a, singletons + a.shape))
+
+    nd_b, nd_a = b.ndim, a.ndim
+    nd_max = max(nd_b, nd_a)
+    if nd_a == 0 or nd_b == 0:
+        return xp.multiply(a, b)
+
+    a_shape = eager_shape(a)
+    b_shape = eager_shape(b)
+
+    # Equalise the shapes by prepending smaller one with 1s
+    a_shape = (1,) * max(0, nd_b - nd_a) + a_shape
+    b_shape = (1,) * max(0, nd_a - nd_b) + b_shape
+
+    # Insert empty dimensions
+    a_arr = expand_dims(a, axis=tuple(range(nd_b - nd_a)), xp=xp)
+    b_arr = expand_dims(b, axis=tuple(range(nd_a - nd_b)), xp=xp)
+
+    # Compute the product
+    a_arr = expand_dims(a_arr, axis=tuple(range(1, nd_max * 2, 2)), xp=xp)
+    b_arr = expand_dims(b_arr, axis=tuple(range(0, nd_max * 2, 2)), xp=xp)
+    result = xp.multiply(a_arr, b_arr)
+
+    # Reshape back and return
+    res_shape = tuple(a_s * b_s for a_s, b_s in zip(a_shape, b_shape, strict=True))
+    return xp.reshape(result, res_shape)
+
+
+def nan_to_num(  # numpydoc ignore=PR01,RT01
+    x: Array,
+    /,
+    fill_value: int | float = 0.0,
+    *,
+    xp: ModuleType,
+) -> Array:
+    """See docstring in `array_api_extra._delegation.py`."""
+
+    def perform_replacements(  # numpydoc ignore=PR01,RT01
+        x: Array,
+        fill_value: int | float,
+        xp: ModuleType,
+    ) -> Array:
+        """Internal function to perform the replacements."""
+        x = xp.where(xp.isnan(x), fill_value, x)
+
+        # convert infinities to finite values
+        finfo = xp.finfo(x.dtype)
+        idx_posinf = xp.isinf(x) & ~xp.signbit(x)
+        idx_neginf = xp.isinf(x) & xp.signbit(x)
+        x = xp.where(idx_posinf, finfo.max, x)
+        return xp.where(idx_neginf, finfo.min, x)
+
+    if xp.isdtype(x.dtype, "complex floating"):
+        return perform_replacements(
+            xp.real(x),
+            fill_value,
+            xp,
+        ) + 1j * perform_replacements(
+            xp.imag(x),
+            fill_value,
+            xp,
+        )
+
+    if xp.isdtype(x.dtype, "numeric"):
+        return perform_replacements(x, fill_value, xp)
+
+    return x
+
+
+def nunique(x: Array, /, *, xp: ModuleType | None = None) -> Array:
+    """
+    Count the number of unique elements in an array.
+
+    Compatible with JAX and Dask, whose laziness would be otherwise
+    problematic.
+
+    Parameters
+    ----------
+    x : Array
+        Input array.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array: 0-dimensional integer array
+        The number of unique elements in `x`. It can be lazy.
+    """
+    if xp is None:
+        xp = array_namespace(x)
+
+    if is_jax_array(x):
+        # size= is JAX-specific
+        # https://github.com/data-apis/array-api/issues/883
+        _, counts = xp.unique_counts(x, size=_compat.size(x))
+        return (counts > 0).sum()
+
+    # There are 3 general use cases:
+    # 1. backend has unique_counts and it returns an array with known shape
+    # 2. backend has unique_counts and it returns a None-sized array;
+    #    e.g. Dask, ndonnx
+    # 3. backend does not have unique_counts; e.g. wrapped JAX
+    if capabilities(xp, device=_compat.device(x))["data-dependent shapes"]:
+        # xp has unique_counts; O(n) complexity
+        _, counts = xp.unique_counts(x)
+        n = _compat.size(counts)
+        if n is None:
+            return xp.sum(xp.ones_like(counts))
+        return xp.asarray(n, device=_compat.device(x))
+
+    # xp does not have unique_counts; O(n*logn) complexity
+    x = xp.reshape(x, (-1,))
+    x = xp.sort(x, stable=False)
+    mask = x != xp.roll(x, -1)
+    default_int = default_dtype(xp, "integral", device=_compat.device(x))
+    return xp.maximum(
+        # Special cases:
+        # - array is size 0
+        # - array has all elements equal to each other
+        xp.astype(xp.any(~mask), default_int),
+        xp.sum(xp.astype(mask, default_int)),
+    )
+
+
+def pad(
+    x: Array,
+    pad_width: int | tuple[int, int] | Sequence[tuple[int, int]],
+    *,
+    constant_values: complex = 0,
+    xp: ModuleType,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """See docstring in `array_api_extra._delegation.py`."""
+    # make pad_width a list of length-2 tuples of ints
+    if isinstance(pad_width, int):
+        pad_width_seq = [(pad_width, pad_width)] * x.ndim
+    elif (
+        isinstance(pad_width, tuple)
+        and len(pad_width) == 2
+        and all(isinstance(i, int) for i in pad_width)
+    ):
+        pad_width_seq = [cast(tuple[int, int], pad_width)] * x.ndim
+    else:
+        pad_width_seq = cast(list[tuple[int, int]], list(pad_width))
+
+    slices: list[slice] = []
+    newshape: list[int] = []
+    for ax, w_tpl in enumerate(pad_width_seq):
+        if len(w_tpl) != 2:
+            msg = f"expect a 2-tuple (before, after), got {w_tpl}."
+            raise ValueError(msg)
+
+        sh = eager_shape(x)[ax]
+
+        if w_tpl[0] == 0 and w_tpl[1] == 0:
+            sl = slice(None, None, None)
+        else:
+            stop: int | None
+            start, stop = w_tpl
+            stop = None if stop == 0 else -stop
+
+            sl = slice(start, stop, None)
+            sh += w_tpl[0] + w_tpl[1]
+
+        newshape.append(sh)
+        slices.append(sl)
+
+    padded = xp.full(
+        tuple(newshape),
+        fill_value=constant_values,
+        dtype=x.dtype,
+        device=_compat.device(x),
+    )
+    return at(padded, tuple(slices)).set(x)
+
+
+def setdiff1d(
+    x1: Array | complex,
+    x2: Array | complex,
+    /,
+    *,
+    assume_unique: bool = False,
+    xp: ModuleType,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """See docstring in `array_api_extra._delegation.py`."""
+
+    # https://github.com/microsoft/pyright/issues/10103
+    x1_, x2_ = asarrays(x1, x2, xp=xp)
+
+    if assume_unique:
+        x1_ = xp.reshape(x1_, (-1,))
+        x2_ = xp.reshape(x2_, (-1,))
+    else:
+        x1_ = xp.unique_values(x1_)
+        x2_ = xp.unique_values(x2_)
+
+    return x1_[_helpers.in1d(x1_, x2_, assume_unique=True, invert=True, xp=xp)]
+
+
+def sinc(x: Array, /, *, xp: ModuleType) -> Array:
+    # numpydoc ignore=PR01,RT01
+    """See docstring in `array_api_extra._delegation.py`."""
+
+    # no scalars in `where` - array-api#807
+    y = xp.pi * xp.where(
+        xp.astype(x, xp.bool),
+        x,
+        xp.asarray(xp.finfo(x.dtype).eps, dtype=x.dtype, device=_compat.device(x)),
+    )
+    return xp.sin(y) / y
+
+
+def partition(  # numpydoc ignore=PR01,RT01
+    x: Array,
+    kth: int,  # noqa: ARG001
+    /,
+    axis: int = -1,
+    *,
+    xp: ModuleType,
+) -> Array:
+    """See docstring in `array_api_extra._delegation.py`."""
+    return xp.sort(x, axis=axis, stable=False)
+
+
+def argpartition(  # numpydoc ignore=PR01,RT01
+    x: Array,
+    kth: int,  # noqa: ARG001
+    /,
+    axis: int = -1,
+    *,
+    xp: ModuleType,
+) -> Array:
+    """See docstring in `array_api_extra._delegation.py`."""
+    return xp.argsort(x, axis=axis, stable=False)
+
+
+def isin(  # numpydoc ignore=PR01,RT01
+    a: Array,
+    b: Array,
+    /,
+    *,
+    assume_unique: bool = False,
+    invert: bool = False,
+    xp: ModuleType,
+) -> Array:
+    """See docstring in `array_api_extra._delegation.py`."""
+    original_a_shape = a.shape
+    a = xp.reshape(a, (-1,))
+    b = xp.reshape(b, (-1,))
+    return xp.reshape(
+        _helpers.in1d(a, b, assume_unique=assume_unique, invert=invert, xp=xp),
+        original_a_shape,
+    )
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_lazy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_lazy.py
new file mode 100644
index 0000000000000000000000000000000000000000..d509500132a4b8886f5ccca93d7d6bd2aa25b4dc
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_lazy.py
@@ -0,0 +1,357 @@
+"""Public API Functions."""
+
+from __future__ import annotations
+
+import math
+from collections.abc import Callable, Sequence
+from functools import partial, wraps
+from types import ModuleType
+from typing import TYPE_CHECKING, Any, ParamSpec, TypeAlias, cast, overload
+
+from ._funcs import broadcast_shapes
+from ._utils import _compat
+from ._utils._compat import (
+    array_namespace,
+    is_dask_namespace,
+    is_jax_namespace,
+)
+from ._utils._helpers import is_python_scalar
+from ._utils._typing import Array, DType
+
+if TYPE_CHECKING:  # pragma: no cover
+    import numpy as np
+    from numpy.typing import ArrayLike
+
+    NumPyObject: TypeAlias = np.ndarray[Any, Any] | np.generic
+else:
+    # Sphinx hack
+    NumPyObject = Any
+
+P = ParamSpec("P")
+
+
+@overload
+def lazy_apply(  # type: ignore[valid-type]
+    func: Callable[P, Array | ArrayLike],
+    *args: Array | complex | None,
+    shape: tuple[int | None, ...] | None = None,
+    dtype: DType | None = None,
+    as_numpy: bool = False,
+    xp: ModuleType | None = None,
+    **kwargs: P.kwargs,  # pyright: ignore[reportGeneralTypeIssues]
+) -> Array: ...  # numpydoc ignore=GL08
+
+
+@overload
+def lazy_apply(  # type: ignore[valid-type]
+    func: Callable[P, Sequence[Array | ArrayLike]],
+    *args: Array | complex | None,
+    shape: Sequence[tuple[int | None, ...]],
+    dtype: Sequence[DType] | None = None,
+    as_numpy: bool = False,
+    xp: ModuleType | None = None,
+    **kwargs: P.kwargs,  # pyright: ignore[reportGeneralTypeIssues]
+) -> tuple[Array, ...]: ...  # numpydoc ignore=GL08
+
+
+def lazy_apply(  # type: ignore[valid-type]  # numpydoc ignore=GL07,SA04
+    func: Callable[P, Array | ArrayLike | Sequence[Array | ArrayLike]],
+    *args: Array | complex | None,
+    shape: tuple[int | None, ...] | Sequence[tuple[int | None, ...]] | None = None,
+    dtype: DType | Sequence[DType] | None = None,
+    as_numpy: bool = False,
+    xp: ModuleType | None = None,
+    **kwargs: P.kwargs,  # pyright: ignore[reportGeneralTypeIssues]
+) -> Array | tuple[Array, ...]:
+    """
+    Lazily apply an eager function.
+
+    If the backend of the input arrays is lazy, e.g. Dask or jitted JAX, the execution
+    of the function is delayed until the graph is materialized; if it's eager, the
+    function is executed immediately.
+
+    Parameters
+    ----------
+    func : callable
+        The function to apply.
+
+        It must accept one or more array API compliant arrays as positional arguments.
+        If `as_numpy=True`, inputs are converted to NumPy before they are passed to
+        `func`.
+        It must return either a single array-like or a sequence of array-likes.
+
+        `func` must be a pure function, i.e. without side effects, as depending on the
+        backend it may be executed more than once or never.
+    *args : Array | int | float | complex | bool | None
+        One or more Array API compliant arrays, Python scalars, or None's.
+
+        If `as_numpy=True`, you need to be able to apply :func:`numpy.asarray` to
+        non-None args to convert them to NumPy; read notes below about specific
+        backends.
+    shape : tuple[int | None, ...] | Sequence[tuple[int | None, ...]], optional
+        Output shape or sequence of output shapes, one for each output of `func`.
+        Default: assume single output and broadcast shapes of the input arrays.
+    dtype : DType | Sequence[DType], optional
+        Output dtype or sequence of output dtypes, one for each output of `func`.
+        dtype(s) must belong to the same array namespace as the input arrays.
+        Default: infer the result type(s) from the input arrays.
+    as_numpy : bool, optional
+        If True, convert the input arrays to NumPy before passing them to `func`.
+        This is particularly useful to make NumPy-only functions, e.g. written in Cython
+       or Numba, work transparently with array API-compliant arrays.
+        Default: False.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `args`. Default: infer.
+    **kwargs : Any, optional
+        Additional keyword arguments to pass verbatim to `func`.
+        They cannot contain Array objects.
+
+    Returns
+    -------
+    Array | tuple[Array, ...]
+        The result(s) of `func` applied to the input arrays, wrapped in the same
+        array namespace as the inputs.
+        If shape is omitted or a single `tuple[int | None, ...]`, return a single array.
+        Otherwise, return a tuple of arrays.
+
+    Notes
+    -----
+    JAX
+        This allows applying eager functions to jitted JAX arrays, which are lazy.
+        The function won't be applied until the JAX array is materialized.
+        When running inside ``jax.jit``, `shape` must be fully known, i.e. it cannot
+        contain any `None` elements.
+
+        .. warning::
+
+            `func` must never raise inside ``jax.jit``, as the resulting behavior is
+            undefined.
+
+        Using this with `as_numpy=False` is particularly useful to apply non-jittable
+        JAX functions to arrays on GPU devices.
+        If ``as_numpy=True``, the :doc:`jax:transfer_guard` may prevent arrays on a GPU
+        device from being transferred back to CPU. This is treated as an implicit
+        transfer.
+
+    PyTorch, CuPy
+        If ``as_numpy=True``, these backends raise by default if you attempt to convert
+        arrays on a GPU device to NumPy.
+
+    Sparse
+        If ``as_numpy=True``, by default sparse prevents implicit densification through
+        :func:`numpy.asarray`. `This safety mechanism can be disabled
+        `_.
+
+    Dask
+        This allows applying eager functions to Dask arrays.
+        The Dask graph won't be computed until the user calls ``compute()`` or
+        ``persist()`` down the line.
+
+        The function name will be prominently visible on the user-facing Dask
+        dashboard and on Prometheus metrics, so it is recommended for it to be
+        meaningful.
+
+        `lazy_apply` doesn't know if `func` reduces along any axes; also, shape
+        changes are non-trivial in chunked Dask arrays. For these reasons, all inputs
+        will be rechunked into a single chunk.
+
+        .. warning::
+
+           The whole operation needs to fit in memory all at once on a single worker.
+
+        The outputs will also be returned as a single chunk and you should consider
+        rechunking them into smaller chunks afterwards.
+
+        If you want to distribute the calculation across multiple workers, you
+        should use :func:`dask.array.map_blocks`, :func:`dask.array.map_overlap`,
+        :func:`dask.array.blockwise`, or a native Dask wrapper instead of
+        `lazy_apply`.
+
+    Dask wrapping around other backends
+        If ``as_numpy=False``, `func` will receive in input eager arrays of the meta
+        namespace, as defined by the ``._meta`` attribute of the input Dask arrays.
+        The outputs of `func` will be wrapped by the meta namespace, and then wrapped
+        again by Dask.
+
+    Raises
+    ------
+    ValueError
+        When ``xp=jax.numpy``, the output `shape` is unknown (it contains ``None`` on
+        one or more axes) and this function was called inside ``jax.jit``.
+    RuntimeError
+        When ``xp=sparse`` and auto-densification is disabled.
+    Exception (backend-specific)
+        When the backend disallows implicit device to host transfers and the input
+        arrays are on a non-CPU device, e.g. on GPU.
+
+    See Also
+    --------
+    jax.transfer_guard
+    jax.pure_callback
+    dask.array.map_blocks
+    dask.array.map_overlap
+    dask.array.blockwise
+    """
+    args_not_none = [arg for arg in args if arg is not None]
+    array_args = [arg for arg in args_not_none if not is_python_scalar(arg)]
+    if not array_args:
+        msg = "Must have at least one argument array"
+        raise ValueError(msg)
+    if xp is None:
+        xp = array_namespace(*args)
+
+    # Normalize and validate shape and dtype
+    shapes: list[tuple[int | None, ...]]
+    dtypes: list[DType]
+    multi_output = False
+
+    if shape is None:
+        shapes = [broadcast_shapes(*(arg.shape for arg in array_args))]
+    elif all(isinstance(s, int | None) for s in shape):
+        # Do not test for shape to be a tuple
+        # https://github.com/data-apis/array-api/issues/891#issuecomment-2637430522
+        shapes = [cast(tuple[int | None, ...], shape)]
+    else:
+        shapes = list(shape)  # type: ignore[arg-type]  # pyright: ignore[reportAssignmentType]
+        multi_output = True
+
+    if dtype is None:
+        dtypes = [xp.result_type(*args_not_none)] * len(shapes)
+    elif multi_output:
+        if not isinstance(dtype, Sequence):
+            msg = "Got multiple shapes but only one dtype"
+            raise ValueError(msg)
+        dtypes = list(dtype)  # pyright: ignore[reportUnknownArgumentType]
+    else:
+        if isinstance(dtype, Sequence):
+            msg = "Got single shape but multiple dtypes"
+            raise ValueError(msg)
+
+        dtypes = [dtype]
+
+    if len(shapes) != len(dtypes):
+        msg = f"Got {len(shapes)} shapes and {len(dtypes)} dtypes"
+        raise ValueError(msg)
+    del shape
+    del dtype
+    # End of shape and dtype parsing
+
+    # Backend-specific branches
+    if is_dask_namespace(xp):
+        import dask
+
+        metas: list[Array] = [arg._meta for arg in array_args]  # pylint: disable=protected-access    # pyright: ignore[reportAttributeAccessIssue]
+        meta_xp = array_namespace(*metas)
+
+        wrapped = dask.delayed(  # type: ignore[attr-defined]  # pyright: ignore[reportPrivateImportUsage]
+            _lazy_apply_wrapper(func, as_numpy, multi_output, meta_xp),
+            pure=True,
+        )
+        # This finalizes each arg, which is the same as arg.rechunk(-1).
+        # Please read docstring above for why we're not using
+        # dask.array.map_blocks or dask.array.blockwise!
+        delayed_out = wrapped(*args, **kwargs)
+
+        out = tuple(
+            xp.from_delayed(
+                delayed_out[i],  # pyright: ignore[reportIndexIssue]
+                # Dask's unknown shapes diverge from the Array API specification
+                shape=tuple(math.nan if s is None else s for s in shape),
+                dtype=dtype,
+                meta=metas[0],
+            )
+            for i, (shape, dtype) in enumerate(zip(shapes, dtypes, strict=True))
+        )
+
+    elif is_jax_namespace(xp) and _is_jax_jit_enabled(xp):
+        # Delay calling func with jax.pure_callback, which will forward to func eager
+        # JAX arrays. Do not use jax.pure_callback when running outside of the JIT,
+        # as it does not support raising exceptions:
+        # https://github.com/jax-ml/jax/issues/26102
+        import jax
+
+        if any(None in shape for shape in shapes):
+            msg = "Output shape must be fully known when running inside jax.jit"
+            raise ValueError(msg)
+
+        # Shield kwargs from being coerced into JAX arrays.
+        # jax.pure_callback calls jax.jit under the hood, but without the chance of
+        # passing static_argnames / static_argnums.
+        wrapped = _lazy_apply_wrapper(
+            partial(func, **kwargs), as_numpy, multi_output, xp
+        )
+
+        # suppress unused-ignore to run mypy in -e lint as well as -e dev
+        out = cast(  # type: ignore[bad-cast,unused-ignore]
+            tuple[Array, ...],
+            jax.pure_callback(
+                wrapped,
+                tuple(
+                    jax.ShapeDtypeStruct(shape, dtype)  # pyright: ignore[reportUnknownArgumentType]
+                    for shape, dtype in zip(shapes, dtypes, strict=True)
+                ),
+                *args,
+            ),
+        )
+
+    else:
+        # Eager backends, including non-jitted JAX
+        wrapped = _lazy_apply_wrapper(func, as_numpy, multi_output, xp)
+        out = wrapped(*args, **kwargs)
+
+    return out if multi_output else out[0]
+
+
+def _is_jax_jit_enabled(xp: ModuleType) -> bool:  # numpydoc ignore=PR01,RT01
+    """Return True if this function is being called inside ``jax.jit``."""
+    import jax  # pylint: disable=import-outside-toplevel
+
+    x = xp.asarray(False)
+    try:
+        return bool(x)
+    except jax.errors.TracerBoolConversionError:
+        return True
+
+
+def _lazy_apply_wrapper(  # numpydoc ignore=PR01,RT01
+    func: Callable[..., Array | ArrayLike | Sequence[Array | ArrayLike]],
+    as_numpy: bool,
+    multi_output: bool,
+    xp: ModuleType,
+) -> Callable[..., tuple[Array, ...]]:
+    """
+    Helper of `lazy_apply`.
+
+    Given a function that accepts one or more arrays as positional arguments and returns
+    a single array-like or a sequence of array-likes, return a function that accepts the
+    same number of Array API arrays and always returns a tuple of Array API array.
+
+    Any keyword arguments are passed through verbatim to the wrapped function.
+    """
+
+    # On Dask, @wraps causes the graph key to contain the wrapped function's name
+    @wraps(func)
+    def wrapper(
+        *args: Array | complex | None, **kwargs: Any
+    ) -> tuple[Array, ...]:  # numpydoc ignore=GL08
+        args_list = []
+        device = None
+        for arg in args:
+            if arg is not None and not is_python_scalar(arg):
+                if device is None:
+                    device = _compat.device(arg)
+                if as_numpy:
+                    import numpy as np
+
+                    arg = cast(Array, np.asarray(arg))  # pyright: ignore[reportInvalidCast] # noqa: PLW2901
+            args_list.append(arg)
+        assert device is not None
+
+        out = func(*args_list, **kwargs)
+
+        if multi_output:
+            assert isinstance(out, Sequence)
+            return tuple(xp.asarray(o, device=device) for o in out)
+        return (xp.asarray(out, device=device),)
+
+    return wrapper
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_testing.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_testing.py
new file mode 100644
index 0000000000000000000000000000000000000000..30e2f1efb7b0e017673c871acddd2bb6a74522cf
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_testing.py
@@ -0,0 +1,304 @@
+"""
+Testing utilities.
+
+Note that this is private API; don't expect it to be stable.
+See also ..testing for public testing utilities.
+"""
+
+from __future__ import annotations
+
+import math
+from types import ModuleType
+from typing import Any, cast
+
+import numpy as np
+import pytest
+
+from ._utils._compat import (
+    array_namespace,
+    is_array_api_strict_namespace,
+    is_cupy_namespace,
+    is_dask_namespace,
+    is_jax_namespace,
+    is_numpy_namespace,
+    is_pydata_sparse_namespace,
+    is_torch_array,
+    is_torch_namespace,
+    to_device,
+)
+from ._utils._typing import Array, Device
+
+__all__ = ["as_numpy_array", "xp_assert_close", "xp_assert_equal", "xp_assert_less"]
+
+
+def _check_ns_shape_dtype(
+    actual: Array,
+    desired: Array,
+    check_dtype: bool,
+    check_shape: bool,
+    check_scalar: bool,
+) -> ModuleType:  # numpydoc ignore=RT03
+    """
+    Assert that namespace, shape and dtype of the two arrays match.
+
+    Parameters
+    ----------
+    actual : Array
+        The array produced by the tested function.
+    desired : Array
+        The expected array (typically hardcoded).
+    check_dtype, check_shape : bool, default: True
+        Whether to check agreement between actual and desired dtypes and shapes
+    check_scalar : bool, default: False
+        NumPy only: whether to check agreement between actual and desired types -
+        0d array vs scalar.
+
+    Returns
+    -------
+    Arrays namespace.
+    """
+    actual_xp = array_namespace(actual)  # Raises on scalars and lists
+    desired_xp = array_namespace(desired)
+
+    msg = f"namespaces do not match: {actual_xp} != f{desired_xp}"
+    assert actual_xp == desired_xp, msg
+
+    # Dask uses nan instead of None for unknown shapes
+    actual_shape = cast(tuple[float, ...], actual.shape)
+    desired_shape = cast(tuple[float, ...], desired.shape)
+    assert None not in actual_shape  # Requires explicit support
+    assert None not in desired_shape
+    if is_dask_namespace(desired_xp):
+        if any(math.isnan(i) for i in actual_shape):
+            actual_shape = actual.compute().shape  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+        if any(math.isnan(i) for i in desired_shape):
+            desired_shape = desired.compute().shape  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+
+    if check_shape:
+        msg = f"shapes do not match: {actual_shape} != f{desired_shape}"
+        assert actual_shape == desired_shape, msg
+    else:
+        # Ignore shape, but check flattened size. This is normally done by
+        # np.testing.assert_array_equal etc even when strict=False, but not for
+        # non-materializable arrays.
+        actual_size = math.prod(actual_shape)  # pyright: ignore[reportUnknownArgumentType]
+        desired_size = math.prod(desired_shape)  # pyright: ignore[reportUnknownArgumentType]
+        msg = f"sizes do not match: {actual_size} != f{desired_size}"
+        assert actual_size == desired_size, msg
+
+    if check_dtype:
+        msg = f"dtypes do not match: {actual.dtype} != {desired.dtype}"
+        assert actual.dtype == desired.dtype, msg
+
+    if is_numpy_namespace(actual_xp) and check_scalar:
+        # only NumPy distinguishes between scalars and arrays; we do if check_scalar.
+        _msg = (
+            "array-ness does not match:\n Actual: "
+            f"{type(actual)}\n Desired: {type(desired)}"
+        )
+        assert np.isscalar(actual) == np.isscalar(desired), _msg
+
+    return desired_xp
+
+
+def _is_materializable(x: Array) -> bool:
+    """
+    Return True if you can call `as_numpy_array(x)`; False otherwise.
+    """
+    # Important: here we assume that we're not tracing -
+    # e.g. we're not inside `jax.jit`` nor `cupy.cuda.Stream.begin_capture`.
+    return not is_torch_array(x) or x.device.type != "meta"  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+
+
+def as_numpy_array(array: Array, *, xp: ModuleType) -> np.typing.NDArray[Any]:
+    """
+    Convert array to NumPy, bypassing GPU-CPU transfer guards and densification guards.
+    """
+    if is_cupy_namespace(xp):
+        return xp.asnumpy(array)
+    if is_pydata_sparse_namespace(xp):
+        return array.todense()  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+
+    if is_torch_namespace(xp):
+        array = to_device(array, "cpu")
+    if is_array_api_strict_namespace(xp):
+        cpu: Device = xp.Device("CPU_DEVICE")
+        array = to_device(array, cpu)
+    if is_jax_namespace(xp):
+        import jax
+
+        # Note: only needed if the transfer guard is enabled
+        cpu = cast(Device, jax.devices("cpu")[0])
+        array = to_device(array, cpu)
+
+    return np.asarray(array)
+
+
+def xp_assert_equal(
+    actual: Array,
+    desired: Array,
+    *,
+    err_msg: str = "",
+    check_dtype: bool = True,
+    check_shape: bool = True,
+    check_scalar: bool = False,
+) -> None:
+    """
+    Array-API compatible version of `np.testing.assert_array_equal`.
+
+    Parameters
+    ----------
+    actual : Array
+        The array produced by the tested function.
+    desired : Array
+        The expected array (typically hardcoded).
+    err_msg : str, optional
+        Error message to display on failure.
+    check_dtype, check_shape : bool, default: True
+        Whether to check agreement between actual and desired dtypes and shapes
+    check_scalar : bool, default: False
+        NumPy only: whether to check agreement between actual and desired types -
+        0d array vs scalar.
+
+    See Also
+    --------
+    xp_assert_close : Similar function for inexact equality checks.
+    numpy.testing.assert_array_equal : Similar function for NumPy arrays.
+    """
+    xp = _check_ns_shape_dtype(actual, desired, check_dtype, check_shape, check_scalar)
+    if not _is_materializable(actual):
+        return
+    actual_np = as_numpy_array(actual, xp=xp)
+    desired_np = as_numpy_array(desired, xp=xp)
+    np.testing.assert_array_equal(actual_np, desired_np, err_msg=err_msg)
+
+
+def xp_assert_less(
+    x: Array,
+    y: Array,
+    *,
+    err_msg: str = "",
+    check_dtype: bool = True,
+    check_shape: bool = True,
+    check_scalar: bool = False,
+) -> None:
+    """
+    Array-API compatible version of `np.testing.assert_array_less`.
+
+    Parameters
+    ----------
+    x, y : Array
+        The arrays to compare according to ``x < y`` (elementwise).
+    err_msg : str, optional
+        Error message to display on failure.
+    check_dtype, check_shape : bool, default: True
+        Whether to check agreement between actual and desired dtypes and shapes
+    check_scalar : bool, default: False
+        NumPy only: whether to check agreement between actual and desired types -
+        0d array vs scalar.
+
+    See Also
+    --------
+    xp_assert_close : Similar function for inexact equality checks.
+    numpy.testing.assert_array_equal : Similar function for NumPy arrays.
+    """
+    xp = _check_ns_shape_dtype(x, y, check_dtype, check_shape, check_scalar)
+    if not _is_materializable(x):
+        return
+    x_np = as_numpy_array(x, xp=xp)
+    y_np = as_numpy_array(y, xp=xp)
+    np.testing.assert_array_less(x_np, y_np, err_msg=err_msg)
+
+
+def xp_assert_close(
+    actual: Array,
+    desired: Array,
+    *,
+    rtol: float | None = None,
+    atol: float = 0,
+    err_msg: str = "",
+    check_dtype: bool = True,
+    check_shape: bool = True,
+    check_scalar: bool = False,
+) -> None:
+    """
+    Array-API compatible version of `np.testing.assert_allclose`.
+
+    Parameters
+    ----------
+    actual : Array
+        The array produced by the tested function.
+    desired : Array
+        The expected array (typically hardcoded).
+    rtol : float, optional
+        Relative tolerance. Default: dtype-dependent.
+    atol : float, optional
+        Absolute tolerance. Default: 0.
+    err_msg : str, optional
+        Error message to display on failure.
+    check_dtype, check_shape : bool, default: True
+        Whether to check agreement between actual and desired dtypes and shapes
+    check_scalar : bool, default: False
+        NumPy only: whether to check agreement between actual and desired types -
+        0d array vs scalar.
+
+    See Also
+    --------
+    xp_assert_equal : Similar function for exact equality checks.
+    isclose : Public function for checking closeness.
+    numpy.testing.assert_allclose : Similar function for NumPy arrays.
+
+    Notes
+    -----
+    The default `atol` and `rtol` differ from `xp.all(xpx.isclose(a, b))`.
+    """
+    xp = _check_ns_shape_dtype(actual, desired, check_dtype, check_shape, check_scalar)
+    if not _is_materializable(actual):
+        return
+
+    if rtol is None:
+        if xp.isdtype(actual.dtype, ("real floating", "complex floating")):
+            # multiplier of 4 is used as for `np.float64` this puts the default `rtol`
+            # roughly half way between sqrt(eps) and the default for
+            # `numpy.testing.assert_allclose`, 1e-7
+            rtol = xp.finfo(actual.dtype).eps ** 0.5 * 4
+        else:
+            rtol = 1e-7
+
+    actual_np = as_numpy_array(actual, xp=xp)
+    desired_np = as_numpy_array(desired, xp=xp)
+    np.testing.assert_allclose(  # pyright: ignore[reportCallIssue]
+        actual_np,
+        desired_np,
+        rtol=rtol,  # pyright: ignore[reportArgumentType]
+        atol=atol,
+        err_msg=err_msg,
+    )
+
+
+def xfail(
+    request: pytest.FixtureRequest, *, reason: str, strict: bool | None = None
+) -> None:
+    """
+    XFAIL the currently running test.
+
+    Unlike ``pytest.xfail``, allow rest of test to execute instead of immediately
+    halting it, so that it may result in a XPASS.
+    xref https://github.com/pandas-dev/pandas/issues/38902
+
+    Parameters
+    ----------
+    request : pytest.FixtureRequest
+        ``request`` argument of the test function.
+    reason : str
+        Reason for the expected failure.
+    strict: bool, optional
+        If True, the test will be marked as failed if it passes.
+        If False, the test will be marked as passed if it fails.
+        Default: ``xfail_strict`` value in ``pyproject.toml``, or False if absent.
+    """
+    if strict is not None:
+        marker = pytest.mark.xfail(reason=reason, strict=strict)
+    else:
+        marker = pytest.mark.xfail(reason=reason)
+    request.node.add_marker(marker)
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new file mode 100644
index 0000000000000000000000000000000000000000..3628c45f0e0a48ba403abd0ba4a6bec76dc8a9f1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/__init__.py
@@ -0,0 +1 @@
+"""Modules housing private utility functions."""
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_compat.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_compat.py
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+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_compat.py
@@ -0,0 +1,74 @@
+"""Acquire helpers from array-api-compat."""
+# Allow packages that vendor both `array-api-extra` and
+# `array-api-compat` to override the import location
+
+# pylint: disable=duplicate-code
+try:
+    from ...._array_api_compat_vendor import (
+        array_namespace,
+        device,
+        is_array_api_obj,
+        is_array_api_strict_namespace,
+        is_cupy_array,
+        is_cupy_namespace,
+        is_dask_array,
+        is_dask_namespace,
+        is_jax_array,
+        is_jax_namespace,
+        is_lazy_array,
+        is_numpy_array,
+        is_numpy_namespace,
+        is_pydata_sparse_array,
+        is_pydata_sparse_namespace,
+        is_torch_array,
+        is_torch_namespace,
+        is_writeable_array,
+        size,
+        to_device,
+    )
+except ImportError:
+    from array_api_compat import (
+        array_namespace,
+        device,
+        is_array_api_obj,
+        is_array_api_strict_namespace,
+        is_cupy_array,
+        is_cupy_namespace,
+        is_dask_array,
+        is_dask_namespace,
+        is_jax_array,
+        is_jax_namespace,
+        is_lazy_array,
+        is_numpy_array,
+        is_numpy_namespace,
+        is_pydata_sparse_array,
+        is_pydata_sparse_namespace,
+        is_torch_array,
+        is_torch_namespace,
+        is_writeable_array,
+        size,
+        to_device,
+    )
+
+__all__ = [
+    "array_namespace",
+    "device",
+    "is_array_api_obj",
+    "is_array_api_strict_namespace",
+    "is_cupy_array",
+    "is_cupy_namespace",
+    "is_dask_array",
+    "is_dask_namespace",
+    "is_jax_array",
+    "is_jax_namespace",
+    "is_lazy_array",
+    "is_numpy_array",
+    "is_numpy_namespace",
+    "is_pydata_sparse_array",
+    "is_pydata_sparse_namespace",
+    "is_torch_array",
+    "is_torch_namespace",
+    "is_writeable_array",
+    "size",
+    "to_device",
+]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_compat.pyi b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_compat.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..95c6bc8a1baed1f083d907994e5c939d6cc325f2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_compat.pyi
@@ -0,0 +1,45 @@
+"""Static type stubs for `_compat.py`."""
+
+# https://github.com/scikit-learn/scikit-learn/pull/27910#issuecomment-2568023972
+from __future__ import annotations
+
+from types import ModuleType
+from typing import Any, TypeGuard
+
+# TODO import from typing (requires Python >=3.13)
+from typing_extensions import TypeIs
+
+from ._typing import Array, Device
+
+# pylint: disable=missing-class-docstring,unused-argument
+
+def array_namespace(
+    *xs: Array | complex | None,
+    api_version: str | None = None,
+    use_compat: bool | None = None,
+) -> ModuleType: ...
+def device(x: Array, /) -> Device: ...
+def is_array_api_obj(x: object, /) -> TypeIs[Array]: ...
+def is_array_api_strict_namespace(xp: ModuleType, /) -> bool: ...
+def is_cupy_namespace(xp: ModuleType, /) -> bool: ...
+def is_dask_namespace(xp: ModuleType, /) -> bool: ...
+def is_jax_namespace(xp: ModuleType, /) -> bool: ...
+def is_numpy_namespace(xp: ModuleType, /) -> bool: ...
+def is_pydata_sparse_namespace(xp: ModuleType, /) -> bool: ...
+def is_torch_namespace(xp: ModuleType, /) -> bool: ...
+def is_cupy_array(x: object, /) -> TypeGuard[Array]: ...
+def is_dask_array(x: object, /) -> TypeGuard[Array]: ...
+def is_jax_array(x: object, /) -> TypeGuard[Array]: ...
+def is_numpy_array(x: object, /) -> TypeGuard[Array]: ...
+def is_pydata_sparse_array(x: object, /) -> TypeGuard[Array]: ...
+def is_torch_array(x: object, /) -> TypeGuard[Array]: ...
+def is_lazy_array(x: object, /) -> TypeGuard[Array]: ...
+def is_writeable_array(x: object, /) -> TypeGuard[Array]: ...
+def size(x: Array, /) -> int | None: ...
+def to_device(
+    x: Array,
+    device: Device,  # pylint: disable=redefined-outer-name
+    /,
+    *,
+    stream: int | Any | None = None,
+) -> Array: ...
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_helpers.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_helpers.py
new file mode 100644
index 0000000000000000000000000000000000000000..22da8259eff73d6d0cecfba6d25514de70c23d3b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_helpers.py
@@ -0,0 +1,619 @@
+"""Helper functions used by `array_api_extra/_funcs.py`."""
+
+from __future__ import annotations
+
+import io
+import math
+import pickle
+import types
+from collections.abc import Callable, Generator, Iterable, Iterator
+from functools import wraps
+from types import ModuleType
+from typing import (
+    TYPE_CHECKING,
+    Any,
+    ClassVar,
+    Generic,
+    Literal,
+    ParamSpec,
+    TypeAlias,
+    TypeVar,
+    cast,
+)
+
+from . import _compat
+from ._compat import (
+    array_namespace,
+    is_array_api_obj,
+    is_dask_namespace,
+    is_jax_namespace,
+    is_numpy_array,
+    is_pydata_sparse_namespace,
+    is_torch_namespace,
+)
+from ._typing import Array, Device
+
+if TYPE_CHECKING:  # pragma: no cover
+    # TODO import from typing (requires Python >=3.12 and >=3.13)
+    from typing_extensions import TypeIs, override
+else:
+
+    def override(func):
+        return func
+
+
+P = ParamSpec("P")
+T = TypeVar("T")
+
+
+__all__ = [
+    "asarrays",
+    "capabilities",
+    "eager_shape",
+    "in1d",
+    "is_python_scalar",
+    "jax_autojit",
+    "mean",
+    "meta_namespace",
+    "pickle_flatten",
+    "pickle_unflatten",
+]
+
+
+def in1d(
+    x1: Array,
+    x2: Array,
+    /,
+    *,
+    assume_unique: bool = False,
+    invert: bool = False,
+    xp: ModuleType | None = None,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """
+    Check whether each element of an array is also present in a second array.
+
+    Returns a boolean array the same length as `x1` that is True
+    where an element of `x1` is in `x2` and False otherwise.
+
+    This function has been adapted using the original implementation
+    present in numpy:
+    https://github.com/numpy/numpy/blob/v1.26.0/numpy/lib/arraysetops.py#L524-L758
+    """
+    if xp is None:
+        xp = array_namespace(x1, x2)
+
+    x1_shape = eager_shape(x1)
+    x2_shape = eager_shape(x2)
+
+    # This code is run to make the code significantly faster
+    if x2_shape[0] < 10 * x1_shape[0] ** 0.145 and isinstance(x2, Iterable):
+        if invert:
+            mask = xp.ones(x1_shape[0], dtype=xp.bool, device=_compat.device(x1))
+            for a in x2:
+                mask &= x1 != a
+        else:
+            mask = xp.zeros(x1_shape[0], dtype=xp.bool, device=_compat.device(x1))
+            for a in x2:
+                mask |= x1 == a
+        return mask
+
+    rev_idx = xp.empty(0)  # placeholder
+    if not assume_unique:
+        x1, rev_idx = xp.unique_inverse(x1)
+        x2 = xp.unique_values(x2)
+
+    ar = xp.concat((x1, x2))
+    device_ = _compat.device(ar)
+    # We need this to be a stable sort.
+    order = xp.argsort(ar, stable=True)
+    reverse_order = xp.argsort(order, stable=True)
+    sar = xp.take(ar, order, axis=0)
+    ar_size = _compat.size(sar)
+    assert ar_size is not None, "xp.unique*() on lazy backends raises"
+    if ar_size >= 1:
+        bool_ar = sar[1:] != sar[:-1] if invert else sar[1:] == sar[:-1]
+    else:
+        bool_ar = xp.asarray([False]) if invert else xp.asarray([True])
+    flag = xp.concat((bool_ar, xp.asarray([invert], device=device_)))
+    ret = xp.take(flag, reverse_order, axis=0)
+
+    if assume_unique:
+        return ret[: x1.shape[0]]
+    return xp.take(ret, rev_idx, axis=0)
+
+
+def mean(
+    x: Array,
+    /,
+    *,
+    axis: int | tuple[int, ...] | None = None,
+    keepdims: bool = False,
+    xp: ModuleType | None = None,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """
+    Complex mean, https://github.com/data-apis/array-api/issues/846.
+    """
+    if xp is None:
+        xp = array_namespace(x)
+
+    if xp.isdtype(x.dtype, "complex floating"):
+        x_real = xp.real(x)
+        x_imag = xp.imag(x)
+        mean_real = xp.mean(x_real, axis=axis, keepdims=keepdims)
+        mean_imag = xp.mean(x_imag, axis=axis, keepdims=keepdims)
+        return mean_real + (mean_imag * xp.asarray(1j))
+    return xp.mean(x, axis=axis, keepdims=keepdims)
+
+
+def is_python_scalar(x: object) -> TypeIs[complex]:  # numpydoc ignore=PR01,RT01
+    """Return True if `x` is a Python scalar, False otherwise."""
+    # isinstance(x, float) returns True for np.float64
+    # isinstance(x, complex) returns True for np.complex128
+    # bool is a subclass of int
+    return isinstance(x, int | float | complex) and not is_numpy_array(x)
+
+
+def asarrays(
+    a: Array | complex,
+    b: Array | complex,
+    xp: ModuleType,
+) -> tuple[Array, Array]:
+    """
+    Ensure both `a` and `b` are arrays.
+
+    If `b` is a python scalar, it is converted to the same dtype as `a`, and vice versa.
+
+    Behavior is not specified when mixing a Python ``float`` and an array with an
+    integer data type; this may give ``float32``, ``float64``, or raise an exception.
+    Behavior is implementation-specific.
+
+    Similarly, behavior is not specified when mixing a Python ``complex`` and an array
+    with a real-valued data type; this may give ``complex64``, ``complex128``, or raise
+    an exception. Behavior is implementation-specific.
+
+    Parameters
+    ----------
+    a, b : Array | int | float | complex | bool
+        Input arrays or scalars. At least one must be an array.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    Array, Array
+        The input arrays, possibly converted to arrays if they were scalars.
+
+    See Also
+    --------
+    mixing-arrays-with-python-scalars : Array API specification for the behavior.
+    """
+    a_scalar = is_python_scalar(a)
+    b_scalar = is_python_scalar(b)
+    if not a_scalar and not b_scalar:
+        # This includes misc. malformed input e.g. str
+        return a, b  # type: ignore[return-value]
+
+    swap = False
+    if a_scalar:
+        swap = True
+        b, a = a, b
+
+    if is_array_api_obj(a):
+        # a is an Array API object
+        # b is a int | float | complex | bool
+        xa = a
+
+        # https://data-apis.org/array-api/draft/API_specification/type_promotion.html#mixing-arrays-with-python-scalars
+        same_dtype = {
+            bool: "bool",
+            int: ("integral", "real floating", "complex floating"),
+            float: ("real floating", "complex floating"),
+            complex: "complex floating",
+        }
+        kind = same_dtype[type(cast(complex, b))]
+        if xp.isdtype(a.dtype, kind):
+            xb = xp.asarray(b, dtype=a.dtype, device=_compat.device(a))
+        else:
+            # Undefined behaviour. Let the function deal with it, if it can.
+            xb = xp.asarray(b, device=_compat.device(a))
+
+    else:
+        # Neither a nor b are Array API objects.
+        # Note: we can only reach this point when one explicitly passes
+        # xp=xp to the calling function; otherwise we fail earlier on
+        # array_namespace(a, b).
+        xa, xb = xp.asarray(a), xp.asarray(b)
+
+    return (xb, xa) if swap else (xa, xb)
+
+
+def ndindex(*x: int) -> Generator[tuple[int, ...]]:
+    """
+    Generate all N-dimensional indices for a given array shape.
+
+    Given the shape of an array, an ndindex instance iterates over the N-dimensional
+    index of the array. At each iteration a tuple of indices is returned, the last
+    dimension is iterated over first.
+
+    This has an identical API to numpy.ndindex.
+
+    Parameters
+    ----------
+    *x : int
+        The shape of the array.
+    """
+    if not x:
+        yield ()
+        return
+    for i in ndindex(*x[:-1]):
+        for j in range(x[-1]):
+            yield *i, j
+
+
+def eager_shape(x: Array, /, axis: int | None = None) -> tuple[int, ...]:
+    """
+    Return shape of an array. Raise if shape is not fully defined.
+
+    Parameters
+    ----------
+    x : Array
+        Input array.
+    axis : int, optional
+        If provided, only returns the tuple (shape[axis],).
+
+    Returns
+    -------
+    tuple[int, ...]
+        Shape of the array.
+    """
+    shape = x.shape
+    if axis is not None:
+        s = shape[axis]
+        # Dask arrays uses non-standard NaN instead of None
+        if s is None or math.isnan(s):
+            msg = f"Unsupported lazy shape for axis {axis}"
+            raise TypeError(msg)
+        return (s,)
+
+    if any(s is None or math.isnan(s) for s in shape):
+        msg = "Unsupported lazy shape"
+        raise TypeError(msg)
+    return cast(tuple[int, ...], shape)
+
+
+def meta_namespace(
+    *arrays: Array | complex | None, xp: ModuleType | None = None
+) -> ModuleType:
+    """
+    Get the namespace of Dask chunks.
+
+    On all other backends, just return the namespace of the arrays.
+
+    Parameters
+    ----------
+    *arrays : Array | int | float | complex | bool | None
+        Input arrays.
+    xp : array_namespace, optional
+        The standard-compatible namespace for the input arrays. Default: infer.
+
+    Returns
+    -------
+    array_namespace
+        If xp is Dask, the namespace of the Dask chunks;
+        otherwise, the namespace of the arrays.
+    """
+    xp = array_namespace(*arrays) if xp is None else xp
+    if not is_dask_namespace(xp):
+        return xp
+    # Quietly skip scalars and None's
+    metas = [cast(Array | None, getattr(a, "_meta", None)) for a in arrays]
+    return array_namespace(*metas)
+
+
+def capabilities(
+    xp: ModuleType, *, device: Device | None = None
+) -> dict[str, int | None]:
+    """
+    Return patched ``xp.__array_namespace_info__().capabilities()``.
+
+    TODO this helper should be eventually removed once all the special cases
+    it handles are fixed in the respective backends.
+
+    Parameters
+    ----------
+    xp : array_namespace
+        The standard-compatible namespace.
+    device : Device, optional
+        The device to use.
+
+    Returns
+    -------
+    dict
+        Capabilities of the namespace.
+    """
+    out = xp.__array_namespace_info__().capabilities()
+    if is_pydata_sparse_namespace(xp):
+        if out["boolean indexing"]:
+            # FIXME https://github.com/pydata/sparse/issues/876
+            # boolean indexing is supported, but not when the index is a sparse array.
+            # boolean indexing by list or numpy array is not part of the Array API.
+            out = out.copy()
+            out["boolean indexing"] = False
+    elif is_jax_namespace(xp):
+        if out["boolean indexing"]:  # pragma: no cover
+            # Backwards compatibility with jax <0.6.0
+            # https://github.com/jax-ml/jax/issues/27418
+            out = out.copy()
+            out["boolean indexing"] = False
+    elif is_torch_namespace(xp):
+        # FIXME https://github.com/data-apis/array-api/issues/945
+        device = xp.get_default_device() if device is None else xp.device(device)
+        if device.type == "meta":  # type: ignore[union-attr]  # pyright: ignore[reportAttributeAccessIssue,reportOptionalMemberAccess]
+            out = out.copy()
+            out["boolean indexing"] = False
+            out["data-dependent shapes"] = False
+
+    return out
+
+
+_BASIC_PICKLED_TYPES = frozenset((
+    bool, int, float, complex, str, bytes, bytearray,
+    list, tuple, dict, set, frozenset, range, slice,
+    types.NoneType, types.EllipsisType,
+))  # fmt: skip
+_BASIC_REST_TYPES = frozenset((
+    type, types.BuiltinFunctionType, types.FunctionType, types.ModuleType
+))  # fmt: skip
+
+FlattenRest: TypeAlias = tuple[object, ...]
+
+
+def pickle_flatten(
+    obj: object, cls: type[T] | tuple[type[T], ...]
+) -> tuple[list[T], FlattenRest]:
+    """
+    Use the pickle machinery to extract objects out of an arbitrary container.
+
+    Unlike regular ``pickle.dumps``, this function always succeeds.
+
+    Parameters
+    ----------
+    obj : object
+        The object to pickle.
+    cls : type | tuple[type, ...]
+        One or multiple classes to extract from the object.
+        The instances of these classes inside ``obj`` will not be pickled.
+
+    Returns
+    -------
+    instances : list[cls]
+        All instances of ``cls`` found inside ``obj`` (not pickled).
+    rest
+        Opaque object containing the pickled bytes plus all other objects where
+        ``__reduce__`` / ``__reduce_ex__`` is either not implemented or raised.
+        These are unpickleable objects, types, modules, and functions.
+
+        This object is *typically* hashable save for fairly exotic objects
+        that are neither pickleable nor hashable.
+
+        This object is pickleable if everything except ``instances`` was pickleable
+        in the input object.
+
+    See Also
+    --------
+    pickle_unflatten : Reverse function.
+
+    Examples
+    --------
+    >>> class A:
+    ...     def __repr__(self):
+    ...         return ""
+    >>> class NS:
+    ...     def __repr__(self):
+    ...         return ""
+    ...     def __reduce__(self):
+    ...         assert False, "not serializable"
+    >>> obj = {1: A(), 2: [A(), NS(), A()]}
+    >>> instances, rest = pickle_flatten(obj, A)
+    >>> instances
+    [, , ]
+    >>> pickle_unflatten(instances, rest)
+    {1: , 2: [, , ]}
+
+    This can be also used to swap inner objects; the only constraint is that
+    the number of objects in and out must be the same:
+
+    >>> pickle_unflatten(["foo", "bar", "baz"], rest)
+    {1: "foo", 2: ["bar", , "baz"]}
+    """
+    instances: list[T] = []
+    rest: list[object] = []
+
+    class Pickler(pickle.Pickler):  # numpydoc ignore=GL08
+        """
+        Use the `pickle.Pickler.persistent_id` hook to extract objects.
+        """
+
+        @override
+        def persistent_id(
+            self, obj: object
+        ) -> Literal[0, 1, None]:  # numpydoc ignore=GL08
+            if isinstance(obj, cls):
+                instances.append(obj)  # type: ignore[arg-type]
+                return 0
+
+            typ_ = type(obj)
+            if typ_ in _BASIC_PICKLED_TYPES:  # No subclasses!
+                # If obj is a collection, recursively descend inside it
+                return None
+            if typ_ in _BASIC_REST_TYPES:
+                rest.append(obj)
+                return 1
+
+            try:
+                # Note: a class that defines __slots__ without defining __getstate__
+                # cannot be pickled with __reduce__(), but can with __reduce_ex__(5)
+                _ = obj.__reduce_ex__(pickle.HIGHEST_PROTOCOL)
+            except Exception:  # pylint: disable=broad-exception-caught
+                rest.append(obj)
+                return 1
+
+            # Object can be pickled. Let the Pickler recursively descend inside it.
+            return None
+
+    f = io.BytesIO()
+    p = Pickler(f, protocol=pickle.HIGHEST_PROTOCOL)
+    p.dump(obj)
+    return instances, (f.getvalue(), *rest)
+
+
+def pickle_unflatten(instances: Iterable[object], rest: FlattenRest) -> Any:
+    """
+    Reverse of ``pickle_flatten``.
+
+    Parameters
+    ----------
+    instances : Iterable
+        Inner objects to be reinserted into the flattened container.
+    rest : FlattenRest
+        Extra bits, as returned by ``pickle_flatten``.
+
+    Returns
+    -------
+    object
+        The outer object originally passed to ``pickle_flatten`` after a
+        pickle->unpickle round-trip.
+
+    See Also
+    --------
+    pickle_flatten : Serializing function.
+    pickle.loads : Standard unpickle function.
+
+    Notes
+    -----
+    The `instances` iterable must yield at least the same number of elements as the ones
+    returned by ``pickle_flatten``, but the elements do not need to be the same objects
+    or even the same types of objects. Excess elements, if any, will be left untouched.
+    """
+    iters = iter(instances), iter(rest)
+    pik = cast(bytes, next(iters[1]))
+
+    class Unpickler(pickle.Unpickler):  # numpydoc ignore=GL08
+        """Mirror of the overridden Pickler in pickle_flatten."""
+
+        @override
+        def persistent_load(self, pid: Literal[0, 1]) -> object:  # numpydoc ignore=GL08
+            try:
+                return next(iters[pid])
+            except StopIteration as e:
+                msg = "Not enough objects to unpickle"
+                raise ValueError(msg) from e
+
+    f = io.BytesIO(pik)
+    return Unpickler(f).load()
+
+
+class _AutoJITWrapper(Generic[T]):  # numpydoc ignore=PR01
+    """
+    Helper of :func:`jax_autojit`.
+
+    Wrap arbitrary inputs and outputs of the jitted function and
+    convert them to/from PyTrees.
+    """
+
+    _obj: Any
+    _is_iter: bool
+    _registered: ClassVar[bool] = False
+    __slots__: tuple[str, ...] = ("_is_iter", "_obj")
+
+    def __init__(self, obj: T) -> None:  # numpydoc ignore=GL08
+        self._register()
+        if isinstance(obj, Iterator):
+            self._obj = list(obj)
+            self._is_iter = True
+        else:
+            self._obj = obj
+            self._is_iter = False
+
+    @property
+    def obj(self) -> T:  # numpydoc ignore=RT01
+        """Return wrapped object."""
+        return iter(self._obj) if self._is_iter else self._obj
+
+    @classmethod
+    def _register(cls) -> None:  # numpydoc ignore=SS06
+        """
+        Register upon first use instead of at import time, to avoid
+        globally importing JAX.
+        """
+        if not cls._registered:
+            import jax
+
+            jax.tree_util.register_pytree_node(
+                cls,
+                lambda instance: pickle_flatten(instance, jax.Array),  # pyright: ignore[reportUnknownArgumentType]
+                lambda aux_data, children: pickle_unflatten(children, aux_data),  # pyright: ignore[reportUnknownArgumentType]
+            )
+            cls._registered = True
+
+
+def jax_autojit(
+    func: Callable[P, T],
+) -> Callable[P, T]:  # numpydoc ignore=PR01,RT01,SS03
+    """
+    Wrap `func` with ``jax.jit``, with the following differences:
+
+    - Python scalar arguments and return values are not automatically converted to
+      ``jax.Array`` objects.
+    - All non-array arguments are automatically treated as static.
+      Unlike ``jax.jit``, static arguments must be either hashable or serializable with
+      ``pickle``.
+    - Unlike ``jax.jit``, non-array arguments and return values are not limited to
+      tuple/list/dict, but can be any object serializable with ``pickle``.
+    - Automatically descend into non-array arguments and find ``jax.Array`` objects
+      inside them, then rebuild the arguments when entering `func`, swapping the JAX
+      concrete arrays with tracer objects.
+    - Automatically descend into non-array return values and find ``jax.Array`` objects
+      inside them, then rebuild them downstream of exiting the JIT, swapping the JAX
+      tracer objects with concrete arrays.
+    - Returned iterators are immediately completely consumed.
+
+    See Also
+    --------
+    jax.jit : JAX JIT compilation function.
+
+    Notes
+    -----
+    These are useful choices *for testing purposes only*, which is how this function is
+    intended to be used. The output of ``jax.jit`` is a C++ level callable, that
+    directly dispatches to the compiled kernel after the initial call. In comparison,
+    ``jax_autojit`` incurs a much higher dispatch time.
+
+    Additionally, consider::
+
+        def f(x: Array, y: float, plus: bool) -> Array:
+            return x + y if plus else x - y
+
+        j1 = jax.jit(f, static_argnames="plus")
+        j2 = jax_autojit(f)
+
+    In the above example, ``j2`` requires a lot less setup to be tested effectively than
+    ``j1``, but on the flip side it means that it will be re-traced for every different
+    value of ``y``, which likely makes it not fit for purpose in production.
+    """
+    import jax
+
+    @jax.jit  # type: ignore[misc]  # pyright: ignore[reportUntypedFunctionDecorator]
+    def inner(  # numpydoc ignore=GL08
+        wargs: _AutoJITWrapper[Any],
+    ) -> _AutoJITWrapper[T]:
+        args, kwargs = wargs.obj
+        res = func(*args, **kwargs)  # pyright: ignore[reportCallIssue]
+        return _AutoJITWrapper(res)
+
+    @wraps(func)
+    def outer(*args: P.args, **kwargs: P.kwargs) -> T:  # numpydoc ignore=GL08
+        wargs = _AutoJITWrapper((args, kwargs))
+        return inner(wargs).obj
+
+    return outer
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_typing.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_typing.py
new file mode 100644
index 0000000000000000000000000000000000000000..8204be4759610b1ddb33b3579ccaa5f3a1f0866a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_typing.py
@@ -0,0 +1,10 @@
+# numpydoc ignore=GL08
+# pylint: disable=missing-module-docstring,duplicate-code
+
+Array = object
+DType = object
+Device = object
+GetIndex = object
+SetIndex = object
+
+__all__ = ["Array", "DType", "Device", "GetIndex", "SetIndex"]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_typing.pyi b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_typing.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..35c255fc9ad5c6c93e1b988dc9fe1fc6543ee0a6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/_lib/_utils/_typing.pyi
@@ -0,0 +1,105 @@
+"""Static typing helpers."""
+
+from __future__ import annotations
+
+from types import EllipsisType
+from typing import Protocol, TypeAlias
+
+# TODO import from typing (requires Python >=3.12)
+from typing_extensions import override
+
+# TODO: use array-api-typing once it is available
+
+class Array(Protocol):  # pylint: disable=missing-class-docstring
+    # Unary operations
+    def __abs__(self) -> Array: ...
+    def __pos__(self) -> Array: ...
+    def __neg__(self) -> Array: ...
+    def __invert__(self) -> Array: ...
+    # Binary operations
+    def __add__(self, other: Array | complex, /) -> Array: ...
+    def __sub__(self, other: Array | complex, /) -> Array: ...
+    def __mul__(self, other: Array | complex, /) -> Array: ...
+    def __truediv__(self, other: Array | complex, /) -> Array: ...
+    def __floordiv__(self, other: Array | complex, /) -> Array: ...
+    def __mod__(self, other: Array | complex, /) -> Array: ...
+    def __pow__(self, other: Array | complex, /) -> Array: ...
+    def __matmul__(self, other: Array, /) -> Array: ...
+    def __and__(self, other: Array | int, /) -> Array: ...
+    def __or__(self, other: Array | int, /) -> Array: ...
+    def __xor__(self, other: Array | int, /) -> Array: ...
+    def __lshift__(self, other: Array | int, /) -> Array: ...
+    def __rshift__(self, other: Array | int, /) -> Array: ...
+    def __lt__(self, other: Array | complex, /) -> Array: ...
+    def __le__(self, other: Array | complex, /) -> Array: ...
+    def __gt__(self, other: Array | complex, /) -> Array: ...
+    def __ge__(self, other: Array | complex, /) -> Array: ...
+    @override
+    def __eq__(self, other: Array | complex, /) -> Array: ...  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
+    @override
+    def __ne__(self, other: Array | complex, /) -> Array: ...  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
+    # Reflected operations
+    def __radd__(self, other: Array | complex, /) -> Array: ...
+    def __rsub__(self, other: Array | complex, /) -> Array: ...
+    def __rmul__(self, other: Array | complex, /) -> Array: ...
+    def __rtruediv__(self, other: Array | complex, /) -> Array: ...
+    def __rfloordiv__(self, other: Array | complex, /) -> Array: ...
+    def __rmod__(self, other: Array | complex, /) -> Array: ...
+    def __rpow__(self, other: Array | complex, /) -> Array: ...
+    def __rmatmul__(self, other: Array, /) -> Array: ...
+    def __rand__(self, other: Array | int, /) -> Array: ...
+    def __ror__(self, other: Array | int, /) -> Array: ...
+    def __rxor__(self, other: Array | int, /) -> Array: ...
+    def __rlshift__(self, other: Array | int, /) -> Array: ...
+    def __rrshift__(self, other: Array | int, /) -> Array: ...
+    # Attributes
+    @property
+    def dtype(self) -> DType: ...
+    @property
+    def device(self) -> Device: ...
+    @property
+    def mT(self) -> Array: ...  # pylint: disable=invalid-name
+    @property
+    def ndim(self) -> int: ...
+    @property
+    def shape(self) -> tuple[int | None, ...]: ...
+    @property
+    def size(self) -> int | None: ...
+    @property
+    def T(self) -> Array: ...  # pylint: disable=invalid-name
+    # Collection operations (note: an Array does not have to be Sized or Iterable)
+    def __getitem__(self, key: GetIndex, /) -> Array: ...
+    def __setitem__(self, key: SetIndex, value: Array | complex, /) -> None: ...
+    # Materialization methods (may raise on lazy arrays)
+    def __bool__(self) -> bool: ...
+    def __complex__(self) -> complex: ...
+    def __float__(self) -> float: ...
+    def __index__(self) -> int: ...
+    def __int__(self) -> int: ...
+
+    # Misc methods (frequently not implemented in Arrays wrapped by array-api-compat)
+    # def __array_namespace__(*, api_version: str | None) -> ModuleType: ...
+    # def __dlpack__(
+    #     *,
+    #     stream: int | Any | None = None,
+    #     max_version: tuple[int, int] | None = None,
+    #     dl_device: tuple[int, int] | None = None,  # tuple[Enum, int]
+    #     copy: bool | None = None,
+    # ) -> Any: ...
+    # def __dlpack_device__() -> tuple[int, int]: ...  # tuple[Enum, int]
+    # def to_device(device: Device, /, *, stream: int | Any | None = None) -> Array: ...
+
+class DType(Protocol):  # pylint: disable=missing-class-docstring
+    pass
+
+class Device(Protocol):  # pylint: disable=missing-class-docstring
+    pass
+
+SetIndex: TypeAlias = (
+    int | slice | EllipsisType | Array | tuple[int | slice | EllipsisType | Array, ...]
+)
+GetIndex: TypeAlias = (
+    SetIndex | None | tuple[int | slice | EllipsisType | None | Array, ...]
+)
+
+__all__ = ["Array", "DType", "Device", "GetIndex", "SetIndex"]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/testing.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/testing.py
new file mode 100644
index 0000000000000000000000000000000000000000..d40fea1a085319c82a7d89e21f2182b5be5ad3c9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/array_api_extra/testing.py
@@ -0,0 +1,415 @@
+"""
+Public testing utilities.
+
+See also _lib._testing for additional private testing utilities.
+"""
+
+from __future__ import annotations
+
+import contextlib
+import enum
+import warnings
+from collections.abc import Callable, Generator, Iterator, Sequence
+from functools import wraps
+from types import ModuleType
+from typing import TYPE_CHECKING, Any, ParamSpec, TypeVar, cast
+
+from ._lib._utils._compat import is_dask_namespace, is_jax_namespace
+from ._lib._utils._helpers import jax_autojit, pickle_flatten, pickle_unflatten
+
+__all__ = ["lazy_xp_function", "patch_lazy_xp_functions"]
+
+if TYPE_CHECKING:  # pragma: no cover
+    # TODO import override from typing (requires Python >=3.12)
+    import pytest
+    from dask.typing import Graph, Key, SchedulerGetCallable
+    from typing_extensions import override
+
+else:
+    # Sphinx hacks
+    SchedulerGetCallable = object
+
+    def override(func):
+        return func
+
+
+P = ParamSpec("P")
+T = TypeVar("T")
+
+_ufuncs_tags: dict[object, dict[str, Any]] = {}
+
+
+class Deprecated(enum.Enum):
+    """Unique type for deprecated parameters."""
+
+    DEPRECATED = 1
+
+
+DEPRECATED = Deprecated.DEPRECATED
+
+
+def lazy_xp_function(
+    func: Callable[..., Any],
+    *,
+    allow_dask_compute: bool | int = False,
+    jax_jit: bool = True,
+    static_argnums: Deprecated = DEPRECATED,
+    static_argnames: Deprecated = DEPRECATED,
+) -> None:  # numpydoc ignore=GL07
+    """
+    Tag a function to be tested on lazy backends.
+
+    Tag a function so that when any tests are executed with ``xp=jax.numpy`` the
+    function is replaced with a jitted version of itself, and when it is executed with
+    ``xp=dask.array`` the function will raise if it attempts to materialize the graph.
+    This will be later expanded to provide test coverage for other lazy backends.
+
+    In order for the tag to be effective, the test or a fixture must call
+    :func:`patch_lazy_xp_functions`.
+
+    Parameters
+    ----------
+    func : callable
+        Function to be tested.
+    allow_dask_compute : bool | int, optional
+        Whether `func` is allowed to internally materialize the Dask graph, or maximum
+        number of times it is allowed to do so. This is typically triggered by
+        ``bool()``, ``float()``, or ``np.asarray()``.
+
+        Set to 1 if you are aware that `func` converts the input parameters to NumPy and
+        want to let it do so at least for the time being, knowing that it is going to be
+        extremely detrimental for performance.
+
+        If a test needs values higher than 1 to pass, it is a canary that the conversion
+        to NumPy/bool/float is happening multiple times, which translates to multiple
+        computations of the whole graph. Short of making the function fully lazy, you
+        should at least add explicit calls to ``np.asarray()`` early in the function.
+        *Note:* the counter of `allow_dask_compute` resets after each call to `func`, so
+        a test function that invokes `func` multiple times should still work with this
+        parameter set to 1.
+
+        Set to True to allow `func` to materialize the graph an unlimited number
+        of times.
+
+        Default: False, meaning that `func` must be fully lazy and never materialize the
+        graph.
+    jax_jit : bool, optional
+        Set to True to replace `func` with a smart variant of ``jax.jit(func)`` after
+        calling the :func:`patch_lazy_xp_functions` test helper with ``xp=jax.numpy``.
+        This is the default behaviour.
+        Set to False if `func` is only compatible with eager (non-jitted) JAX.
+
+        Unlike with vanilla ``jax.jit``, all arguments and return types that are not JAX
+        arrays are treated as static; the function can accept and return arbitrary
+        wrappers around JAX arrays. This difference is because, in real life, most users
+        won't wrap the function directly with ``jax.jit`` but rather they will use it
+        within their own code, which is itself then wrapped by ``jax.jit``, and
+        internally consume the function's outputs.
+
+        In other words, the pattern that is being tested is::
+
+            >>> @jax.jit
+            ... def user_func(x):
+            ...     y = user_prepares_inputs(x)
+            ...     z = func(y, some_static_arg=True)
+            ...     return user_consumes(z)
+
+        Default: True.
+    static_argnums :
+        Deprecated; ignored
+    static_argnames :
+        Deprecated; ignored
+
+    See Also
+    --------
+    patch_lazy_xp_functions : Companion function to call from the test or fixture.
+    jax.jit : JAX function to compile a function for performance.
+
+    Examples
+    --------
+    In ``test_mymodule.py``::
+
+      from array_api_extra.testing import lazy_xp_function from mymodule import myfunc
+
+      lazy_xp_function(myfunc)
+
+      def test_myfunc(xp):
+          a = xp.asarray([1, 2])
+          # When xp=jax.numpy, this is similar to `b = jax.jit(myfunc)(a)`
+          # When xp=dask.array, crash on compute() or persist()
+          b = myfunc(a)
+
+    Notes
+    -----
+    In order for this tag to be effective, the test function must be imported into the
+    test module globals without its namespace; alternatively its namespace must be
+    declared in a ``lazy_xp_modules`` list in the test module globals.
+
+    Example 1::
+
+      from mymodule import myfunc
+
+      lazy_xp_function(myfunc)
+
+      def test_myfunc(xp):
+          x = myfunc(xp.asarray([1, 2]))
+
+    Example 2::
+
+      import mymodule
+
+      lazy_xp_modules = [mymodule]
+      lazy_xp_function(mymodule.myfunc)
+
+      def test_myfunc(xp):
+          x = mymodule.myfunc(xp.asarray([1, 2]))
+
+    A test function can circumvent this monkey-patching system by using a namespace
+    outside of the two above patterns. You need to sanitize your code to make sure this
+    only happens intentionally.
+
+    Example 1::
+
+      import mymodule
+      from mymodule import myfunc
+
+      lazy_xp_function(myfunc)
+
+      def test_myfunc(xp):
+          a = xp.asarray([1, 2])
+          b = myfunc(a)  # This is wrapped when xp=jax.numpy or xp=dask.array
+          c = mymodule.myfunc(a)  # This is not
+
+    Example 2::
+
+      import mymodule
+
+      class naked:
+          myfunc = mymodule.myfunc
+
+      lazy_xp_modules = [mymodule]
+      lazy_xp_function(mymodule.myfunc)
+
+      def test_myfunc(xp):
+          a = xp.asarray([1, 2])
+          b = mymodule.myfunc(a)  # This is wrapped when xp=jax.numpy or xp=dask.array
+          c = naked.myfunc(a)  # This is not
+    """
+    if static_argnums is not DEPRECATED or static_argnames is not DEPRECATED:
+        warnings.warn(
+            (
+                "The `static_argnums` and `static_argnames` parameters are deprecated "
+                "and ignored. They will be removed in a future version."
+            ),
+            DeprecationWarning,
+            stacklevel=2,
+        )
+    tags = {
+        "allow_dask_compute": allow_dask_compute,
+        "jax_jit": jax_jit,
+    }
+
+    try:
+        func._lazy_xp_function = tags  # type: ignore[attr-defined]  # pylint: disable=protected-access  # pyright: ignore[reportFunctionMemberAccess]
+    except AttributeError:  # @cython.vectorize
+        _ufuncs_tags[func] = tags
+
+
+def patch_lazy_xp_functions(
+    request: pytest.FixtureRequest,
+    monkeypatch: pytest.MonkeyPatch | None = None,
+    *,
+    xp: ModuleType,
+) -> contextlib.AbstractContextManager[None]:
+    """
+    Test lazy execution of functions tagged with :func:`lazy_xp_function`.
+
+    If ``xp==jax.numpy``, search for all functions which have been tagged with
+    :func:`lazy_xp_function` in the globals of the module that defines the current test,
+    as well as in the ``lazy_xp_modules`` list in the globals of the same module,
+    and wrap them with :func:`jax.jit`. Unwrap them at the end of the test.
+
+    If ``xp==dask.array``, wrap the functions with a decorator that disables
+    ``compute()`` and ``persist()`` and ensures that exceptions and warnings are raised
+    eagerly.
+
+    This function should be typically called by your library's `xp` fixture that runs
+    tests on multiple backends::
+
+        @pytest.fixture(params=[
+            numpy,
+            array_api_strict,
+            pytest.param(jax.numpy, marks=pytest.mark.thread_unsafe),
+            pytest.param(dask.array, marks=pytest.mark.thread_unsafe),
+        ])
+        def xp(request):
+            with patch_lazy_xp_functions(request, xp=request.param):
+                yield request.param
+
+    but it can be otherwise be called by the test itself too.
+
+    Parameters
+    ----------
+    request : pytest.FixtureRequest
+        Pytest fixture, as acquired by the test itself or by one of its fixtures.
+    monkeypatch : pytest.MonkeyPatch
+        Deprecated
+    xp : array_namespace
+        Array namespace to be tested.
+
+    See Also
+    --------
+    lazy_xp_function : Tag a function to be tested on lazy backends.
+    pytest.FixtureRequest : `request` test function parameter.
+
+    Notes
+    -----
+    This context manager monkey-patches modules and as such is thread unsafe
+    on Dask and JAX. If you run your test suite with
+    `pytest-run-parallel `_,
+    you should mark these backends with ``@pytest.mark.thread_unsafe``, as shown in
+    the example above.
+    """
+    mod = cast(ModuleType, request.module)
+    mods = [mod, *cast(list[ModuleType], getattr(mod, "lazy_xp_modules", []))]
+
+    to_revert: list[tuple[ModuleType, str, object]] = []
+
+    def temp_setattr(mod: ModuleType, name: str, func: object) -> None:
+        """
+        Variant of monkeypatch.setattr, which allows monkey-patching only selected
+        parameters of a test so that pytest-run-parallel can run on the remainder.
+        """
+        assert hasattr(mod, name)
+        to_revert.append((mod, name, getattr(mod, name)))
+        setattr(mod, name, func)
+
+    if monkeypatch is not None:
+        warnings.warn(
+            (
+                "The `monkeypatch` parameter is deprecated and will be removed in a "
+                "future version. "
+                "Use `patch_lazy_xp_function` as a context manager instead."
+            ),
+            DeprecationWarning,
+            stacklevel=2,
+        )
+        # Enable using patch_lazy_xp_function not as a context manager
+        temp_setattr = monkeypatch.setattr  # type: ignore[assignment]  # pyright: ignore[reportAssignmentType]
+
+    def iter_tagged() -> Iterator[
+        tuple[ModuleType, str, Callable[..., Any], dict[str, Any]]
+    ]:
+        for mod in mods:
+            for name, func in mod.__dict__.items():
+                tags: dict[str, Any] | None = None
+                with contextlib.suppress(AttributeError):
+                    tags = func._lazy_xp_function  # pylint: disable=protected-access
+                if tags is None:
+                    with contextlib.suppress(KeyError, TypeError):
+                        tags = _ufuncs_tags[func]
+                if tags is not None:
+                    yield mod, name, func, tags
+
+    if is_dask_namespace(xp):
+        for mod, name, func, tags in iter_tagged():
+            n = tags["allow_dask_compute"]
+            if n is True:
+                n = 1_000_000
+            elif n is False:
+                n = 0
+            wrapped = _dask_wrap(func, n)
+            temp_setattr(mod, name, wrapped)
+
+    elif is_jax_namespace(xp):
+        for mod, name, func, tags in iter_tagged():
+            if tags["jax_jit"]:
+                wrapped = jax_autojit(func)
+                temp_setattr(mod, name, wrapped)
+
+    # We can't just decorate patch_lazy_xp_functions with
+    # @contextlib.contextmanager because it would not work with the
+    # deprecated monkeypatch when not used as a context manager.
+    @contextlib.contextmanager
+    def revert_on_exit() -> Generator[None]:
+        try:
+            yield
+        finally:
+            for mod, name, orig_func in to_revert:
+                setattr(mod, name, orig_func)
+
+    return revert_on_exit()
+
+
+class CountingDaskScheduler(SchedulerGetCallable):
+    """
+    Dask scheduler that counts how many times `dask.compute` is called.
+
+    If the number of times exceeds 'max_count', it raises an error.
+    This is a wrapper around Dask's own 'synchronous' scheduler.
+
+    Parameters
+    ----------
+    max_count : int
+        Maximum number of allowed calls to `dask.compute`.
+    msg : str
+        Assertion to raise when the count exceeds `max_count`.
+    """
+
+    count: int
+    max_count: int
+    msg: str
+
+    def __init__(self, max_count: int, msg: str):  # numpydoc ignore=GL08
+        self.count = 0
+        self.max_count = max_count
+        self.msg = msg
+
+    @override
+    def __call__(
+        self, dsk: Graph, keys: Sequence[Key] | Key, **kwargs: Any
+    ) -> Any:  # numpydoc ignore=GL08
+        import dask
+
+        self.count += 1
+        # This should yield a nice traceback to the
+        # offending line in the user's code
+        assert self.count <= self.max_count, self.msg
+
+        return dask.get(dsk, keys, **kwargs)  # type: ignore[attr-defined]  # pyright: ignore[reportPrivateImportUsage]
+
+
+def _dask_wrap(
+    func: Callable[P, T], n: int
+) -> Callable[P, T]:  # numpydoc ignore=PR01,RT01
+    """
+    Wrap `func` to raise if it attempts to call `dask.compute` more than `n` times.
+
+    After the function returns, materialize the graph in order to re-raise exceptions.
+    """
+    import dask
+    import dask.array as da
+
+    func_name = getattr(func, "__name__", str(func))
+    n_str = f"only up to {n}" if n else "no"
+    msg = (
+        f"Called `dask.compute()` or `dask.persist()` {n + 1} times, "
+        f"but {n_str} calls are allowed. Set "
+        f"`lazy_xp_function({func_name}, allow_dask_compute={n + 1})` "
+        "to allow for more (but note that this will harm performance). "
+    )
+
+    @wraps(func)
+    def wrapper(*args: P.args, **kwargs: P.kwargs) -> T:  # numpydoc ignore=GL08
+        scheduler = CountingDaskScheduler(n, msg)
+        with dask.config.set({"scheduler": scheduler}):  # pyright: ignore[reportPrivateImportUsage]
+            out = func(*args, **kwargs)
+
+        # Block until the graph materializes and reraise exceptions. This allows
+        # `pytest.raises` and `pytest.warns` to work as expected. Note that this would
+        # not work on scheduler='distributed', as it would not block.
+        arrays, rest = pickle_flatten(out, da.Array)
+        arrays = dask.persist(arrays, scheduler="threads")[0]  # type: ignore[attr-defined,no-untyped-call]  # pyright: ignore[reportPrivateImportUsage]
+        return pickle_unflatten(arrays, rest)  # pyright: ignore[reportUnknownArgumentType]
+
+    return wrapper
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/__init__.py
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index 0000000000000000000000000000000000000000..2654c8a3d21ed3db207f6204816d852e6b4c0efc
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/__init__.py
@@ -0,0 +1,20 @@
+from .main import minimize
+from .utils import show_versions
+
+# PEP0440 compatible formatted version, see:
+# https://www.python.org/dev/peps/pep-0440/
+#
+# Final release markers:
+#   X.Y.0   # For first release after an increment in Y
+#   X.Y.Z   # For bugfix releases
+#
+# Admissible pre-release markers:
+#   X.YaN   # Alpha release
+#   X.YbN   # Beta release
+#   X.YrcN  # Release Candidate
+#
+# Dev branch marker is: 'X.Y.dev' or 'X.Y.devN' where N is an integer.
+# 'X.Y.dev0' is the canonical version of 'X.Y.dev'.
+__version__ = "1.1.3"
+
+__all__ = ["minimize", "show_versions"]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/framework.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/framework.py
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index 0000000000000000000000000000000000000000..9afea66281067e27a486ff317a4bffa03ec3e68b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/framework.py
@@ -0,0 +1,1240 @@
+import warnings
+
+import numpy as np
+from scipy.optimize import lsq_linear
+
+from .models import Models, Quadratic
+from .settings import Options, Constants
+from .subsolvers import (
+    cauchy_geometry,
+    spider_geometry,
+    normal_byrd_omojokun,
+    tangential_byrd_omojokun,
+    constrained_tangential_byrd_omojokun,
+)
+from .subsolvers.optim import qr_tangential_byrd_omojokun
+from .utils import get_arrays_tol
+
+
+TINY = np.finfo(float).tiny
+EPS = np.finfo(float).eps
+
+
+class TrustRegion:
+    """
+    Trust-region framework.
+    """
+
+    def __init__(self, pb, options, constants):
+        """
+        Initialize the trust-region framework.
+
+        Parameters
+        ----------
+        pb : `cobyqa.problem.Problem`
+            Problem to solve.
+        options : dict
+            Options of the solver.
+        constants : dict
+            Constants of the solver.
+
+        Raises
+        ------
+        `cobyqa.utils.MaxEvalError`
+            If the maximum number of evaluations is reached.
+        `cobyqa.utils.TargetSuccess`
+            If a nearly feasible point has been found with an objective
+            function value below the target.
+        `cobyqa.utils.FeasibleSuccess`
+            If a feasible point has been found for a feasibility problem.
+        `numpy.linalg.LinAlgError`
+            If the initial interpolation system is ill-defined.
+        """
+        # Set the initial penalty parameter.
+        self._penalty = 0.0
+
+        # Initialize the models.
+        self._pb = pb
+        self._models = Models(self._pb, options, self.penalty)
+        self._constants = constants
+
+        # Set the index of the best interpolation point.
+        self._best_index = 0
+        self.set_best_index()
+
+        # Set the initial Lagrange multipliers.
+        self._lm_linear_ub = np.zeros(self.m_linear_ub)
+        self._lm_linear_eq = np.zeros(self.m_linear_eq)
+        self._lm_nonlinear_ub = np.zeros(self.m_nonlinear_ub)
+        self._lm_nonlinear_eq = np.zeros(self.m_nonlinear_eq)
+        self.set_multipliers(self.x_best)
+
+        # Set the initial trust-region radius and the resolution.
+        self._resolution = options[Options.RHOBEG]
+        self._radius = self.resolution
+
+    @property
+    def n(self):
+        """
+        Number of variables.
+
+        Returns
+        -------
+        int
+            Number of variables.
+        """
+        return self._pb.n
+
+    @property
+    def m_linear_ub(self):
+        """
+        Number of linear inequality constraints.
+
+        Returns
+        -------
+        int
+            Number of linear inequality constraints.
+        """
+        return self._pb.m_linear_ub
+
+    @property
+    def m_linear_eq(self):
+        """
+        Number of linear equality constraints.
+
+        Returns
+        -------
+        int
+            Number of linear equality constraints.
+        """
+        return self._pb.m_linear_eq
+
+    @property
+    def m_nonlinear_ub(self):
+        """
+        Number of nonlinear inequality constraints.
+
+        Returns
+        -------
+        int
+            Number of nonlinear inequality constraints.
+        """
+        return self._pb.m_nonlinear_ub
+
+    @property
+    def m_nonlinear_eq(self):
+        """
+        Number of nonlinear equality constraints.
+
+        Returns
+        -------
+        int
+            Number of nonlinear equality constraints.
+        """
+        return self._pb.m_nonlinear_eq
+
+    @property
+    def radius(self):
+        """
+        Trust-region radius.
+
+        Returns
+        -------
+        float
+            Trust-region radius.
+        """
+        return self._radius
+
+    @radius.setter
+    def radius(self, radius):
+        """
+        Set the trust-region radius.
+
+        Parameters
+        ----------
+        radius : float
+            New trust-region radius.
+        """
+        self._radius = radius
+        if (
+            self.radius
+            <= self._constants[Constants.DECREASE_RADIUS_THRESHOLD]
+            * self.resolution
+        ):
+            self._radius = self.resolution
+
+    @property
+    def resolution(self):
+        """
+        Resolution of the trust-region framework.
+
+        The resolution is a lower bound on the trust-region radius.
+
+        Returns
+        -------
+        float
+            Resolution of the trust-region framework.
+        """
+        return self._resolution
+
+    @resolution.setter
+    def resolution(self, resolution):
+        """
+        Set the resolution of the trust-region framework.
+
+        Parameters
+        ----------
+        resolution : float
+            New resolution of the trust-region framework.
+        """
+        self._resolution = resolution
+
+    @property
+    def penalty(self):
+        """
+        Penalty parameter.
+
+        Returns
+        -------
+        float
+            Penalty parameter.
+        """
+        return self._penalty
+
+    @property
+    def models(self):
+        """
+        Models of the objective function and constraints.
+
+        Returns
+        -------
+        `cobyqa.models.Models`
+            Models of the objective function and constraints.
+        """
+        return self._models
+
+    @property
+    def best_index(self):
+        """
+        Index of the best interpolation point.
+
+        Returns
+        -------
+        int
+            Index of the best interpolation point.
+        """
+        return self._best_index
+
+    @property
+    def x_best(self):
+        """
+        Best interpolation point.
+
+        Its value is interpreted as relative to the origin, not the base point.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Best interpolation point.
+        """
+        return self.models.interpolation.point(self.best_index)
+
+    @property
+    def fun_best(self):
+        """
+        Value of the objective function at `x_best`.
+
+        Returns
+        -------
+        float
+            Value of the objective function at `x_best`.
+        """
+        return self.models.fun_val[self.best_index]
+
+    @property
+    def cub_best(self):
+        """
+        Values of the nonlinear inequality constraints at `x_best`.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m_nonlinear_ub,)
+            Values of the nonlinear inequality constraints at `x_best`.
+        """
+        return self.models.cub_val[self.best_index, :]
+
+    @property
+    def ceq_best(self):
+        """
+        Values of the nonlinear equality constraints at `x_best`.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m_nonlinear_eq,)
+            Values of the nonlinear equality constraints at `x_best`.
+        """
+        return self.models.ceq_val[self.best_index, :]
+
+    def lag_model(self, x):
+        """
+        Evaluate the Lagrangian model at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which the Lagrangian model is evaluated.
+
+        Returns
+        -------
+        float
+            Value of the Lagrangian model at `x`.
+        """
+        return (
+            self.models.fun(x)
+            + self._lm_linear_ub
+            @ (self._pb.linear.a_ub @ x - self._pb.linear.b_ub)
+            + self._lm_linear_eq
+            @ (self._pb.linear.a_eq @ x - self._pb.linear.b_eq)
+            + self._lm_nonlinear_ub @ self.models.cub(x)
+            + self._lm_nonlinear_eq @ self.models.ceq(x)
+        )
+
+    def lag_model_grad(self, x):
+        """
+        Evaluate the gradient of the Lagrangian model at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which the gradient of the Lagrangian model is evaluated.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Gradient of the Lagrangian model at `x`.
+        """
+        return (
+            self.models.fun_grad(x)
+            + self._lm_linear_ub @ self._pb.linear.a_ub
+            + self._lm_linear_eq @ self._pb.linear.a_eq
+            + self._lm_nonlinear_ub @ self.models.cub_grad(x)
+            + self._lm_nonlinear_eq @ self.models.ceq_grad(x)
+        )
+
+    def lag_model_hess(self):
+        """
+        Evaluate the Hessian matrix of the Lagrangian model at a given point.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n, n)
+            Hessian matrix of the Lagrangian model at `x`.
+        """
+        hess = self.models.fun_hess()
+        if self.m_nonlinear_ub > 0:
+            hess += self._lm_nonlinear_ub @ self.models.cub_hess()
+        if self.m_nonlinear_eq > 0:
+            hess += self._lm_nonlinear_eq @ self.models.ceq_hess()
+        return hess
+
+    def lag_model_hess_prod(self, v):
+        """
+        Evaluate the right product of the Hessian matrix of the Lagrangian
+        model with a given vector.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Vector with which the Hessian matrix of the Lagrangian model is
+            multiplied from the right.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Right product of the Hessian matrix of the Lagrangian model with
+            `v`.
+        """
+        return (
+            self.models.fun_hess_prod(v)
+            + self._lm_nonlinear_ub @ self.models.cub_hess_prod(v)
+            + self._lm_nonlinear_eq @ self.models.ceq_hess_prod(v)
+        )
+
+    def lag_model_curv(self, v):
+        """
+        Evaluate the curvature of the Lagrangian model along a given direction.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Direction along which the curvature of the Lagrangian model is
+            evaluated.
+
+        Returns
+        -------
+        float
+            Curvature of the Lagrangian model along `v`.
+        """
+        return (
+            self.models.fun_curv(v)
+            + self._lm_nonlinear_ub @ self.models.cub_curv(v)
+            + self._lm_nonlinear_eq @ self.models.ceq_curv(v)
+        )
+
+    def sqp_fun(self, step):
+        """
+        Evaluate the objective function of the SQP subproblem.
+
+        Parameters
+        ----------
+        step : `numpy.ndarray`, shape (n,)
+            Step along which the objective function of the SQP subproblem is
+            evaluated.
+
+        Returns
+        -------
+        float
+            Value of the objective function of the SQP subproblem along `step`.
+        """
+        return step @ (
+            self.models.fun_grad(self.x_best)
+            + 0.5 * self.lag_model_hess_prod(step)
+        )
+
+    def sqp_cub(self, step):
+        """
+        Evaluate the linearization of the nonlinear inequality constraints.
+
+        Parameters
+        ----------
+        step : `numpy.ndarray`, shape (n,)
+            Step along which the linearization of the nonlinear inequality
+            constraints is evaluated.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m_nonlinear_ub,)
+            Value of the linearization of the nonlinear inequality constraints
+            along `step`.
+        """
+        return (
+            self.models.cub(self.x_best)
+            + self.models.cub_grad(self.x_best) @ step
+        )
+
+    def sqp_ceq(self, step):
+        """
+        Evaluate the linearization of the nonlinear equality constraints.
+
+        Parameters
+        ----------
+        step : `numpy.ndarray`, shape (n,)
+            Step along which the linearization of the nonlinear equality
+            constraints is evaluated.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m_nonlinear_ub,)
+            Value of the linearization of the nonlinear equality constraints
+            along `step`.
+        """
+        return (
+            self.models.ceq(self.x_best)
+            + self.models.ceq_grad(self.x_best) @ step
+        )
+
+    def merit(self, x, fun_val=None, cub_val=None, ceq_val=None):
+        """
+        Evaluate the merit function at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which the merit function is evaluated.
+        fun_val : float, optional
+            Value of the objective function at `x`. If not provided, the
+            objective function is evaluated at `x`.
+        cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,), optional
+            Values of the nonlinear inequality constraints. If not provided,
+            the nonlinear inequality constraints are evaluated at `x`.
+        ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,), optional
+            Values of the nonlinear equality constraints. If not provided,
+            the nonlinear equality constraints are evaluated at `x`.
+
+        Returns
+        -------
+        float
+            Value of the merit function at `x`.
+        """
+        if fun_val is None or cub_val is None or ceq_val is None:
+            fun_val, cub_val, ceq_val = self._pb(x, self.penalty)
+        m_val = fun_val
+        if self._penalty > 0.0:
+            c_val = self._pb.violation(x, cub_val=cub_val, ceq_val=ceq_val)
+            if np.count_nonzero(c_val):
+                m_val += self._penalty * np.linalg.norm(c_val)
+        return m_val
+
+    def get_constraint_linearizations(self, x):
+        """
+        Get the linearizations of the constraints at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which the linearizations of the constraints are evaluated.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m_linear_ub + m_nonlinear_ub, n)
+            Left-hand side matrix of the linearized inequality constraints.
+        `numpy.ndarray`, shape (m_linear_ub + m_nonlinear_ub,)
+            Right-hand side vector of the linearized inequality constraints.
+        `numpy.ndarray`, shape (m_linear_eq + m_nonlinear_eq, n)
+            Left-hand side matrix of the linearized equality constraints.
+        `numpy.ndarray`, shape (m_linear_eq + m_nonlinear_eq,)
+            Right-hand side vector of the linearized equality constraints.
+        """
+        aub = np.block(
+            [
+                [self._pb.linear.a_ub],
+                [self.models.cub_grad(x)],
+            ]
+        )
+        bub = np.block(
+            [
+                self._pb.linear.b_ub - self._pb.linear.a_ub @ x,
+                -self.models.cub(x),
+            ]
+        )
+        aeq = np.block(
+            [
+                [self._pb.linear.a_eq],
+                [self.models.ceq_grad(x)],
+            ]
+        )
+        beq = np.block(
+            [
+                self._pb.linear.b_eq - self._pb.linear.a_eq @ x,
+                -self.models.ceq(x),
+            ]
+        )
+        return aub, bub, aeq, beq
+
+    def get_trust_region_step(self, options):
+        """
+        Get the trust-region step.
+
+        The trust-region step is computed by solving the derivative-free
+        trust-region SQP subproblem using a Byrd-Omojokun composite-step
+        approach. For more details, see Section 5.2.3 of [1]_.
+
+        Parameters
+        ----------
+        options : dict
+            Options of the solver.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Normal step.
+        `numpy.ndarray`, shape (n,)
+            Tangential step.
+
+        References
+        ----------
+        .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization
+           Methods and Software*. PhD thesis, Department of Applied
+           Mathematics, The Hong Kong Polytechnic University, Hong Kong, China,
+           2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294.
+        """
+        # Evaluate the linearizations of the constraints.
+        aub, bub, aeq, beq = self.get_constraint_linearizations(self.x_best)
+        xl = self._pb.bounds.xl - self.x_best
+        xu = self._pb.bounds.xu - self.x_best
+
+        # Evaluate the normal step.
+        radius = self._constants[Constants.BYRD_OMOJOKUN_FACTOR] * self.radius
+        normal_step = normal_byrd_omojokun(
+            aub,
+            bub,
+            aeq,
+            beq,
+            xl,
+            xu,
+            radius,
+            options[Options.DEBUG],
+            **self._constants,
+        )
+        if options[Options.DEBUG]:
+            tol = get_arrays_tol(xl, xu)
+            if (np.any(normal_step + tol < xl)
+                    or np.any(xu < normal_step - tol)):
+                warnings.warn(
+                    "the normal step does not respect the bound constraint.",
+                    RuntimeWarning,
+                    2,
+                )
+            if np.linalg.norm(normal_step) > 1.1 * radius:
+                warnings.warn(
+                    "the normal step does not respect the trust-region "
+                    "constraint.",
+                    RuntimeWarning,
+                    2,
+                )
+
+        # Evaluate the tangential step.
+        radius = np.sqrt(self.radius**2.0 - normal_step @ normal_step)
+        xl -= normal_step
+        xu -= normal_step
+        bub = np.maximum(bub - aub @ normal_step, 0.0)
+        g_best = self.models.fun_grad(self.x_best) + self.lag_model_hess_prod(
+            normal_step
+        )
+        if self._pb.type in ["unconstrained", "bound-constrained"]:
+            tangential_step = tangential_byrd_omojokun(
+                g_best,
+                self.lag_model_hess_prod,
+                xl,
+                xu,
+                radius,
+                options[Options.DEBUG],
+                **self._constants,
+            )
+        else:
+            tangential_step = constrained_tangential_byrd_omojokun(
+                g_best,
+                self.lag_model_hess_prod,
+                xl,
+                xu,
+                aub,
+                bub,
+                aeq,
+                radius,
+                options["debug"],
+                **self._constants,
+            )
+        if options[Options.DEBUG]:
+            tol = get_arrays_tol(xl, xu)
+            if np.any(tangential_step + tol < xl) or np.any(
+                xu < tangential_step - tol
+            ):
+                warnings.warn(
+                    "The tangential step does not respect the bound "
+                    "constraints.",
+                    RuntimeWarning,
+                    2,
+                )
+            if (
+                np.linalg.norm(normal_step + tangential_step)
+                > 1.1 * np.sqrt(2.0) * self.radius
+            ):
+                warnings.warn(
+                    "The trial step does not respect the trust-region "
+                    "constraint.",
+                    RuntimeWarning,
+                    2,
+                )
+        return normal_step, tangential_step
+
+    def get_geometry_step(self, k_new, options):
+        """
+        Get the geometry-improving step.
+
+        Three different geometry-improving steps are computed and the best one
+        is returned. For more details, see Section 5.2.7 of [1]_.
+
+        Parameters
+        ----------
+        k_new : int
+            Index of the interpolation point to be modified.
+        options : dict
+            Options of the solver.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Geometry-improving step.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the computation of a determinant fails.
+
+        References
+        ----------
+        .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization
+           Methods and Software*. PhD thesis, Department of Applied
+           Mathematics, The Hong Kong Polytechnic University, Hong Kong, China,
+           2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294.
+        """
+        if options[Options.DEBUG]:
+            assert (
+                k_new != self.best_index
+            ), "The index `k_new` must be different from the best index."
+
+        # Build the k_new-th Lagrange polynomial.
+        coord_vec = np.squeeze(np.eye(1, self.models.npt, k_new))
+        lag = Quadratic(
+            self.models.interpolation,
+            coord_vec,
+            options[Options.DEBUG],
+        )
+        g_lag = lag.grad(self.x_best, self.models.interpolation)
+
+        # Compute a simple constrained Cauchy step.
+        xl = self._pb.bounds.xl - self.x_best
+        xu = self._pb.bounds.xu - self.x_best
+        step = cauchy_geometry(
+            0.0,
+            g_lag,
+            lambda v: lag.curv(v, self.models.interpolation),
+            xl,
+            xu,
+            self.radius,
+            options[Options.DEBUG],
+        )
+        sigma = self.models.determinants(self.x_best + step, k_new)
+
+        # Compute the solution on the straight lines joining the interpolation
+        # points to the k-th one, and choose it if it provides a larger value
+        # of the determinant of the interpolation system in absolute value.
+        xpt = (
+            self.models.interpolation.xpt
+            - self.models.interpolation.xpt[:, self.best_index, np.newaxis]
+        )
+        xpt[:, [0, self.best_index]] = xpt[:, [self.best_index, 0]]
+        step_alt = spider_geometry(
+            0.0,
+            g_lag,
+            lambda v: lag.curv(v, self.models.interpolation),
+            xpt[:, 1:],
+            xl,
+            xu,
+            self.radius,
+            options[Options.DEBUG],
+        )
+        sigma_alt = self.models.determinants(self.x_best + step_alt, k_new)
+        if abs(sigma_alt) > abs(sigma):
+            step = step_alt
+            sigma = sigma_alt
+
+        # Compute a Cauchy step on the tangent space of the active constraints.
+        if self._pb.type in [
+            "linearly constrained",
+            "nonlinearly constrained",
+        ]:
+            aub, bub, aeq, beq = (
+                self.get_constraint_linearizations(self.x_best))
+            tol_bd = get_arrays_tol(xl, xu)
+            tol_ub = get_arrays_tol(bub)
+            free_xl = xl <= -tol_bd
+            free_xu = xu >= tol_bd
+            free_ub = bub >= tol_ub
+
+            # Compute the Cauchy step.
+            n_act, q = qr_tangential_byrd_omojokun(
+                aub,
+                aeq,
+                free_xl,
+                free_xu,
+                free_ub,
+            )
+            g_lag_proj = q[:, n_act:] @ (q[:, n_act:].T @ g_lag)
+            norm_g_lag_proj = np.linalg.norm(g_lag_proj)
+            if 0 < n_act < self._pb.n and norm_g_lag_proj > TINY * self.radius:
+                step_alt = (self.radius / norm_g_lag_proj) * g_lag_proj
+                if lag.curv(step_alt, self.models.interpolation) < 0.0:
+                    step_alt = -step_alt
+
+                # Evaluate the constraint violation at the Cauchy step.
+                cbd = np.block([xl - step_alt, step_alt - xu])
+                cub = aub @ step_alt - bub
+                ceq = aeq @ step_alt - beq
+                maxcv_val = max(
+                    np.max(array, initial=0.0)
+                    for array in [cbd, cub, np.abs(ceq)]
+                )
+
+                # Accept the new step if it is nearly feasible and do not
+                # drastically worsen the determinant of the interpolation
+                # system in absolute value.
+                tol = np.max(np.abs(step_alt[~free_xl]), initial=0.0)
+                tol = np.max(np.abs(step_alt[~free_xu]), initial=tol)
+                tol = np.max(np.abs(aub[~free_ub, :] @ step_alt), initial=tol)
+                tol = min(10.0 * tol, 1e-2 * np.linalg.norm(step_alt))
+                if maxcv_val <= tol:
+                    sigma_alt = self.models.determinants(
+                        self.x_best + step_alt, k_new
+                    )
+                    if abs(sigma_alt) >= 0.1 * abs(sigma):
+                        step = np.clip(step_alt, xl, xu)
+
+        if options[Options.DEBUG]:
+            tol = get_arrays_tol(xl, xu)
+            if np.any(step + tol < xl) or np.any(xu < step - tol):
+                warnings.warn(
+                    "The geometry step does not respect the bound "
+                    "constraints.",
+                    RuntimeWarning,
+                    2,
+                )
+            if np.linalg.norm(step) > 1.1 * self.radius:
+                warnings.warn(
+                    "The geometry step does not respect the "
+                    "trust-region constraint.",
+                    RuntimeWarning,
+                    2,
+                )
+        return step
+
+    def get_second_order_correction_step(self, step, options):
+        """
+        Get the second-order correction step.
+
+        Parameters
+        ----------
+        step : `numpy.ndarray`, shape (n,)
+            Trust-region step.
+        options : dict
+            Options of the solver.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Second-order correction step.
+        """
+        # Evaluate the linearizations of the constraints.
+        aub, bub, aeq, beq = self.get_constraint_linearizations(self.x_best)
+        xl = self._pb.bounds.xl - self.x_best
+        xu = self._pb.bounds.xu - self.x_best
+        radius = np.linalg.norm(step)
+        soc_step = normal_byrd_omojokun(
+            aub,
+            bub,
+            aeq,
+            beq,
+            xl,
+            xu,
+            radius,
+            options[Options.DEBUG],
+            **self._constants,
+        )
+        if options[Options.DEBUG]:
+            tol = get_arrays_tol(xl, xu)
+            if np.any(soc_step + tol < xl) or np.any(xu < soc_step - tol):
+                warnings.warn(
+                    "The second-order correction step does not "
+                    "respect the bound constraints.",
+                    RuntimeWarning,
+                    2,
+                )
+            if np.linalg.norm(soc_step) > 1.1 * radius:
+                warnings.warn(
+                    "The second-order correction step does not "
+                    "respect the trust-region constraint.",
+                    RuntimeWarning,
+                    2,
+                )
+        return soc_step
+
+    def get_reduction_ratio(self, step, fun_val, cub_val, ceq_val):
+        """
+        Get the reduction ratio.
+
+        Parameters
+        ----------
+        step : `numpy.ndarray`, shape (n,)
+            Trust-region step.
+        fun_val : float
+            Objective function value at the trial point.
+        cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,)
+            Nonlinear inequality constraint values at the trial point.
+        ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,)
+            Nonlinear equality constraint values at the trial point.
+
+        Returns
+        -------
+        float
+            Reduction ratio.
+        """
+        merit_old = self.merit(
+            self.x_best,
+            self.fun_best,
+            self.cub_best,
+            self.ceq_best,
+        )
+        merit_new = self.merit(self.x_best + step, fun_val, cub_val, ceq_val)
+        merit_model_old = self.merit(
+            self.x_best,
+            0.0,
+            self.models.cub(self.x_best),
+            self.models.ceq(self.x_best),
+        )
+        merit_model_new = self.merit(
+            self.x_best + step,
+            self.sqp_fun(step),
+            self.sqp_cub(step),
+            self.sqp_ceq(step),
+        )
+        if abs(merit_model_old - merit_model_new) > TINY * abs(
+            merit_old - merit_new
+        ):
+            return (merit_old - merit_new) / abs(
+                merit_model_old - merit_model_new
+            )
+        else:
+            return -1.0
+
+    def increase_penalty(self, step):
+        """
+        Increase the penalty parameter.
+
+        Parameters
+        ----------
+        step : `numpy.ndarray`, shape (n,)
+            Trust-region step.
+        """
+        aub, bub, aeq, beq = self.get_constraint_linearizations(self.x_best)
+        viol_diff = max(
+            np.linalg.norm(
+                np.block(
+                    [
+                        np.maximum(0.0, -bub),
+                        beq,
+                    ]
+                )
+            )
+            - np.linalg.norm(
+                np.block(
+                    [
+                        np.maximum(0.0, aub @ step - bub),
+                        aeq @ step - beq,
+                    ]
+                )
+            ),
+            0.0,
+        )
+        sqp_val = self.sqp_fun(step)
+
+        threshold = np.linalg.norm(
+            np.block(
+                [
+                    self._lm_linear_ub,
+                    self._lm_linear_eq,
+                    self._lm_nonlinear_ub,
+                    self._lm_nonlinear_eq,
+                ]
+            )
+        )
+        if abs(viol_diff) > TINY * abs(sqp_val):
+            threshold = max(threshold, sqp_val / viol_diff)
+        best_index_save = self.best_index
+        if (
+            self._penalty
+            <= self._constants[Constants.PENALTY_INCREASE_THRESHOLD]
+                * threshold
+        ):
+            self._penalty = max(
+                self._constants[Constants.PENALTY_INCREASE_FACTOR] * threshold,
+                1.0,
+            )
+            self.set_best_index()
+        return best_index_save == self.best_index
+
+    def decrease_penalty(self):
+        """
+        Decrease the penalty parameter.
+        """
+        self._penalty = min(self._penalty, self._get_low_penalty())
+        self.set_best_index()
+
+    def set_best_index(self):
+        """
+        Set the index of the best point.
+        """
+        best_index = self.best_index
+        m_best = self.merit(
+            self.x_best,
+            self.models.fun_val[best_index],
+            self.models.cub_val[best_index, :],
+            self.models.ceq_val[best_index, :],
+        )
+        r_best = self._pb.maxcv(
+            self.x_best,
+            self.models.cub_val[best_index, :],
+            self.models.ceq_val[best_index, :],
+        )
+        tol = (
+            10.0
+            * EPS
+            * max(self.models.n, self.models.npt)
+            * max(abs(m_best), 1.0)
+        )
+        for k in range(self.models.npt):
+            if k != self.best_index:
+                x_val = self.models.interpolation.point(k)
+                m_val = self.merit(
+                    x_val,
+                    self.models.fun_val[k],
+                    self.models.cub_val[k, :],
+                    self.models.ceq_val[k, :],
+                )
+                r_val = self._pb.maxcv(
+                    x_val,
+                    self.models.cub_val[k, :],
+                    self.models.ceq_val[k, :],
+                )
+                if m_val < m_best or (m_val < m_best + tol and r_val < r_best):
+                    best_index = k
+                    m_best = m_val
+                    r_best = r_val
+        self._best_index = best_index
+
+    def get_index_to_remove(self, x_new=None):
+        """
+        Get the index of the interpolation point to remove.
+
+        If `x_new` is not provided, the index returned should be used during
+        the geometry-improvement phase. Otherwise, the index returned is the
+        best index for included `x_new` in the interpolation set.
+
+        Parameters
+        ----------
+        x_new : `numpy.ndarray`, shape (n,), optional
+            New point to be included in the interpolation set.
+
+        Returns
+        -------
+        int
+            Index of the interpolation point to remove.
+        float
+            Distance between `x_best` and the removed point.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the computation of a determinant fails.
+        """
+        dist_sq = np.sum(
+            (
+                self.models.interpolation.xpt
+                - self.models.interpolation.xpt[:, self.best_index, np.newaxis]
+            )
+            ** 2.0,
+            axis=0,
+        )
+        if x_new is None:
+            sigma = 1.0
+            weights = dist_sq
+        else:
+            sigma = self.models.determinants(x_new)
+            weights = (
+                np.maximum(
+                    1.0,
+                    dist_sq
+                    / max(
+                        self._constants[Constants.LOW_RADIUS_FACTOR]
+                        * self.radius,
+                        self.resolution,
+                    )
+                    ** 2.0,
+                )
+                ** 3.0
+            )
+            weights[self.best_index] = -1.0  # do not remove the best point
+        k_max = np.argmax(weights * np.abs(sigma))
+        return k_max, np.sqrt(dist_sq[k_max])
+
+    def update_radius(self, step, ratio):
+        """
+        Update the trust-region radius.
+
+        Parameters
+        ----------
+        step : `numpy.ndarray`, shape (n,)
+            Trust-region step.
+        ratio : float
+            Reduction ratio.
+        """
+        s_norm = np.linalg.norm(step)
+        if ratio <= self._constants[Constants.LOW_RATIO]:
+            self.radius *= self._constants[Constants.DECREASE_RADIUS_FACTOR]
+        elif ratio <= self._constants[Constants.HIGH_RATIO]:
+            self.radius = max(
+                self._constants[Constants.DECREASE_RADIUS_FACTOR]
+                * self.radius,
+                s_norm,
+            )
+        else:
+            self.radius = min(
+                self._constants[Constants.INCREASE_RADIUS_FACTOR]
+                * self.radius,
+                max(
+                    self._constants[Constants.DECREASE_RADIUS_FACTOR]
+                    * self.radius,
+                    self._constants[Constants.INCREASE_RADIUS_THRESHOLD]
+                    * s_norm,
+                ),
+            )
+
+    def enhance_resolution(self, options):
+        """
+        Enhance the resolution of the trust-region framework.
+
+        Parameters
+        ----------
+        options : dict
+            Options of the solver.
+        """
+        if (
+            self._constants[Constants.LARGE_RESOLUTION_THRESHOLD]
+            * options[Options.RHOEND]
+            < self.resolution
+        ):
+            self.resolution *= self._constants[
+                Constants.DECREASE_RESOLUTION_FACTOR
+            ]
+        elif (
+            self._constants[Constants.MODERATE_RESOLUTION_THRESHOLD]
+            * options[Options.RHOEND]
+            < self.resolution
+        ):
+            self.resolution = np.sqrt(self.resolution
+                                      * options[Options.RHOEND])
+        else:
+            self.resolution = options[Options.RHOEND]
+
+        # Reduce the trust-region radius.
+        self._radius = max(
+            self._constants[Constants.DECREASE_RADIUS_FACTOR] * self._radius,
+            self.resolution,
+        )
+
+    def shift_x_base(self, options):
+        """
+        Shift the base point to `x_best`.
+
+        Parameters
+        ----------
+        options : dict
+            Options of the solver.
+        """
+        self.models.shift_x_base(np.copy(self.x_best), options)
+
+    def set_multipliers(self, x):
+        """
+        Set the Lagrange multipliers.
+
+        This method computes and set the Lagrange multipliers of the linear and
+        nonlinear constraints to be the QP multipliers.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which the Lagrange multipliers are computed.
+        """
+        # Build the constraints of the least-squares problem.
+        incl_linear_ub = self._pb.linear.a_ub @ x >= self._pb.linear.b_ub
+        incl_nonlinear_ub = self.cub_best >= 0.0
+        incl_xl = self._pb.bounds.xl >= x
+        incl_xu = self._pb.bounds.xu <= x
+        m_linear_ub = np.count_nonzero(incl_linear_ub)
+        m_nonlinear_ub = np.count_nonzero(incl_nonlinear_ub)
+        m_xl = np.count_nonzero(incl_xl)
+        m_xu = np.count_nonzero(incl_xu)
+
+        if (
+            m_linear_ub + m_nonlinear_ub + self.m_linear_eq
+                + self.m_nonlinear_eq > 0
+        ):
+            identity = np.eye(self._pb.n)
+            c_jac = np.r_[
+                -identity[incl_xl, :],
+                identity[incl_xu, :],
+                self._pb.linear.a_ub[incl_linear_ub, :],
+                self.models.cub_grad(x, incl_nonlinear_ub),
+                self._pb.linear.a_eq,
+                self.models.ceq_grad(x),
+            ]
+
+            # Solve the least-squares problem.
+            g_best = self.models.fun_grad(x)
+            xl_lm = np.full(c_jac.shape[0], -np.inf)
+            xl_lm[: m_xl + m_xu + m_linear_ub + m_nonlinear_ub] = 0.0
+            res = lsq_linear(
+                c_jac.T,
+                -g_best,
+                bounds=(xl_lm, np.inf),
+                method="bvls",
+            )
+
+            # Extract the Lagrange multipliers.
+            self._lm_linear_ub[incl_linear_ub] = res.x[
+                m_xl + m_xu:m_xl + m_xu + m_linear_ub
+            ]
+            self._lm_linear_ub[~incl_linear_ub] = 0.0
+            self._lm_nonlinear_ub[incl_nonlinear_ub] = res.x[
+                m_xl
+                + m_xu
+                + m_linear_ub:m_xl
+                + m_xu
+                + m_linear_ub
+                + m_nonlinear_ub
+            ]
+            self._lm_nonlinear_ub[~incl_nonlinear_ub] = 0.0
+            self._lm_linear_eq[:] = res.x[
+                m_xl
+                + m_xu
+                + m_linear_ub
+                + m_nonlinear_ub:m_xl
+                + m_xu
+                + m_linear_ub
+                + m_nonlinear_ub
+                + self.m_linear_eq
+            ]
+            self._lm_nonlinear_eq[:] = res.x[
+                m_xl + m_xu + m_linear_ub + m_nonlinear_ub + self.m_linear_eq:
+            ]
+
+    def _get_low_penalty(self):
+        r_val_ub = np.c_[
+            (
+                self.models.interpolation.x_base[np.newaxis, :]
+                + self.models.interpolation.xpt.T
+            )
+            @ self._pb.linear.a_ub.T
+            - self._pb.linear.b_ub[np.newaxis, :],
+            self.models.cub_val,
+        ]
+        r_val_eq = (
+            self.models.interpolation.x_base[np.newaxis, :]
+            + self.models.interpolation.xpt.T
+        ) @ self._pb.linear.a_eq.T - self._pb.linear.b_eq[np.newaxis, :]
+        r_val_eq = np.block(
+            [
+                r_val_eq,
+                -r_val_eq,
+                self.models.ceq_val,
+                -self.models.ceq_val,
+            ]
+        )
+        r_val = np.block([r_val_ub, r_val_eq])
+        c_min = np.nanmin(r_val, axis=0)
+        c_max = np.nanmax(r_val, axis=0)
+        indices = (
+            c_min
+            < self._constants[Constants.THRESHOLD_RATIO_CONSTRAINTS] * c_max
+        )
+        if np.any(indices):
+            f_min = np.nanmin(self.models.fun_val)
+            f_max = np.nanmax(self.models.fun_val)
+            c_min_neg = np.minimum(0.0, c_min[indices])
+            c_diff = np.min(c_max[indices] - c_min_neg)
+            if c_diff > TINY * (f_max - f_min):
+                penalty = (f_max - f_min) / c_diff
+            else:
+                penalty = np.inf
+        else:
+            penalty = 0.0
+        return penalty
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/main.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/main.py
new file mode 100644
index 0000000000000000000000000000000000000000..01e5159e0dfebed9a78c6948cb99bfb1d744b6c7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/main.py
@@ -0,0 +1,1506 @@
+import warnings
+
+import numpy as np
+from scipy.optimize import (
+    Bounds,
+    LinearConstraint,
+    NonlinearConstraint,
+    OptimizeResult,
+)
+
+from .framework import TrustRegion
+from .problem import (
+    ObjectiveFunction,
+    BoundConstraints,
+    LinearConstraints,
+    NonlinearConstraints,
+    Problem,
+)
+from .utils import (
+    MaxEvalError,
+    TargetSuccess,
+    CallbackSuccess,
+    FeasibleSuccess,
+    exact_1d_array,
+)
+from .settings import (
+    ExitStatus,
+    Options,
+    Constants,
+    DEFAULT_OPTIONS,
+    DEFAULT_CONSTANTS,
+    PRINT_OPTIONS,
+)
+
+
+def minimize(
+    fun,
+    x0,
+    args=(),
+    bounds=None,
+    constraints=(),
+    callback=None,
+    options=None,
+    **kwargs,
+):
+    r"""
+    Minimize a scalar function using the COBYQA method.
+
+    The Constrained Optimization BY Quadratic Approximations (COBYQA) method is
+    a derivative-free optimization method designed to solve general nonlinear
+    optimization problems. A complete description of COBYQA is given in [3]_.
+
+    Parameters
+    ----------
+    fun : {callable, None}
+        Objective function to be minimized.
+
+            ``fun(x, *args) -> float``
+
+        where ``x`` is an array with shape (n,) and `args` is a tuple. If `fun`
+        is ``None``, the objective function is assumed to be the zero function,
+        resulting in a feasibility problem.
+    x0 : array_like, shape (n,)
+        Initial guess.
+    args : tuple, optional
+        Extra arguments passed to the objective function.
+    bounds : {`scipy.optimize.Bounds`, array_like, shape (n, 2)}, optional
+        Bound constraints of the problem. It can be one of the cases below.
+
+        #. An instance of `scipy.optimize.Bounds`. For the time being, the
+           argument ``keep_feasible`` is disregarded, and all the constraints
+           are considered unrelaxable and will be enforced.
+        #. An array with shape (n, 2). The bound constraints for ``x[i]`` are
+           ``bounds[i][0] <= x[i] <= bounds[i][1]``. Set ``bounds[i][0]`` to
+           :math:`-\infty` if there is no lower bound, and set ``bounds[i][1]``
+           to :math:`\infty` if there is no upper bound.
+
+        The COBYQA method always respect the bound constraints.
+    constraints : {Constraint, list}, optional
+        General constraints of the problem. It can be one of the cases below.
+
+        #. An instance of `scipy.optimize.LinearConstraint`. The argument
+           ``keep_feasible`` is disregarded.
+        #. An instance of `scipy.optimize.NonlinearConstraint`. The arguments
+           ``jac``, ``hess``, ``keep_feasible``, ``finite_diff_rel_step``, and
+           ``finite_diff_jac_sparsity`` are disregarded.
+
+        #. A list, each of whose elements are described in the cases above.
+
+    callback : callable, optional
+        A callback executed at each objective function evaluation. The method
+        terminates if a ``StopIteration`` exception is raised by the callback
+        function. Its signature can be one of the following:
+
+            ``callback(intermediate_result)``
+
+        where ``intermediate_result`` is a keyword parameter that contains an
+        instance of `scipy.optimize.OptimizeResult`, with attributes ``x``
+        and ``fun``, being the point at which the objective function is
+        evaluated and the value of the objective function, respectively. The
+        name of the parameter must be ``intermediate_result`` for the callback
+        to be passed an instance of `scipy.optimize.OptimizeResult`.
+
+        Alternatively, the callback function can have the signature:
+
+            ``callback(xk)``
+
+        where ``xk`` is the point at which the objective function is evaluated.
+        Introspection is used to determine which of the signatures to invoke.
+    options : dict, optional
+        Options passed to the solver. Accepted keys are:
+
+            disp : bool, optional
+                Whether to print information about the optimization procedure.
+                Default is ``False``.
+            maxfev : int, optional
+                Maximum number of function evaluations. Default is ``500 * n``.
+            maxiter : int, optional
+                Maximum number of iterations. Default is ``1000 * n``.
+            target : float, optional
+                Target on the objective function value. The optimization
+                procedure is terminated when the objective function value of a
+                feasible point is less than or equal to this target. Default is
+                ``-numpy.inf``.
+            feasibility_tol : float, optional
+                Tolerance on the constraint violation. If the maximum
+                constraint violation at a point is less than or equal to this
+                tolerance, the point is considered feasible. Default is
+                ``numpy.sqrt(numpy.finfo(float).eps)``.
+            radius_init : float, optional
+                Initial trust-region radius. Typically, this value should be in
+                the order of one tenth of the greatest expected change to `x0`.
+                Default is ``1.0``.
+            radius_final : float, optional
+                Final trust-region radius. It should indicate the accuracy
+                required in the final values of the variables. Default is
+                ``1e-6``.
+            nb_points : int, optional
+                Number of interpolation points used to build the quadratic
+                models of the objective and constraint functions. Default is
+                ``2 * n + 1``.
+            scale : bool, optional
+                Whether to scale the variables according to the bounds. Default
+                is ``False``.
+            filter_size : int, optional
+                Maximum number of points in the filter. The filter is used to
+                select the best point returned by the optimization procedure.
+                Default is ``sys.maxsize``.
+            store_history : bool, optional
+                Whether to store the history of the function evaluations.
+                Default is ``False``.
+            history_size : int, optional
+                Maximum number of function evaluations to store in the history.
+                Default is ``sys.maxsize``.
+            debug : bool, optional
+                Whether to perform additional checks during the optimization
+                procedure. This option should be used only for debugging
+                purposes and is highly discouraged to general users. Default is
+                ``False``.
+
+        Other constants (from the keyword arguments) are described below. They
+        are not intended to be changed by general users. They should only be
+        changed by users with a deep understanding of the algorithm, who want
+        to experiment with different settings.
+
+    Returns
+    -------
+    `scipy.optimize.OptimizeResult`
+        Result of the optimization procedure, with the following fields:
+
+            message : str
+                Description of the cause of the termination.
+            success : bool
+                Whether the optimization procedure terminated successfully.
+            status : int
+                Termination status of the optimization procedure.
+            x : `numpy.ndarray`, shape (n,)
+                Solution point.
+            fun : float
+                Objective function value at the solution point.
+            maxcv : float
+                Maximum constraint violation at the solution point.
+            nfev : int
+                Number of function evaluations.
+            nit : int
+                Number of iterations.
+
+        If ``store_history`` is True, the result also has the following fields:
+
+            fun_history : `numpy.ndarray`, shape (nfev,)
+                History of the objective function values.
+            maxcv_history : `numpy.ndarray`, shape (nfev,)
+                History of the maximum constraint violations.
+
+        A description of the termination statuses is given below.
+
+        .. list-table::
+            :widths: 25 75
+            :header-rows: 1
+
+            * - Exit status
+              - Description
+            * - 0
+              - The lower bound for the trust-region radius has been reached.
+            * - 1
+              - The target objective function value has been reached.
+            * - 2
+              - All variables are fixed by the bound constraints.
+            * - 3
+              - The callback requested to stop the optimization procedure.
+            * - 4
+              - The feasibility problem received has been solved successfully.
+            * - 5
+              - The maximum number of function evaluations has been exceeded.
+            * - 6
+              - The maximum number of iterations has been exceeded.
+            * - -1
+              - The bound constraints are infeasible.
+            * - -2
+              - A linear algebra error occurred.
+
+    Other Parameters
+    ----------------
+    decrease_radius_factor : float, optional
+        Factor by which the trust-region radius is reduced when the reduction
+        ratio is low or negative. Default is ``0.5``.
+    increase_radius_factor : float, optional
+        Factor by which the trust-region radius is increased when the reduction
+        ratio is large. Default is ``numpy.sqrt(2.0)``.
+    increase_radius_threshold : float, optional
+        Threshold that controls the increase of the trust-region radius when
+        the reduction ratio is large. Default is ``2.0``.
+    decrease_radius_threshold : float, optional
+        Threshold used to determine whether the trust-region radius should be
+        reduced to the resolution. Default is ``1.4``.
+    decrease_resolution_factor : float, optional
+        Factor by which the resolution is reduced when the current value is far
+        from its final value. Default is ``0.1``.
+    large_resolution_threshold : float, optional
+        Threshold used to determine whether the resolution is far from its
+        final value. Default is ``250.0``.
+    moderate_resolution_threshold : float, optional
+        Threshold used to determine whether the resolution is close to its
+        final value. Default is ``16.0``.
+    low_ratio : float, optional
+        Threshold used to determine whether the reduction ratio is low. Default
+        is ``0.1``.
+    high_ratio : float, optional
+        Threshold used to determine whether the reduction ratio is high.
+        Default is ``0.7``.
+    very_low_ratio : float, optional
+        Threshold used to determine whether the reduction ratio is very low.
+        This is used to determine whether the models should be reset. Default
+        is ``0.01``.
+    penalty_increase_threshold : float, optional
+        Threshold used to determine whether the penalty parameter should be
+        increased. Default is ``1.5``.
+    penalty_increase_factor : float, optional
+        Factor by which the penalty parameter is increased. Default is ``2.0``.
+    short_step_threshold : float, optional
+        Factor used to determine whether the trial step is too short. Default
+        is ``0.5``.
+    low_radius_factor : float, optional
+        Factor used to determine which interpolation point should be removed
+        from the interpolation set at each iteration. Default is ``0.1``.
+    byrd_omojokun_factor : float, optional
+        Factor by which the trust-region radius is reduced for the computations
+        of the normal step in the Byrd-Omojokun composite-step approach.
+        Default is ``0.8``.
+    threshold_ratio_constraints : float, optional
+        Threshold used to determine which constraints should be taken into
+        account when decreasing the penalty parameter. Default is ``2.0``.
+    large_shift_factor : float, optional
+        Factor used to determine whether the point around which the quadratic
+        models are built should be updated. Default is ``10.0``.
+    large_gradient_factor : float, optional
+        Factor used to determine whether the models should be reset. Default is
+        ``10.0``.
+    resolution_factor : float, optional
+        Factor by which the resolution is decreased. Default is ``2.0``.
+    improve_tcg : bool, optional
+        Whether to improve the steps computed by the truncated conjugate
+        gradient method when the trust-region boundary is reached. Default is
+        ``True``.
+
+    References
+    ----------
+    .. [1] J. Nocedal and S. J. Wright. *Numerical Optimization*. Springer Ser.
+       Oper. Res. Financ. Eng. Springer, New York, NY, USA, second edition,
+       2006. `doi:10.1007/978-0-387-40065-5
+       `_.
+    .. [2] M. J. D. Powell. A direct search optimization method that models the
+       objective and constraint functions by linear interpolation. In S. Gomez
+       and J.-P. Hennart, editors, *Advances in Optimization and Numerical
+       Analysis*, volume 275 of Math. Appl., pages 51--67. Springer, Dordrecht,
+       Netherlands, 1994. `doi:10.1007/978-94-015-8330-5_4
+       `_.
+    .. [3] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods
+       and Software*. PhD thesis, Department of Applied Mathematics, The Hong
+       Kong Polytechnic University, Hong Kong, China, 2022. URL:
+       https://theses.lib.polyu.edu.hk/handle/200/12294.
+
+    Examples
+    --------
+    To demonstrate how to use `minimize`, we first minimize the Rosenbrock
+    function implemented in `scipy.optimize` in an unconstrained setting.
+
+    .. testsetup::
+
+        import numpy as np
+        np.set_printoptions(precision=3, suppress=True)
+
+    >>> from cobyqa import minimize
+    >>> from scipy.optimize import rosen
+
+    To solve the problem using COBYQA, run:
+
+    >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2]
+    >>> res = minimize(rosen, x0)
+    >>> res.x
+    array([1., 1., 1., 1., 1.])
+
+    To see how bound and constraints are handled using `minimize`, we solve
+    Example 16.4 of [1]_, defined as
+
+    .. math::
+
+        \begin{aligned}
+            \min_{x \in \mathbb{R}^2}   & \quad (x_1 - 1)^2 + (x_2 - 2.5)^2\\
+            \text{s.t.}                 & \quad -x_1 + 2x_2 \le 2,\\
+                                        & \quad x_1 + 2x_2 \le 6,\\
+                                        & \quad x_1 - 2x_2 \le 2,\\
+                                        & \quad x_1 \ge 0,\\
+                                        & \quad x_2 \ge 0.
+        \end{aligned}
+
+    >>> import numpy as np
+    >>> from scipy.optimize import Bounds, LinearConstraint
+
+    Its objective function can be implemented as:
+
+    >>> def fun(x):
+    ...     return (x[0] - 1.0)**2 + (x[1] - 2.5)**2
+
+    This problem can be solved using `minimize` as:
+
+    >>> x0 = [2.0, 0.0]
+    >>> bounds = Bounds([0.0, 0.0], np.inf)
+    >>> constraints = LinearConstraint([
+    ...     [-1.0, 2.0],
+    ...     [1.0, 2.0],
+    ...     [1.0, -2.0],
+    ... ], -np.inf, [2.0, 6.0, 2.0])
+    >>> res = minimize(fun, x0, bounds=bounds, constraints=constraints)
+    >>> res.x
+    array([1.4, 1.7])
+
+    To see how nonlinear constraints are handled, we solve Problem (F) of [2]_,
+    defined as
+
+    .. math::
+
+        \begin{aligned}
+            \min_{x \in \mathbb{R}^2}   & \quad -x_1 - x_2\\
+            \text{s.t.}                 & \quad x_1^2 - x_2 \le 0,\\
+                                        & \quad x_1^2 + x_2^2 \le 1.
+        \end{aligned}
+
+    >>> from scipy.optimize import NonlinearConstraint
+
+    Its objective and constraint functions can be implemented as:
+
+    >>> def fun(x):
+    ...     return -x[0] - x[1]
+    >>>
+    >>> def cub(x):
+    ...     return [x[0]**2 - x[1], x[0]**2 + x[1]**2]
+
+    This problem can be solved using `minimize` as:
+
+    >>> x0 = [1.0, 1.0]
+    >>> constraints = NonlinearConstraint(cub, -np.inf, [0.0, 1.0])
+    >>> res = minimize(fun, x0, constraints=constraints)
+    >>> res.x
+    array([0.707, 0.707])
+
+    Finally, to see how to supply linear and nonlinear constraints
+    simultaneously, we solve Problem (G) of [2]_, defined as
+
+    .. math::
+
+        \begin{aligned}
+            \min_{x \in \mathbb{R}^3}   & \quad x_3\\
+            \text{s.t.}                 & \quad 5x_1 - x_2 + x_3 \ge 0,\\
+                                        & \quad -5x_1 - x_2 + x_3 \ge 0,\\
+                                        & \quad x_1^2 + x_2^2 + 4x_2 \le x_3.
+        \end{aligned}
+
+    Its objective and nonlinear constraint functions can be implemented as:
+
+    >>> def fun(x):
+    ...     return x[2]
+    >>>
+    >>> def cub(x):
+    ...     return x[0]**2 + x[1]**2 + 4.0*x[1] - x[2]
+
+    This problem can be solved using `minimize` as:
+
+    >>> x0 = [1.0, 1.0, 1.0]
+    >>> constraints = [
+    ...     LinearConstraint(
+    ...         [[5.0, -1.0, 1.0], [-5.0, -1.0, 1.0]],
+    ...         [0.0, 0.0],
+    ...         np.inf,
+    ...     ),
+    ...     NonlinearConstraint(cub, -np.inf, 0.0),
+    ... ]
+    >>> res = minimize(fun, x0, constraints=constraints)
+    >>> res.x
+    array([ 0., -3., -3.])
+    """
+    # Get basic options that are needed for the initialization.
+    if options is None:
+        options = {}
+    else:
+        options = dict(options)
+    verbose = options.get(Options.VERBOSE, DEFAULT_OPTIONS[Options.VERBOSE])
+    verbose = bool(verbose)
+    feasibility_tol = options.get(
+        Options.FEASIBILITY_TOL,
+        DEFAULT_OPTIONS[Options.FEASIBILITY_TOL],
+    )
+    feasibility_tol = float(feasibility_tol)
+    scale = options.get(Options.SCALE, DEFAULT_OPTIONS[Options.SCALE])
+    scale = bool(scale)
+    store_history = options.get(
+        Options.STORE_HISTORY,
+        DEFAULT_OPTIONS[Options.STORE_HISTORY],
+    )
+    store_history = bool(store_history)
+    if Options.HISTORY_SIZE in options and options[Options.HISTORY_SIZE] <= 0:
+        raise ValueError("The size of the history must be positive.")
+    history_size = options.get(
+        Options.HISTORY_SIZE,
+        DEFAULT_OPTIONS[Options.HISTORY_SIZE],
+    )
+    history_size = int(history_size)
+    if Options.FILTER_SIZE in options and options[Options.FILTER_SIZE] <= 0:
+        raise ValueError("The size of the filter must be positive.")
+    filter_size = options.get(
+        Options.FILTER_SIZE,
+        DEFAULT_OPTIONS[Options.FILTER_SIZE],
+    )
+    filter_size = int(filter_size)
+    debug = options.get(Options.DEBUG, DEFAULT_OPTIONS[Options.DEBUG])
+    debug = bool(debug)
+
+    # Initialize the objective function.
+    if not isinstance(args, tuple):
+        args = (args,)
+    obj = ObjectiveFunction(fun, verbose, debug, *args)
+
+    # Initialize the bound constraints.
+    if not hasattr(x0, "__len__"):
+        x0 = [x0]
+    n_orig = len(x0)
+    bounds = BoundConstraints(_get_bounds(bounds, n_orig))
+
+    # Initialize the constraints.
+    linear_constraints, nonlinear_constraints = _get_constraints(constraints)
+    linear = LinearConstraints(linear_constraints, n_orig, debug)
+    nonlinear = NonlinearConstraints(nonlinear_constraints, verbose, debug)
+
+    # Initialize the problem (and remove the fixed variables).
+    pb = Problem(
+        obj,
+        x0,
+        bounds,
+        linear,
+        nonlinear,
+        callback,
+        feasibility_tol,
+        scale,
+        store_history,
+        history_size,
+        filter_size,
+        debug,
+    )
+
+    # Set the default options.
+    _set_default_options(options, pb.n)
+    constants = _set_default_constants(**kwargs)
+
+    # Initialize the models and skip the computations whenever possible.
+    if not pb.bounds.is_feasible:
+        # The bound constraints are infeasible.
+        return _build_result(
+            pb,
+            0.0,
+            False,
+            ExitStatus.INFEASIBLE_ERROR,
+            0,
+            options,
+        )
+    elif pb.n == 0:
+        # All variables are fixed by the bound constraints.
+        return _build_result(
+            pb,
+            0.0,
+            True,
+            ExitStatus.FIXED_SUCCESS,
+            0,
+            options,
+        )
+    if verbose:
+        print("Starting the optimization procedure.")
+        print(f"Initial trust-region radius: {options[Options.RHOBEG]}.")
+        print(f"Final trust-region radius: {options[Options.RHOEND]}.")
+        print(
+            f"Maximum number of function evaluations: "
+            f"{options[Options.MAX_EVAL]}."
+        )
+        print(f"Maximum number of iterations: {options[Options.MAX_ITER]}.")
+        print()
+    try:
+        framework = TrustRegion(pb, options, constants)
+    except TargetSuccess:
+        # The target on the objective function value has been reached
+        return _build_result(
+            pb,
+            0.0,
+            True,
+            ExitStatus.TARGET_SUCCESS,
+            0,
+            options,
+        )
+    except CallbackSuccess:
+        # The callback raised a StopIteration exception.
+        return _build_result(
+            pb,
+            0.0,
+            True,
+            ExitStatus.CALLBACK_SUCCESS,
+            0,
+            options,
+        )
+    except FeasibleSuccess:
+        # The feasibility problem has been solved successfully.
+        return _build_result(
+            pb,
+            0.0,
+            True,
+            ExitStatus.FEASIBLE_SUCCESS,
+            0,
+            options,
+        )
+    except MaxEvalError:
+        # The maximum number of function evaluations has been exceeded.
+        return _build_result(
+            pb,
+            0.0,
+            False,
+            ExitStatus.MAX_ITER_WARNING,
+            0,
+            options,
+        )
+    except np.linalg.LinAlgError:
+        # The construction of the initial interpolation set failed.
+        return _build_result(
+            pb,
+            0.0,
+            False,
+            ExitStatus.LINALG_ERROR,
+            0,
+            options,
+        )
+
+    # Start the optimization procedure.
+    success = False
+    n_iter = 0
+    k_new = None
+    n_short_steps = 0
+    n_very_short_steps = 0
+    n_alt_models = 0
+    while True:
+        # Stop the optimization procedure if the maximum number of iterations
+        # has been exceeded. We do not write the main loop as a for loop
+        # because we want to access the number of iterations outside the loop.
+        if n_iter >= options[Options.MAX_ITER]:
+            status = ExitStatus.MAX_ITER_WARNING
+            break
+        n_iter += 1
+
+        # Update the point around which the quadratic models are built.
+        if (
+            np.linalg.norm(
+                framework.x_best - framework.models.interpolation.x_base
+            )
+            >= constants[Constants.LARGE_SHIFT_FACTOR] * framework.radius
+        ):
+            framework.shift_x_base(options)
+
+        # Evaluate the trial step.
+        radius_save = framework.radius
+        normal_step, tangential_step = framework.get_trust_region_step(options)
+        step = normal_step + tangential_step
+        s_norm = np.linalg.norm(step)
+
+        # If the trial step is too short, we do not attempt to evaluate the
+        # objective and constraint functions. Instead, we reduce the
+        # trust-region radius and check whether the resolution should be
+        # enhanced and whether the geometry of the interpolation set should be
+        # improved. Otherwise, we entertain a classical iteration. The
+        # criterion for performing an exceptional jump is taken from NEWUOA.
+        if (
+            s_norm
+            <= constants[Constants.SHORT_STEP_THRESHOLD] * framework.resolution
+        ):
+            framework.radius *= constants[Constants.DECREASE_RESOLUTION_FACTOR]
+            if radius_save > framework.resolution:
+                n_short_steps = 0
+                n_very_short_steps = 0
+            else:
+                n_short_steps += 1
+                n_very_short_steps += 1
+                if s_norm > 0.1 * framework.resolution:
+                    n_very_short_steps = 0
+            enhance_resolution = n_short_steps >= 5 or n_very_short_steps >= 3
+            if enhance_resolution:
+                n_short_steps = 0
+                n_very_short_steps = 0
+                improve_geometry = False
+            else:
+                try:
+                    k_new, dist_new = framework.get_index_to_remove()
+                except np.linalg.LinAlgError:
+                    status = ExitStatus.LINALG_ERROR
+                    break
+                improve_geometry = dist_new > max(
+                    framework.radius,
+                    constants[Constants.RESOLUTION_FACTOR]
+                    * framework.resolution,
+                )
+        else:
+            # Increase the penalty parameter if necessary.
+            same_best_point = framework.increase_penalty(step)
+            if same_best_point:
+                # Evaluate the objective and constraint functions.
+                try:
+                    fun_val, cub_val, ceq_val = _eval(
+                        pb,
+                        framework,
+                        step,
+                        options,
+                    )
+                except TargetSuccess:
+                    status = ExitStatus.TARGET_SUCCESS
+                    success = True
+                    break
+                except FeasibleSuccess:
+                    status = ExitStatus.FEASIBLE_SUCCESS
+                    success = True
+                    break
+                except CallbackSuccess:
+                    status = ExitStatus.CALLBACK_SUCCESS
+                    success = True
+                    break
+                except MaxEvalError:
+                    status = ExitStatus.MAX_EVAL_WARNING
+                    break
+
+                # Perform a second-order correction step if necessary.
+                merit_old = framework.merit(
+                    framework.x_best,
+                    framework.fun_best,
+                    framework.cub_best,
+                    framework.ceq_best,
+                )
+                merit_new = framework.merit(
+                    framework.x_best + step, fun_val, cub_val, ceq_val
+                )
+                if (
+                    pb.type == "nonlinearly constrained"
+                    and merit_new > merit_old
+                    and np.linalg.norm(normal_step)
+                    > constants[Constants.BYRD_OMOJOKUN_FACTOR] ** 2.0
+                    * framework.radius
+                ):
+                    soc_step = framework.get_second_order_correction_step(
+                        step, options
+                    )
+                    if np.linalg.norm(soc_step) > 0.0:
+                        step += soc_step
+
+                        # Evaluate the objective and constraint functions.
+                        try:
+                            fun_val, cub_val, ceq_val = _eval(
+                                pb,
+                                framework,
+                                step,
+                                options,
+                            )
+                        except TargetSuccess:
+                            status = ExitStatus.TARGET_SUCCESS
+                            success = True
+                            break
+                        except FeasibleSuccess:
+                            status = ExitStatus.FEASIBLE_SUCCESS
+                            success = True
+                            break
+                        except CallbackSuccess:
+                            status = ExitStatus.CALLBACK_SUCCESS
+                            success = True
+                            break
+                        except MaxEvalError:
+                            status = ExitStatus.MAX_EVAL_WARNING
+                            break
+
+                # Calculate the reduction ratio.
+                ratio = framework.get_reduction_ratio(
+                    step,
+                    fun_val,
+                    cub_val,
+                    ceq_val,
+                )
+
+                # Choose an interpolation point to remove.
+                try:
+                    k_new = framework.get_index_to_remove(
+                        framework.x_best + step
+                    )[0]
+                except np.linalg.LinAlgError:
+                    status = ExitStatus.LINALG_ERROR
+                    break
+
+                # Update the interpolation set.
+                try:
+                    ill_conditioned = framework.models.update_interpolation(
+                        k_new, framework.x_best + step, fun_val, cub_val,
+                        ceq_val
+                    )
+                except np.linalg.LinAlgError:
+                    status = ExitStatus.LINALG_ERROR
+                    break
+                framework.set_best_index()
+
+                # Update the trust-region radius.
+                framework.update_radius(step, ratio)
+
+                # Attempt to replace the models by the alternative ones.
+                if framework.radius <= framework.resolution:
+                    if ratio >= constants[Constants.VERY_LOW_RATIO]:
+                        n_alt_models = 0
+                    else:
+                        n_alt_models += 1
+                        grad = framework.models.fun_grad(framework.x_best)
+                        try:
+                            grad_alt = framework.models.fun_alt_grad(
+                                framework.x_best
+                            )
+                        except np.linalg.LinAlgError:
+                            status = ExitStatus.LINALG_ERROR
+                            break
+                        if np.linalg.norm(grad) < constants[
+                            Constants.LARGE_GRADIENT_FACTOR
+                        ] * np.linalg.norm(grad_alt):
+                            n_alt_models = 0
+                        if n_alt_models >= 3:
+                            try:
+                                framework.models.reset_models()
+                            except np.linalg.LinAlgError:
+                                status = ExitStatus.LINALG_ERROR
+                                break
+                            n_alt_models = 0
+
+                # Update the Lagrange multipliers.
+                framework.set_multipliers(framework.x_best + step)
+
+                # Check whether the resolution should be enhanced.
+                try:
+                    k_new, dist_new = framework.get_index_to_remove()
+                except np.linalg.LinAlgError:
+                    status = ExitStatus.LINALG_ERROR
+                    break
+                improve_geometry = (
+                    ill_conditioned
+                    or ratio <= constants[Constants.LOW_RATIO]
+                    and dist_new
+                    > max(
+                        framework.radius,
+                        constants[Constants.RESOLUTION_FACTOR]
+                        * framework.resolution,
+                    )
+                )
+                enhance_resolution = (
+                    radius_save <= framework.resolution
+                    and ratio <= constants[Constants.LOW_RATIO]
+                    and not improve_geometry
+                )
+            else:
+                # When increasing the penalty parameter, the best point so far
+                # may change. In this case, we restart the iteration.
+                enhance_resolution = False
+                improve_geometry = False
+
+        # Reduce the resolution if necessary.
+        if enhance_resolution:
+            if framework.resolution <= options[Options.RHOEND]:
+                success = True
+                status = ExitStatus.RADIUS_SUCCESS
+                break
+            framework.enhance_resolution(options)
+            framework.decrease_penalty()
+
+            if verbose:
+                maxcv_val = pb.maxcv(
+                    framework.x_best, framework.cub_best, framework.ceq_best
+                )
+                _print_step(
+                    f"New trust-region radius: {framework.resolution}",
+                    pb,
+                    pb.build_x(framework.x_best),
+                    framework.fun_best,
+                    maxcv_val,
+                    pb.n_eval,
+                    n_iter,
+                )
+                print()
+
+        # Improve the geometry of the interpolation set if necessary.
+        if improve_geometry:
+            try:
+                step = framework.get_geometry_step(k_new, options)
+            except np.linalg.LinAlgError:
+                status = ExitStatus.LINALG_ERROR
+                break
+
+            # Evaluate the objective and constraint functions.
+            try:
+                fun_val, cub_val, ceq_val = _eval(pb, framework, step, options)
+            except TargetSuccess:
+                status = ExitStatus.TARGET_SUCCESS
+                success = True
+                break
+            except FeasibleSuccess:
+                status = ExitStatus.FEASIBLE_SUCCESS
+                success = True
+                break
+            except CallbackSuccess:
+                status = ExitStatus.CALLBACK_SUCCESS
+                success = True
+                break
+            except MaxEvalError:
+                status = ExitStatus.MAX_EVAL_WARNING
+                break
+
+            # Update the interpolation set.
+            try:
+                framework.models.update_interpolation(
+                    k_new,
+                    framework.x_best + step,
+                    fun_val,
+                    cub_val,
+                    ceq_val,
+                )
+            except np.linalg.LinAlgError:
+                status = ExitStatus.LINALG_ERROR
+                break
+            framework.set_best_index()
+
+    return _build_result(
+        pb,
+        framework.penalty,
+        success,
+        status,
+        n_iter,
+        options,
+    )
+
+
+def _get_bounds(bounds, n):
+    """
+    Uniformize the bounds.
+    """
+    if bounds is None:
+        return Bounds(np.full(n, -np.inf), np.full(n, np.inf))
+    elif isinstance(bounds, Bounds):
+        if bounds.lb.shape != (n,) or bounds.ub.shape != (n,):
+            raise ValueError(f"The bounds must have {n} elements.")
+        return Bounds(bounds.lb, bounds.ub)
+    elif hasattr(bounds, "__len__"):
+        bounds = np.asarray(bounds)
+        if bounds.shape != (n, 2):
+            raise ValueError(
+                "The shape of the bounds is not compatible with "
+                "the number of variables."
+            )
+        return Bounds(bounds[:, 0], bounds[:, 1])
+    else:
+        raise TypeError(
+            "The bounds must be an instance of "
+            "scipy.optimize.Bounds or an array-like object."
+        )
+
+
+def _get_constraints(constraints):
+    """
+    Extract the linear and nonlinear constraints.
+    """
+    if isinstance(constraints, dict) or not hasattr(constraints, "__len__"):
+        constraints = (constraints,)
+
+    # Extract the linear and nonlinear constraints.
+    linear_constraints = []
+    nonlinear_constraints = []
+    for constraint in constraints:
+        if isinstance(constraint, LinearConstraint):
+            lb = exact_1d_array(
+                constraint.lb,
+                "The lower bound of the linear constraints must be a vector.",
+            )
+            ub = exact_1d_array(
+                constraint.ub,
+                "The upper bound of the linear constraints must be a vector.",
+            )
+            linear_constraints.append(
+                LinearConstraint(
+                    constraint.A,
+                    *np.broadcast_arrays(lb, ub),
+                )
+            )
+        elif isinstance(constraint, NonlinearConstraint):
+            lb = exact_1d_array(
+                constraint.lb,
+                "The lower bound of the "
+                "nonlinear constraints must be a "
+                "vector.",
+            )
+            ub = exact_1d_array(
+                constraint.ub,
+                "The upper bound of the "
+                "nonlinear constraints must be a "
+                "vector.",
+            )
+            nonlinear_constraints.append(
+                NonlinearConstraint(
+                    constraint.fun,
+                    *np.broadcast_arrays(lb, ub),
+                )
+            )
+        elif isinstance(constraint, dict):
+            if "type" not in constraint or constraint["type"] not in (
+                "eq",
+                "ineq",
+            ):
+                raise ValueError('The constraint type must be "eq" or "ineq".')
+            if "fun" not in constraint or not callable(constraint["fun"]):
+                raise ValueError("The constraint function must be callable.")
+            nonlinear_constraints.append(
+                {
+                    "fun": constraint["fun"],
+                    "type": constraint["type"],
+                    "args": constraint.get("args", ()),
+                }
+            )
+        else:
+            raise TypeError(
+                "The constraints must be instances of "
+                "scipy.optimize.LinearConstraint, "
+                "scipy.optimize.NonlinearConstraint, or dict."
+            )
+    return linear_constraints, nonlinear_constraints
+
+
+def _set_default_options(options, n):
+    """
+    Set the default options.
+    """
+    if Options.RHOBEG in options and options[Options.RHOBEG] <= 0.0:
+        raise ValueError("The initial trust-region radius must be positive.")
+    if Options.RHOEND in options and options[Options.RHOEND] < 0.0:
+        raise ValueError("The final trust-region radius must be nonnegative.")
+    if Options.RHOBEG in options and Options.RHOEND in options:
+        if options[Options.RHOBEG] < options[Options.RHOEND]:
+            raise ValueError(
+                "The initial trust-region radius must be greater "
+                "than or equal to the final trust-region radius."
+            )
+    elif Options.RHOBEG in options:
+        options[Options.RHOEND.value] = np.min(
+            [
+                DEFAULT_OPTIONS[Options.RHOEND],
+                options[Options.RHOBEG],
+            ]
+        )
+    elif Options.RHOEND in options:
+        options[Options.RHOBEG.value] = np.max(
+            [
+                DEFAULT_OPTIONS[Options.RHOBEG],
+                options[Options.RHOEND],
+            ]
+        )
+    else:
+        options[Options.RHOBEG.value] = DEFAULT_OPTIONS[Options.RHOBEG]
+        options[Options.RHOEND.value] = DEFAULT_OPTIONS[Options.RHOEND]
+    options[Options.RHOBEG.value] = float(options[Options.RHOBEG])
+    options[Options.RHOEND.value] = float(options[Options.RHOEND])
+    if Options.NPT in options and options[Options.NPT] <= 0:
+        raise ValueError("The number of interpolation points must be "
+                         "positive.")
+    if (
+        Options.NPT in options
+        and options[Options.NPT] > ((n + 1) * (n + 2)) // 2
+    ):
+        raise ValueError(
+            f"The number of interpolation points must be at most "
+            f"{((n + 1) * (n + 2)) // 2}."
+        )
+    options.setdefault(Options.NPT.value, DEFAULT_OPTIONS[Options.NPT](n))
+    options[Options.NPT.value] = int(options[Options.NPT])
+    if Options.MAX_EVAL in options and options[Options.MAX_EVAL] <= 0:
+        raise ValueError(
+            "The maximum number of function evaluations must be positive."
+        )
+    options.setdefault(
+        Options.MAX_EVAL.value,
+        np.max(
+            [
+                DEFAULT_OPTIONS[Options.MAX_EVAL](n),
+                options[Options.NPT] + 1,
+            ]
+        ),
+    )
+    options[Options.MAX_EVAL.value] = int(options[Options.MAX_EVAL])
+    if Options.MAX_ITER in options and options[Options.MAX_ITER] <= 0:
+        raise ValueError("The maximum number of iterations must be positive.")
+    options.setdefault(
+        Options.MAX_ITER.value,
+        DEFAULT_OPTIONS[Options.MAX_ITER](n),
+    )
+    options[Options.MAX_ITER.value] = int(options[Options.MAX_ITER])
+    options.setdefault(Options.TARGET.value, DEFAULT_OPTIONS[Options.TARGET])
+    options[Options.TARGET.value] = float(options[Options.TARGET])
+    options.setdefault(
+        Options.FEASIBILITY_TOL.value,
+        DEFAULT_OPTIONS[Options.FEASIBILITY_TOL],
+    )
+    options[Options.FEASIBILITY_TOL.value] = float(
+        options[Options.FEASIBILITY_TOL]
+    )
+    options.setdefault(Options.VERBOSE.value, DEFAULT_OPTIONS[Options.VERBOSE])
+    options[Options.VERBOSE.value] = bool(options[Options.VERBOSE])
+    options.setdefault(Options.SCALE.value, DEFAULT_OPTIONS[Options.SCALE])
+    options[Options.SCALE.value] = bool(options[Options.SCALE])
+    options.setdefault(
+        Options.FILTER_SIZE.value,
+        DEFAULT_OPTIONS[Options.FILTER_SIZE],
+    )
+    options[Options.FILTER_SIZE.value] = int(options[Options.FILTER_SIZE])
+    options.setdefault(
+        Options.STORE_HISTORY.value,
+        DEFAULT_OPTIONS[Options.STORE_HISTORY],
+    )
+    options[Options.STORE_HISTORY.value] = bool(options[Options.STORE_HISTORY])
+    options.setdefault(
+        Options.HISTORY_SIZE.value,
+        DEFAULT_OPTIONS[Options.HISTORY_SIZE],
+    )
+    options[Options.HISTORY_SIZE.value] = int(options[Options.HISTORY_SIZE])
+    options.setdefault(Options.DEBUG.value, DEFAULT_OPTIONS[Options.DEBUG])
+    options[Options.DEBUG.value] = bool(options[Options.DEBUG])
+
+    # Check whether they are any unknown options.
+    for key in options:
+        if key not in Options.__members__.values():
+            warnings.warn(f"Unknown option: {key}.", RuntimeWarning, 3)
+
+
+def _set_default_constants(**kwargs):
+    """
+    Set the default constants.
+    """
+    constants = dict(kwargs)
+    constants.setdefault(
+        Constants.DECREASE_RADIUS_FACTOR.value,
+        DEFAULT_CONSTANTS[Constants.DECREASE_RADIUS_FACTOR],
+    )
+    constants[Constants.DECREASE_RADIUS_FACTOR.value] = float(
+        constants[Constants.DECREASE_RADIUS_FACTOR]
+    )
+    if (
+        constants[Constants.DECREASE_RADIUS_FACTOR] <= 0.0
+        or constants[Constants.DECREASE_RADIUS_FACTOR] >= 1.0
+    ):
+        raise ValueError(
+            "The constant decrease_radius_factor must be in the interval "
+            "(0, 1)."
+        )
+    constants.setdefault(
+        Constants.INCREASE_RADIUS_THRESHOLD.value,
+        DEFAULT_CONSTANTS[Constants.INCREASE_RADIUS_THRESHOLD],
+    )
+    constants[Constants.INCREASE_RADIUS_THRESHOLD.value] = float(
+        constants[Constants.INCREASE_RADIUS_THRESHOLD]
+    )
+    if constants[Constants.INCREASE_RADIUS_THRESHOLD] <= 1.0:
+        raise ValueError(
+            "The constant increase_radius_threshold must be greater than 1."
+        )
+    if (
+        Constants.INCREASE_RADIUS_FACTOR in constants
+        and constants[Constants.INCREASE_RADIUS_FACTOR] <= 1.0
+    ):
+        raise ValueError(
+            "The constant increase_radius_factor must be greater than 1."
+        )
+    if (
+        Constants.DECREASE_RADIUS_THRESHOLD in constants
+        and constants[Constants.DECREASE_RADIUS_THRESHOLD] <= 1.0
+    ):
+        raise ValueError(
+            "The constant decrease_radius_threshold must be greater than 1."
+        )
+    if (
+        Constants.INCREASE_RADIUS_FACTOR in constants
+        and Constants.DECREASE_RADIUS_THRESHOLD in constants
+    ):
+        if (
+            constants[Constants.DECREASE_RADIUS_THRESHOLD]
+            >= constants[Constants.INCREASE_RADIUS_FACTOR]
+        ):
+            raise ValueError(
+                "The constant decrease_radius_threshold must be "
+                "less than increase_radius_factor."
+            )
+    elif Constants.INCREASE_RADIUS_FACTOR in constants:
+        constants[Constants.DECREASE_RADIUS_THRESHOLD.value] = np.min(
+            [
+                DEFAULT_CONSTANTS[Constants.DECREASE_RADIUS_THRESHOLD],
+                0.5 * (1.0 + constants[Constants.INCREASE_RADIUS_FACTOR]),
+            ]
+        )
+    elif Constants.DECREASE_RADIUS_THRESHOLD in constants:
+        constants[Constants.INCREASE_RADIUS_FACTOR.value] = np.max(
+            [
+                DEFAULT_CONSTANTS[Constants.INCREASE_RADIUS_FACTOR],
+                2.0 * constants[Constants.DECREASE_RADIUS_THRESHOLD],
+            ]
+        )
+    else:
+        constants[Constants.INCREASE_RADIUS_FACTOR.value] = DEFAULT_CONSTANTS[
+            Constants.INCREASE_RADIUS_FACTOR
+        ]
+        constants[Constants.DECREASE_RADIUS_THRESHOLD.value] = (
+            DEFAULT_CONSTANTS[Constants.DECREASE_RADIUS_THRESHOLD])
+    constants.setdefault(
+        Constants.DECREASE_RESOLUTION_FACTOR.value,
+        DEFAULT_CONSTANTS[Constants.DECREASE_RESOLUTION_FACTOR],
+    )
+    constants[Constants.DECREASE_RESOLUTION_FACTOR.value] = float(
+        constants[Constants.DECREASE_RESOLUTION_FACTOR]
+    )
+    if (
+        constants[Constants.DECREASE_RESOLUTION_FACTOR] <= 0.0
+        or constants[Constants.DECREASE_RESOLUTION_FACTOR] >= 1.0
+    ):
+        raise ValueError(
+            "The constant decrease_resolution_factor must be in the interval "
+            "(0, 1)."
+        )
+    if (
+        Constants.LARGE_RESOLUTION_THRESHOLD in constants
+        and constants[Constants.LARGE_RESOLUTION_THRESHOLD] <= 1.0
+    ):
+        raise ValueError(
+            "The constant large_resolution_threshold must be greater than 1."
+        )
+    if (
+        Constants.MODERATE_RESOLUTION_THRESHOLD in constants
+        and constants[Constants.MODERATE_RESOLUTION_THRESHOLD] <= 1.0
+    ):
+        raise ValueError(
+            "The constant moderate_resolution_threshold must be greater than "
+            "1."
+        )
+    if (
+        Constants.LARGE_RESOLUTION_THRESHOLD in constants
+        and Constants.MODERATE_RESOLUTION_THRESHOLD in constants
+    ):
+        if (
+            constants[Constants.MODERATE_RESOLUTION_THRESHOLD]
+            > constants[Constants.LARGE_RESOLUTION_THRESHOLD]
+        ):
+            raise ValueError(
+                "The constant moderate_resolution_threshold "
+                "must be at most large_resolution_threshold."
+            )
+    elif Constants.LARGE_RESOLUTION_THRESHOLD in constants:
+        constants[Constants.MODERATE_RESOLUTION_THRESHOLD.value] = np.min(
+            [
+                DEFAULT_CONSTANTS[Constants.MODERATE_RESOLUTION_THRESHOLD],
+                constants[Constants.LARGE_RESOLUTION_THRESHOLD],
+            ]
+        )
+    elif Constants.MODERATE_RESOLUTION_THRESHOLD in constants:
+        constants[Constants.LARGE_RESOLUTION_THRESHOLD.value] = np.max(
+            [
+                DEFAULT_CONSTANTS[Constants.LARGE_RESOLUTION_THRESHOLD],
+                constants[Constants.MODERATE_RESOLUTION_THRESHOLD],
+            ]
+        )
+    else:
+        constants[Constants.LARGE_RESOLUTION_THRESHOLD.value] = (
+            DEFAULT_CONSTANTS[Constants.LARGE_RESOLUTION_THRESHOLD]
+        )
+        constants[Constants.MODERATE_RESOLUTION_THRESHOLD.value] = (
+            DEFAULT_CONSTANTS[Constants.MODERATE_RESOLUTION_THRESHOLD]
+        )
+    if Constants.LOW_RATIO in constants and (
+        constants[Constants.LOW_RATIO] <= 0.0
+        or constants[Constants.LOW_RATIO] >= 1.0
+    ):
+        raise ValueError(
+            "The constant low_ratio must be in the interval (0, 1)."
+        )
+    if Constants.HIGH_RATIO in constants and (
+        constants[Constants.HIGH_RATIO] <= 0.0
+        or constants[Constants.HIGH_RATIO] >= 1.0
+    ):
+        raise ValueError(
+            "The constant high_ratio must be in the interval (0, 1)."
+        )
+    if Constants.LOW_RATIO in constants and Constants.HIGH_RATIO in constants:
+        if constants[Constants.LOW_RATIO] > constants[Constants.HIGH_RATIO]:
+            raise ValueError(
+                "The constant low_ratio must be at most high_ratio."
+            )
+    elif Constants.LOW_RATIO in constants:
+        constants[Constants.HIGH_RATIO.value] = np.max(
+            [
+                DEFAULT_CONSTANTS[Constants.HIGH_RATIO],
+                constants[Constants.LOW_RATIO],
+            ]
+        )
+    elif Constants.HIGH_RATIO in constants:
+        constants[Constants.LOW_RATIO.value] = np.min(
+            [
+                DEFAULT_CONSTANTS[Constants.LOW_RATIO],
+                constants[Constants.HIGH_RATIO],
+            ]
+        )
+    else:
+        constants[Constants.LOW_RATIO.value] = DEFAULT_CONSTANTS[
+            Constants.LOW_RATIO
+        ]
+        constants[Constants.HIGH_RATIO.value] = DEFAULT_CONSTANTS[
+            Constants.HIGH_RATIO
+        ]
+    constants.setdefault(
+        Constants.VERY_LOW_RATIO.value,
+        DEFAULT_CONSTANTS[Constants.VERY_LOW_RATIO],
+    )
+    constants[Constants.VERY_LOW_RATIO.value] = float(
+        constants[Constants.VERY_LOW_RATIO]
+    )
+    if (
+        constants[Constants.VERY_LOW_RATIO] <= 0.0
+        or constants[Constants.VERY_LOW_RATIO] >= 1.0
+    ):
+        raise ValueError(
+            "The constant very_low_ratio must be in the interval (0, 1)."
+        )
+    if (
+        Constants.PENALTY_INCREASE_THRESHOLD in constants
+        and constants[Constants.PENALTY_INCREASE_THRESHOLD] < 1.0
+    ):
+        raise ValueError(
+            "The constant penalty_increase_threshold must be "
+            "greater than or equal to 1."
+        )
+    if (
+        Constants.PENALTY_INCREASE_FACTOR in constants
+        and constants[Constants.PENALTY_INCREASE_FACTOR] <= 1.0
+    ):
+        raise ValueError(
+            "The constant penalty_increase_factor must be greater than 1."
+        )
+    if (
+        Constants.PENALTY_INCREASE_THRESHOLD in constants
+        and Constants.PENALTY_INCREASE_FACTOR in constants
+    ):
+        if (
+            constants[Constants.PENALTY_INCREASE_FACTOR]
+            < constants[Constants.PENALTY_INCREASE_THRESHOLD]
+        ):
+            raise ValueError(
+                "The constant penalty_increase_factor must be "
+                "greater than or equal to "
+                "penalty_increase_threshold."
+            )
+    elif Constants.PENALTY_INCREASE_THRESHOLD in constants:
+        constants[Constants.PENALTY_INCREASE_FACTOR.value] = np.max(
+            [
+                DEFAULT_CONSTANTS[Constants.PENALTY_INCREASE_FACTOR],
+                constants[Constants.PENALTY_INCREASE_THRESHOLD],
+            ]
+        )
+    elif Constants.PENALTY_INCREASE_FACTOR in constants:
+        constants[Constants.PENALTY_INCREASE_THRESHOLD.value] = np.min(
+            [
+                DEFAULT_CONSTANTS[Constants.PENALTY_INCREASE_THRESHOLD],
+                constants[Constants.PENALTY_INCREASE_FACTOR],
+            ]
+        )
+    else:
+        constants[Constants.PENALTY_INCREASE_THRESHOLD.value] = (
+            DEFAULT_CONSTANTS[Constants.PENALTY_INCREASE_THRESHOLD]
+        )
+        constants[Constants.PENALTY_INCREASE_FACTOR.value] = DEFAULT_CONSTANTS[
+            Constants.PENALTY_INCREASE_FACTOR
+        ]
+    constants.setdefault(
+        Constants.SHORT_STEP_THRESHOLD.value,
+        DEFAULT_CONSTANTS[Constants.SHORT_STEP_THRESHOLD],
+    )
+    constants[Constants.SHORT_STEP_THRESHOLD.value] = float(
+        constants[Constants.SHORT_STEP_THRESHOLD]
+    )
+    if (
+        constants[Constants.SHORT_STEP_THRESHOLD] <= 0.0
+        or constants[Constants.SHORT_STEP_THRESHOLD] >= 1.0
+    ):
+        raise ValueError(
+            "The constant short_step_threshold must be in the interval (0, 1)."
+        )
+    constants.setdefault(
+        Constants.LOW_RADIUS_FACTOR.value,
+        DEFAULT_CONSTANTS[Constants.LOW_RADIUS_FACTOR],
+    )
+    constants[Constants.LOW_RADIUS_FACTOR.value] = float(
+        constants[Constants.LOW_RADIUS_FACTOR]
+    )
+    if (
+        constants[Constants.LOW_RADIUS_FACTOR] <= 0.0
+        or constants[Constants.LOW_RADIUS_FACTOR] >= 1.0
+    ):
+        raise ValueError(
+            "The constant low_radius_factor must be in the interval (0, 1)."
+        )
+    constants.setdefault(
+        Constants.BYRD_OMOJOKUN_FACTOR.value,
+        DEFAULT_CONSTANTS[Constants.BYRD_OMOJOKUN_FACTOR],
+    )
+    constants[Constants.BYRD_OMOJOKUN_FACTOR.value] = float(
+        constants[Constants.BYRD_OMOJOKUN_FACTOR]
+    )
+    if (
+        constants[Constants.BYRD_OMOJOKUN_FACTOR] <= 0.0
+        or constants[Constants.BYRD_OMOJOKUN_FACTOR] >= 1.0
+    ):
+        raise ValueError(
+            "The constant byrd_omojokun_factor must be in the interval (0, 1)."
+        )
+    constants.setdefault(
+        Constants.THRESHOLD_RATIO_CONSTRAINTS.value,
+        DEFAULT_CONSTANTS[Constants.THRESHOLD_RATIO_CONSTRAINTS],
+    )
+    constants[Constants.THRESHOLD_RATIO_CONSTRAINTS.value] = float(
+        constants[Constants.THRESHOLD_RATIO_CONSTRAINTS]
+    )
+    if constants[Constants.THRESHOLD_RATIO_CONSTRAINTS] <= 1.0:
+        raise ValueError(
+            "The constant threshold_ratio_constraints must be greater than 1."
+        )
+    constants.setdefault(
+        Constants.LARGE_SHIFT_FACTOR.value,
+        DEFAULT_CONSTANTS[Constants.LARGE_SHIFT_FACTOR],
+    )
+    constants[Constants.LARGE_SHIFT_FACTOR.value] = float(
+        constants[Constants.LARGE_SHIFT_FACTOR]
+    )
+    if constants[Constants.LARGE_SHIFT_FACTOR] < 0.0:
+        raise ValueError("The constant large_shift_factor must be "
+                         "nonnegative.")
+    constants.setdefault(
+        Constants.LARGE_GRADIENT_FACTOR.value,
+        DEFAULT_CONSTANTS[Constants.LARGE_GRADIENT_FACTOR],
+    )
+    constants[Constants.LARGE_GRADIENT_FACTOR.value] = float(
+        constants[Constants.LARGE_GRADIENT_FACTOR]
+    )
+    if constants[Constants.LARGE_GRADIENT_FACTOR] <= 1.0:
+        raise ValueError(
+            "The constant large_gradient_factor must be greater than 1."
+        )
+    constants.setdefault(
+        Constants.RESOLUTION_FACTOR.value,
+        DEFAULT_CONSTANTS[Constants.RESOLUTION_FACTOR],
+    )
+    constants[Constants.RESOLUTION_FACTOR.value] = float(
+        constants[Constants.RESOLUTION_FACTOR]
+    )
+    if constants[Constants.RESOLUTION_FACTOR] <= 1.0:
+        raise ValueError(
+            "The constant resolution_factor must be greater than 1."
+        )
+    constants.setdefault(
+        Constants.IMPROVE_TCG.value,
+        DEFAULT_CONSTANTS[Constants.IMPROVE_TCG],
+    )
+    constants[Constants.IMPROVE_TCG.value] = bool(
+        constants[Constants.IMPROVE_TCG]
+    )
+
+    # Check whether they are any unknown options.
+    for key in kwargs:
+        if key not in Constants.__members__.values():
+            warnings.warn(f"Unknown constant: {key}.", RuntimeWarning, 3)
+    return constants
+
+
+def _eval(pb, framework, step, options):
+    """
+    Evaluate the objective and constraint functions.
+    """
+    if pb.n_eval >= options[Options.MAX_EVAL]:
+        raise MaxEvalError
+    x_eval = framework.x_best + step
+    fun_val, cub_val, ceq_val = pb(x_eval, framework.penalty)
+    r_val = pb.maxcv(x_eval, cub_val, ceq_val)
+    if (
+        fun_val <= options[Options.TARGET]
+        and r_val <= options[Options.FEASIBILITY_TOL]
+    ):
+        raise TargetSuccess
+    if pb.is_feasibility and r_val <= options[Options.FEASIBILITY_TOL]:
+        raise FeasibleSuccess
+    return fun_val, cub_val, ceq_val
+
+
+def _build_result(pb, penalty, success, status, n_iter, options):
+    """
+    Build the result of the optimization process.
+    """
+    # Build the result.
+    x, fun, maxcv = pb.best_eval(penalty)
+    success = success and np.isfinite(fun) and np.isfinite(maxcv)
+    if status not in [ExitStatus.TARGET_SUCCESS, ExitStatus.FEASIBLE_SUCCESS]:
+        success = success and maxcv <= options[Options.FEASIBILITY_TOL]
+    result = OptimizeResult()
+    result.message = {
+        ExitStatus.RADIUS_SUCCESS: "The lower bound for the trust-region "
+                                   "radius has been reached",
+        ExitStatus.TARGET_SUCCESS: "The target objective function value has "
+                                   "been reached",
+        ExitStatus.FIXED_SUCCESS: "All variables are fixed by the bound "
+                                  "constraints",
+        ExitStatus.CALLBACK_SUCCESS: "The callback requested to stop the "
+                                     "optimization procedure",
+        ExitStatus.FEASIBLE_SUCCESS: "The feasibility problem received has "
+                                     "been solved successfully",
+        ExitStatus.MAX_EVAL_WARNING: "The maximum number of function "
+                                     "evaluations has been exceeded",
+        ExitStatus.MAX_ITER_WARNING: "The maximum number of iterations has "
+                                     "been exceeded",
+        ExitStatus.INFEASIBLE_ERROR: "The bound constraints are infeasible",
+        ExitStatus.LINALG_ERROR: "A linear algebra error occurred",
+    }.get(status, "Unknown exit status")
+    result.success = success
+    result.status = status.value
+    result.x = pb.build_x(x)
+    result.fun = fun
+    result.maxcv = maxcv
+    result.nfev = pb.n_eval
+    result.nit = n_iter
+    if options[Options.STORE_HISTORY]:
+        result.fun_history = pb.fun_history
+        result.maxcv_history = pb.maxcv_history
+
+    # Print the result if requested.
+    if options[Options.VERBOSE]:
+        _print_step(
+            result.message,
+            pb,
+            result.x,
+            result.fun,
+            result.maxcv,
+            result.nfev,
+            result.nit,
+        )
+    return result
+
+
+def _print_step(message, pb, x, fun_val, r_val, n_eval, n_iter):
+    """
+    Print information about the current state of the optimization process.
+    """
+    print()
+    print(f"{message}.")
+    print(f"Number of function evaluations: {n_eval}.")
+    print(f"Number of iterations: {n_iter}.")
+    if not pb.is_feasibility:
+        print(f"Least value of {pb.fun_name}: {fun_val}.")
+    print(f"Maximum constraint violation: {r_val}.")
+    with np.printoptions(**PRINT_OPTIONS):
+        print(f"Corresponding point: {x}.")
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/models.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/models.py
new file mode 100644
index 0000000000000000000000000000000000000000..44da70bf03a77e63af9ee45974050d008eed0147
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/models.py
@@ -0,0 +1,1531 @@
+import warnings
+
+import numpy as np
+from scipy.linalg import eigh
+
+from .settings import Options
+from .utils import MaxEvalError, TargetSuccess, FeasibleSuccess
+
+
+EPS = np.finfo(float).eps
+
+
+class Interpolation:
+    """
+    Interpolation set.
+
+    This class stores a base point around which the models are expanded and the
+    interpolation points. The coordinates of the interpolation points are
+    relative to the base point.
+    """
+
+    def __init__(self, pb, options):
+        """
+        Initialize the interpolation set.
+
+        Parameters
+        ----------
+        pb : `cobyqa.problem.Problem`
+            Problem to be solved.
+        options : dict
+            Options of the solver.
+        """
+        # Reduce the initial trust-region radius if necessary.
+        self._debug = options[Options.DEBUG]
+        max_radius = 0.5 * np.min(pb.bounds.xu - pb.bounds.xl)
+        if options[Options.RHOBEG] > max_radius:
+            options[Options.RHOBEG.value] = max_radius
+            options[Options.RHOEND.value] = np.min(
+                [
+                    options[Options.RHOEND],
+                    max_radius,
+                ]
+            )
+
+        # Set the initial point around which the models are expanded.
+        self._x_base = np.copy(pb.x0)
+        very_close_xl_idx = (
+            self.x_base <= pb.bounds.xl + 0.5 * options[Options.RHOBEG]
+        )
+        self.x_base[very_close_xl_idx] = pb.bounds.xl[very_close_xl_idx]
+        close_xl_idx = (
+            pb.bounds.xl + 0.5 * options[Options.RHOBEG] < self.x_base
+        ) & (self.x_base <= pb.bounds.xl + options[Options.RHOBEG])
+        self.x_base[close_xl_idx] = np.minimum(
+            pb.bounds.xl[close_xl_idx] + options[Options.RHOBEG],
+            pb.bounds.xu[close_xl_idx],
+        )
+        very_close_xu_idx = (
+            self.x_base >= pb.bounds.xu - 0.5 * options[Options.RHOBEG]
+        )
+        self.x_base[very_close_xu_idx] = pb.bounds.xu[very_close_xu_idx]
+        close_xu_idx = (
+            self.x_base < pb.bounds.xu - 0.5 * options[Options.RHOBEG]
+        ) & (pb.bounds.xu - options[Options.RHOBEG] <= self.x_base)
+        self.x_base[close_xu_idx] = np.maximum(
+            pb.bounds.xu[close_xu_idx] - options[Options.RHOBEG],
+            pb.bounds.xl[close_xu_idx],
+        )
+
+        # Set the initial interpolation set.
+        self._xpt = np.zeros((pb.n, options[Options.NPT]))
+        for k in range(1, options[Options.NPT]):
+            if k <= pb.n:
+                if very_close_xu_idx[k - 1]:
+                    self.xpt[k - 1, k] = -options[Options.RHOBEG]
+                else:
+                    self.xpt[k - 1, k] = options[Options.RHOBEG]
+            elif k <= 2 * pb.n:
+                if very_close_xl_idx[k - pb.n - 1]:
+                    self.xpt[k - pb.n - 1, k] = 2.0 * options[Options.RHOBEG]
+                elif very_close_xu_idx[k - pb.n - 1]:
+                    self.xpt[k - pb.n - 1, k] = -2.0 * options[Options.RHOBEG]
+                else:
+                    self.xpt[k - pb.n - 1, k] = -options[Options.RHOBEG]
+            else:
+                spread = (k - pb.n - 1) // pb.n
+                k1 = k - (1 + spread) * pb.n - 1
+                k2 = (k1 + spread) % pb.n
+                self.xpt[k1, k] = self.xpt[k1, k1 + 1]
+                self.xpt[k2, k] = self.xpt[k2, k2 + 1]
+        self._lhs_cache = None
+
+    @property
+    def n(self):
+        """
+        Number of variables.
+
+        Returns
+        -------
+        int
+            Number of variables.
+        """
+        return self.xpt.shape[0]
+
+    @property
+    def npt(self):
+        """
+        Number of interpolation points.
+
+        Returns
+        -------
+        int
+            Number of interpolation points.
+        """
+        return self.xpt.shape[1]
+
+    @property
+    def xpt(self):
+        """
+        Interpolation points.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n, npt)
+            Interpolation points.
+        """
+        return self._xpt
+
+    @xpt.setter
+    def xpt(self, xpt):
+        """
+        Set the interpolation points.
+
+        Parameters
+        ----------
+        xpt : `numpy.ndarray`, shape (n, npt)
+            New interpolation points.
+        """
+        if self._debug:
+            assert xpt.shape == (
+                self.n,
+                self.npt,
+            ), "The shape of `xpt` is not valid."
+        self._xpt = xpt
+
+    @property
+    def x_base(self):
+        """
+        Base point around which the models are expanded.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Base point around which the models are expanded.
+        """
+        return self._x_base
+
+    @x_base.setter
+    def x_base(self, x_base):
+        """
+        Set the base point around which the models are expanded.
+
+        Parameters
+        ----------
+        x_base : `numpy.ndarray`, shape (n,)
+            New base point around which the models are expanded.
+        """
+        if self._debug:
+            assert x_base.shape == (
+                self.n,
+            ), "The shape of `x_base` is not valid."
+        self._x_base = x_base
+
+    def point(self, k):
+        """
+        Get the `k`-th interpolation point.
+
+        The return point is relative to the origin.
+
+        Parameters
+        ----------
+        k : int
+            Index of the interpolation point.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            `k`-th interpolation point.
+        """
+        if self._debug:
+            assert 0 <= k < self.npt, "The index `k` is not valid."
+        return self.x_base + self.xpt[:, k]
+
+
+def build_system(interpolation):
+    """
+    Build the left-hand side matrix of the interpolation system. The
+    matrix below stores W * diag(right_scaling),
+    where W is the theoretical matrix of the interpolation system. The
+    right scaling matrices is chosen to keep the elements in
+    the matrix well-balanced.
+
+    Parameters
+    ----------
+    interpolation : `cobyqa.models.Interpolation`
+        Interpolation set.
+    """
+
+    _cache = interpolation._lhs_cache
+    # Compute the scaled directions from the base point to the
+    # interpolation points. We scale the directions to avoid numerical
+    # difficulties.
+    if _cache is not None and np.array_equal(
+        interpolation.xpt, _cache["xpt"]
+    ):
+        return _cache["a"], _cache["right_scaling"], _cache["eigh"]
+
+    scale = np.max(np.linalg.norm(interpolation.xpt, axis=0), initial=EPS)
+    xpt_scale = interpolation.xpt / scale
+
+    n, npt = xpt_scale.shape
+    a = np.zeros((npt + n + 1, npt + n + 1))
+    a[:npt, :npt] = 0.5 * (xpt_scale.T @ xpt_scale) ** 2.0
+    a[:npt, npt] = 1.0
+    a[:npt, npt + 1:] = xpt_scale.T
+    a[npt, :npt] = 1.0
+    a[npt + 1:, :npt] = xpt_scale
+
+    # Build the left and right scaling diagonal matrices.
+    right_scaling = np.empty(npt + n + 1)
+    right_scaling[:npt] = 1.0 / scale**2.0
+    right_scaling[npt] = scale**2.0
+    right_scaling[npt + 1:] = scale
+
+    eig_values, eig_vectors = eigh(a, check_finite=False)
+
+    new_cache = {
+        "xpt": np.copy(interpolation.xpt),
+        "a": np.copy(a),
+        "right_scaling": np.copy(right_scaling),
+        "eigh": (eig_values, eig_vectors),
+    }
+    interpolation._lhs_cache = new_cache
+
+    return a, right_scaling, (eig_values, eig_vectors)
+
+
+class Quadratic:
+    """
+    Quadratic model.
+
+    This class stores the Hessian matrix of the quadratic model using the
+    implicit/explicit representation designed by Powell for NEWUOA [1]_.
+
+    References
+    ----------
+    .. [1] M. J. D. Powell. The NEWUOA software for unconstrained optimization
+       without derivatives. In G. Di Pillo and M. Roma, editors, *Large-Scale
+       Nonlinear Optimization*, volume 83 of Nonconvex Optim. Appl., pages
+       255--297. Springer, Boston, MA, USA, 2006. `doi:10.1007/0-387-30065-1_16
+       `_.
+    """
+
+    def __init__(self, interpolation, values, debug):
+        """
+        Initialize the quadratic model.
+
+        Parameters
+        ----------
+        interpolation : `cobyqa.models.Interpolation`
+            Interpolation set.
+        values : `numpy.ndarray`, shape (npt,)
+            Values of the interpolated function at the interpolation points.
+        debug : bool
+            Whether to make debugging tests during the execution.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the interpolation system is ill-defined.
+        """
+        self._debug = debug
+        if self._debug:
+            assert values.shape == (
+                interpolation.npt,
+            ), "The shape of `values` is not valid."
+        if interpolation.npt < interpolation.n + 1:
+            raise ValueError(
+                f"The number of interpolation points must be at least "
+                f"{interpolation.n + 1}."
+            )
+        self._const, self._grad, self._i_hess, _ = self._get_model(
+            interpolation,
+            values,
+        )
+        self._e_hess = np.zeros((self.n, self.n))
+
+    def __call__(self, x, interpolation):
+        """
+        Evaluate the quadratic model at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which the quadratic model is evaluated.
+        interpolation : `cobyqa.models.Interpolation`
+            Interpolation set.
+
+        Returns
+        -------
+        float
+            Value of the quadratic model at `x`.
+        """
+        if self._debug:
+            assert x.shape == (self.n,), "The shape of `x` is not valid."
+        x_diff = x - interpolation.x_base
+        return (
+            self._const
+            + self._grad @ x_diff
+            + 0.5
+            * (
+                self._i_hess @ (interpolation.xpt.T @ x_diff) ** 2.0
+                + x_diff @ self._e_hess @ x_diff
+            )
+        )
+
+    @property
+    def n(self):
+        """
+        Number of variables.
+
+        Returns
+        -------
+        int
+            Number of variables.
+        """
+        return self._grad.size
+
+    @property
+    def npt(self):
+        """
+        Number of interpolation points used to define the quadratic model.
+
+        Returns
+        -------
+        int
+            Number of interpolation points used to define the quadratic model.
+        """
+        return self._i_hess.size
+
+    def grad(self, x, interpolation):
+        """
+        Evaluate the gradient of the quadratic model at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which the gradient of the quadratic model is evaluated.
+        interpolation : `cobyqa.models.Interpolation`
+            Interpolation set.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Gradient of the quadratic model at `x`.
+        """
+        if self._debug:
+            assert x.shape == (self.n,), "The shape of `x` is not valid."
+        x_diff = x - interpolation.x_base
+        return self._grad + self.hess_prod(x_diff, interpolation)
+
+    def hess(self, interpolation):
+        """
+        Evaluate the Hessian matrix of the quadratic model.
+
+        Parameters
+        ----------
+        interpolation : `cobyqa.models.Interpolation`
+            Interpolation set.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n, n)
+            Hessian matrix of the quadratic model.
+        """
+        return self._e_hess + interpolation.xpt @ (
+            self._i_hess[:, np.newaxis] * interpolation.xpt.T
+        )
+
+    def hess_prod(self, v, interpolation):
+        """
+        Evaluate the right product of the Hessian matrix of the quadratic model
+        with a given vector.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Vector with which the Hessian matrix of the quadratic model is
+            multiplied from the right.
+        interpolation : `cobyqa.models.Interpolation`
+            Interpolation set.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Right product of the Hessian matrix of the quadratic model with
+            `v`.
+        """
+        if self._debug:
+            assert v.shape == (self.n,), "The shape of `v` is not valid."
+        return self._e_hess @ v + interpolation.xpt @ (
+            self._i_hess * (interpolation.xpt.T @ v)
+        )
+
+    def curv(self, v, interpolation):
+        """
+        Evaluate the curvature of the quadratic model along a given direction.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Direction along which the curvature of the quadratic model is
+            evaluated.
+        interpolation : `cobyqa.models.Interpolation`
+            Interpolation set.
+
+        Returns
+        -------
+        float
+            Curvature of the quadratic model along `v`.
+        """
+        if self._debug:
+            assert v.shape == (self.n,), "The shape of `v` is not valid."
+        return (
+            v @ self._e_hess @ v
+            + self._i_hess @ (interpolation.xpt.T @ v) ** 2.0
+        )
+
+    def update(self, interpolation, k_new, dir_old, values_diff):
+        """
+        Update the quadratic model.
+
+        This method applies the derivative-free symmetric Broyden update to the
+        quadratic model. The `knew`-th interpolation point must be updated
+        before calling this method.
+
+        Parameters
+        ----------
+        interpolation : `cobyqa.models.Interpolation`
+            Updated interpolation set.
+        k_new : int
+            Index of the updated interpolation point.
+        dir_old : `numpy.ndarray`, shape (n,)
+            Value of ``interpolation.xpt[:, k_new]`` before the update.
+        values_diff : `numpy.ndarray`, shape (npt,)
+            Differences between the values of the interpolated nonlinear
+            function and the previous quadratic model at the updated
+            interpolation points.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the interpolation system is ill-defined.
+        """
+        if self._debug:
+            assert 0 <= k_new < self.npt, "The index `k_new` is not valid."
+            assert dir_old.shape == (
+                self.n,
+            ), "The shape of `dir_old` is not valid."
+            assert values_diff.shape == (
+                self.npt,
+            ), "The shape of `values_diff` is not valid."
+
+        # Forward the k_new-th element of the implicit Hessian matrix to the
+        # explicit Hessian matrix. This must be done because the implicit
+        # Hessian matrix is related to the interpolation points, and the
+        # k_new-th interpolation point is modified.
+        self._e_hess += self._i_hess[k_new] * np.outer(dir_old, dir_old)
+        self._i_hess[k_new] = 0.0
+
+        # Update the quadratic model.
+        const, grad, i_hess, ill_conditioned = self._get_model(
+            interpolation,
+            values_diff,
+        )
+        self._const += const
+        self._grad += grad
+        self._i_hess += i_hess
+        return ill_conditioned
+
+    def shift_x_base(self, interpolation, new_x_base):
+        """
+        Shift the point around which the quadratic model is defined.
+
+        Parameters
+        ----------
+        interpolation : `cobyqa.models.Interpolation`
+            Previous interpolation set.
+        new_x_base : `numpy.ndarray`, shape (n,)
+            Point that will replace ``interpolation.x_base``.
+        """
+        if self._debug:
+            assert new_x_base.shape == (
+                self.n,
+            ), "The shape of `new_x_base` is not valid."
+        self._const = self(new_x_base, interpolation)
+        self._grad = self.grad(new_x_base, interpolation)
+        shift = new_x_base - interpolation.x_base
+        update = np.outer(
+            shift,
+            (interpolation.xpt - 0.5 * shift[:, np.newaxis]) @ self._i_hess,
+        )
+        self._e_hess += update + update.T
+
+    @staticmethod
+    def solve_systems(interpolation, rhs):
+        """
+        Solve the interpolation systems.
+
+        Parameters
+        ----------
+        interpolation : `cobyqa.models.Interpolation`
+            Interpolation set.
+        rhs : `numpy.ndarray`, shape (npt + n + 1, m)
+            Right-hand side vectors of the ``m`` interpolation systems.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (npt + n + 1, m)
+            Solutions of the interpolation systems.
+        `numpy.ndarray`, shape (m, )
+            Whether the interpolation systems are ill-conditioned.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the interpolation systems are ill-defined.
+        """
+        n, npt = interpolation.xpt.shape
+        assert (
+            rhs.ndim == 2 and rhs.shape[0] == npt + n + 1
+        ), "The shape of `rhs` is not valid."
+
+        # Build the left-hand side matrix of the interpolation system. The
+        # matrix below stores diag(left_scaling) * W * diag(right_scaling),
+        # where W is the theoretical matrix of the interpolation system. The
+        # left and right scaling matrices are chosen to keep the elements in
+        # the matrix well-balanced.
+        a, right_scaling, eig = build_system(interpolation)
+
+        # Build the solution. After a discussion with Mike Saunders and Alexis
+        # Montoison during their visit to the Hong Kong Polytechnic University
+        # in 2024, we decided to use the eigendecomposition of the symmetric
+        # matrix a. This is more stable than the previously employed LBL
+        # decomposition, and allows us to directly detect ill-conditioning of
+        # the system and to build the least-squares solution if necessary.
+        # Numerical experiments have shown that this strategy improves the
+        # performance of the solver.
+        rhs_scaled = rhs * right_scaling[:, np.newaxis]
+        if not (np.all(np.isfinite(a)) and np.all(np.isfinite(rhs_scaled))):
+            raise np.linalg.LinAlgError(
+                "The interpolation system is ill-defined."
+            )
+
+        # calculated in build_system
+        eig_values, eig_vectors = eig
+
+        large_eig_values = np.abs(eig_values) > EPS
+        eig_vectors = eig_vectors[:, large_eig_values]
+        inv_eig_values = 1.0 / eig_values[large_eig_values]
+        ill_conditioned = ~np.all(large_eig_values, 0)
+        left_scaled_solutions = eig_vectors @ (
+            (eig_vectors.T @ rhs_scaled) * inv_eig_values[:, np.newaxis]
+        )
+        return (
+            left_scaled_solutions * right_scaling[:, np.newaxis],
+            ill_conditioned,
+        )
+
+    @staticmethod
+    def _get_model(interpolation, values):
+        """
+        Solve the interpolation system.
+
+        Parameters
+        ----------
+        interpolation : `cobyqa.models.Interpolation`
+            Interpolation set.
+        values : `numpy.ndarray`, shape (npt,)
+            Values of the interpolated function at the interpolation points.
+
+        Returns
+        -------
+        float
+            Constant term of the quadratic model.
+        `numpy.ndarray`, shape (n,)
+            Gradient of the quadratic model at ``interpolation.x_base``.
+        `numpy.ndarray`, shape (npt,)
+            Implicit Hessian matrix of the quadratic model.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the interpolation system is ill-defined.
+        """
+        assert values.shape == (
+            interpolation.npt,
+        ), "The shape of `values` is not valid."
+        n, npt = interpolation.xpt.shape
+        x, ill_conditioned = Quadratic.solve_systems(
+            interpolation,
+            np.block(
+                [
+                    [
+                        values,
+                        np.zeros(n + 1),
+                    ]
+                ]
+            ).T,
+        )
+        return x[npt, 0], x[npt + 1:, 0], x[:npt, 0], ill_conditioned
+
+
+class Models:
+    """
+    Models for a nonlinear optimization problem.
+    """
+
+    def __init__(self, pb, options, penalty):
+        """
+        Initialize the models.
+
+        Parameters
+        ----------
+        pb : `cobyqa.problem.Problem`
+            Problem to be solved.
+        options : dict
+            Options of the solver.
+        penalty : float
+            Penalty parameter used to select the point in the filter to forward
+            to the callback function.
+
+        Raises
+        ------
+        `cobyqa.utils.MaxEvalError`
+            If the maximum number of evaluations is reached.
+        `cobyqa.utils.TargetSuccess`
+            If a nearly feasible point has been found with an objective
+            function value below the target.
+        `cobyqa.utils.FeasibleSuccess`
+            If a feasible point has been found for a feasibility problem.
+        `numpy.linalg.LinAlgError`
+            If the interpolation system is ill-defined.
+        """
+        # Set the initial interpolation set.
+        self._debug = options[Options.DEBUG]
+        self._interpolation = Interpolation(pb, options)
+
+        # Evaluate the nonlinear functions at the initial interpolation points.
+        x_eval = self.interpolation.point(0)
+        fun_init, cub_init, ceq_init = pb(x_eval, penalty)
+        self._fun_val = np.full(options[Options.NPT], np.nan)
+        self._cub_val = np.full((options[Options.NPT], cub_init.size), np.nan)
+        self._ceq_val = np.full((options[Options.NPT], ceq_init.size), np.nan)
+        for k in range(options[Options.NPT]):
+            if k >= options[Options.MAX_EVAL]:
+                raise MaxEvalError
+            if k == 0:
+                self.fun_val[k] = fun_init
+                self.cub_val[k, :] = cub_init
+                self.ceq_val[k, :] = ceq_init
+            else:
+                x_eval = self.interpolation.point(k)
+                self.fun_val[k], self.cub_val[k, :], self.ceq_val[k, :] = pb(
+                    x_eval,
+                    penalty,
+                )
+
+            # Stop the iterations if the problem is a feasibility problem and
+            # the current interpolation point is feasible.
+            if (
+                pb.is_feasibility
+                and pb.maxcv(
+                    self.interpolation.point(k),
+                    self.cub_val[k, :],
+                    self.ceq_val[k, :],
+                )
+                <= options[Options.FEASIBILITY_TOL]
+            ):
+                raise FeasibleSuccess
+
+            # Stop the iterations if the current interpolation point is nearly
+            # feasible and has an objective function value below the target.
+            if (
+                self._fun_val[k] <= options[Options.TARGET]
+                and pb.maxcv(
+                    self.interpolation.point(k),
+                    self.cub_val[k, :],
+                    self.ceq_val[k, :],
+                )
+                <= options[Options.FEASIBILITY_TOL]
+            ):
+                raise TargetSuccess
+
+        # Build the initial quadratic models.
+        self._fun = Quadratic(
+            self.interpolation,
+            self._fun_val,
+            options[Options.DEBUG],
+        )
+        self._cub = np.empty(self.m_nonlinear_ub, dtype=Quadratic)
+        self._ceq = np.empty(self.m_nonlinear_eq, dtype=Quadratic)
+        for i in range(self.m_nonlinear_ub):
+            self._cub[i] = Quadratic(
+                self.interpolation,
+                self.cub_val[:, i],
+                options[Options.DEBUG],
+            )
+        for i in range(self.m_nonlinear_eq):
+            self._ceq[i] = Quadratic(
+                self.interpolation,
+                self.ceq_val[:, i],
+                options[Options.DEBUG],
+            )
+        if self._debug:
+            self._check_interpolation_conditions()
+
+    @property
+    def n(self):
+        """
+        Dimension of the problem.
+
+        Returns
+        -------
+        int
+            Dimension of the problem.
+        """
+        return self.interpolation.n
+
+    @property
+    def npt(self):
+        """
+        Number of interpolation points.
+
+        Returns
+        -------
+        int
+            Number of interpolation points.
+        """
+        return self.interpolation.npt
+
+    @property
+    def m_nonlinear_ub(self):
+        """
+        Number of nonlinear inequality constraints.
+
+        Returns
+        -------
+        int
+            Number of nonlinear inequality constraints.
+        """
+        return self.cub_val.shape[1]
+
+    @property
+    def m_nonlinear_eq(self):
+        """
+        Number of nonlinear equality constraints.
+
+        Returns
+        -------
+        int
+            Number of nonlinear equality constraints.
+        """
+        return self.ceq_val.shape[1]
+
+    @property
+    def interpolation(self):
+        """
+        Interpolation set.
+
+        Returns
+        -------
+        `cobyqa.models.Interpolation`
+            Interpolation set.
+        """
+        return self._interpolation
+
+    @property
+    def fun_val(self):
+        """
+        Values of the objective function at the interpolation points.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (npt,)
+            Values of the objective function at the interpolation points.
+        """
+        return self._fun_val
+
+    @property
+    def cub_val(self):
+        """
+        Values of the nonlinear inequality constraint functions at the
+        interpolation points.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (npt, m_nonlinear_ub)
+            Values of the nonlinear inequality constraint functions at the
+            interpolation points.
+        """
+        return self._cub_val
+
+    @property
+    def ceq_val(self):
+        """
+        Values of the nonlinear equality constraint functions at the
+        interpolation points.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (npt, m_nonlinear_eq)
+            Values of the nonlinear equality constraint functions at the
+            interpolation points.
+        """
+        return self._ceq_val
+
+    def fun(self, x):
+        """
+        Evaluate the quadratic model of the objective function at a given
+        point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which to evaluate the quadratic model of the objective
+            function.
+
+        Returns
+        -------
+        float
+            Value of the quadratic model of the objective function at `x`.
+        """
+        if self._debug:
+            assert x.shape == (self.n,), "The shape of `x` is not valid."
+        return self._fun(x, self.interpolation)
+
+    def fun_grad(self, x):
+        """
+        Evaluate the gradient of the quadratic model of the objective function
+        at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which to evaluate the gradient of the quadratic model of
+            the objective function.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Gradient of the quadratic model of the objective function at `x`.
+        """
+        if self._debug:
+            assert x.shape == (self.n,), "The shape of `x` is not valid."
+        return self._fun.grad(x, self.interpolation)
+
+    def fun_hess(self):
+        """
+        Evaluate the Hessian matrix of the quadratic model of the objective
+        function.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n, n)
+            Hessian matrix of the quadratic model of the objective function.
+        """
+        return self._fun.hess(self.interpolation)
+
+    def fun_hess_prod(self, v):
+        """
+        Evaluate the right product of the Hessian matrix of the quadratic model
+        of the objective function with a given vector.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Vector with which the Hessian matrix of the quadratic model of the
+            objective function is multiplied from the right.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Right product of the Hessian matrix of the quadratic model of the
+            objective function with `v`.
+        """
+        if self._debug:
+            assert v.shape == (self.n,), "The shape of `v` is not valid."
+        return self._fun.hess_prod(v, self.interpolation)
+
+    def fun_curv(self, v):
+        """
+        Evaluate the curvature of the quadratic model of the objective function
+        along a given direction.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Direction along which the curvature of the quadratic model of the
+            objective function is evaluated.
+
+        Returns
+        -------
+        float
+            Curvature of the quadratic model of the objective function along
+            `v`.
+        """
+        if self._debug:
+            assert v.shape == (self.n,), "The shape of `v` is not valid."
+        return self._fun.curv(v, self.interpolation)
+
+    def fun_alt_grad(self, x):
+        """
+        Evaluate the gradient of the alternative quadratic model of the
+        objective function at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which to evaluate the gradient of the alternative
+            quadratic model of the objective function.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Gradient of the alternative quadratic model of the objective
+            function at `x`.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the interpolation system is ill-defined.
+        """
+        if self._debug:
+            assert x.shape == (self.n,), "The shape of `x` is not valid."
+        model = Quadratic(self.interpolation, self.fun_val, self._debug)
+        return model.grad(x, self.interpolation)
+
+    def cub(self, x, mask=None):
+        """
+        Evaluate the quadratic models of the nonlinear inequality functions at
+        a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which to evaluate the quadratic models of the nonlinear
+            inequality functions.
+        mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Values of the quadratic model of the nonlinear inequality
+            functions.
+        """
+        if self._debug:
+            assert x.shape == (self.n,), "The shape of `x` is not valid."
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_ub,
+            ), "The shape of `mask` is not valid."
+        return np.array(
+            [model(x, self.interpolation) for model in self._get_cub(mask)]
+        )
+
+    def cub_grad(self, x, mask=None):
+        """
+        Evaluate the gradients of the quadratic models of the nonlinear
+        inequality functions at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which to evaluate the gradients of the quadratic models of
+            the nonlinear inequality functions.
+        mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Gradients of the quadratic model of the nonlinear inequality
+            functions.
+        """
+        if self._debug:
+            assert x.shape == (self.n,), "The shape of `x` is not valid."
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_ub,
+            ), "The shape of `mask` is not valid."
+        return np.reshape(
+            [model.grad(x, self.interpolation)
+             for model in self._get_cub(mask)],
+            (-1, self.n),
+        )
+
+    def cub_hess(self, mask=None):
+        """
+        Evaluate the Hessian matrices of the quadratic models of the nonlinear
+        inequality functions.
+
+        Parameters
+        ----------
+        mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Hessian matrices of the quadratic models of the nonlinear
+            inequality functions.
+        """
+        if self._debug:
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_ub,
+            ), "The shape of `mask` is not valid."
+        return np.reshape(
+            [model.hess(self.interpolation) for model in self._get_cub(mask)],
+            (-1, self.n, self.n),
+        )
+
+    def cub_hess_prod(self, v, mask=None):
+        """
+        Evaluate the right product of the Hessian matrices of the quadratic
+        models of the nonlinear inequality functions with a given vector.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Vector with which the Hessian matrices of the quadratic models of
+            the nonlinear inequality functions are multiplied from the right.
+        mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Right products of the Hessian matrices of the quadratic models of
+            the nonlinear inequality functions with `v`.
+        """
+        if self._debug:
+            assert v.shape == (self.n,), "The shape of `v` is not valid."
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_ub,
+            ), "The shape of `mask` is not valid."
+        return np.reshape(
+            [
+                model.hess_prod(v, self.interpolation)
+                for model in self._get_cub(mask)
+            ],
+            (-1, self.n),
+        )
+
+    def cub_curv(self, v, mask=None):
+        """
+        Evaluate the curvature of the quadratic models of the nonlinear
+        inequality functions along a given direction.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Direction along which the curvature of the quadratic models of the
+            nonlinear inequality functions is evaluated.
+        mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Curvature of the quadratic models of the nonlinear inequality
+            functions along `v`.
+        """
+        if self._debug:
+            assert v.shape == (self.n,), "The shape of `v` is not valid."
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_ub,
+            ), "The shape of `mask` is not valid."
+        return np.array(
+            [model.curv(v, self.interpolation)
+             for model in self._get_cub(mask)]
+        )
+
+    def ceq(self, x, mask=None):
+        """
+        Evaluate the quadratic models of the nonlinear equality functions at a
+        given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which to evaluate the quadratic models of the nonlinear
+            equality functions.
+        mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Values of the quadratic model of the nonlinear equality functions.
+        """
+        if self._debug:
+            assert x.shape == (self.n,), "The shape of `x` is not valid."
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_eq,
+            ), "The shape of `mask` is not valid."
+        return np.array(
+            [model(x, self.interpolation) for model in self._get_ceq(mask)]
+        )
+
+    def ceq_grad(self, x, mask=None):
+        """
+        Evaluate the gradients of the quadratic models of the nonlinear
+        equality functions at a given point.
+
+        Parameters
+        ----------
+        x : `numpy.ndarray`, shape (n,)
+            Point at which to evaluate the gradients of the quadratic models of
+            the nonlinear equality functions.
+        mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Gradients of the quadratic model of the nonlinear equality
+            functions.
+        """
+        if self._debug:
+            assert x.shape == (self.n,), "The shape of `x` is not valid."
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_eq,
+            ), "The shape of `mask` is not valid."
+        return np.reshape(
+            [model.grad(x, self.interpolation)
+             for model in self._get_ceq(mask)],
+            (-1, self.n),
+        )
+
+    def ceq_hess(self, mask=None):
+        """
+        Evaluate the Hessian matrices of the quadratic models of the nonlinear
+        equality functions.
+
+        Parameters
+        ----------
+        mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Hessian matrices of the quadratic models of the nonlinear equality
+            functions.
+        """
+        if self._debug:
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_eq,
+            ), "The shape of `mask` is not valid."
+        return np.reshape(
+            [model.hess(self.interpolation) for model in self._get_ceq(mask)],
+            (-1, self.n, self.n),
+        )
+
+    def ceq_hess_prod(self, v, mask=None):
+        """
+        Evaluate the right product of the Hessian matrices of the quadratic
+        models of the nonlinear equality functions with a given vector.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Vector with which the Hessian matrices of the quadratic models of
+            the nonlinear equality functions are multiplied from the right.
+        mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Right products of the Hessian matrices of the quadratic models of
+            the nonlinear equality functions with `v`.
+        """
+        if self._debug:
+            assert v.shape == (self.n,), "The shape of `v` is not valid."
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_eq,
+            ), "The shape of `mask` is not valid."
+        return np.reshape(
+            [
+                model.hess_prod(v, self.interpolation)
+                for model in self._get_ceq(mask)
+            ],
+            (-1, self.n),
+        )
+
+    def ceq_curv(self, v, mask=None):
+        """
+        Evaluate the curvature of the quadratic models of the nonlinear
+        equality functions along a given direction.
+
+        Parameters
+        ----------
+        v : `numpy.ndarray`, shape (n,)
+            Direction along which the curvature of the quadratic models of the
+            nonlinear equality functions is evaluated.
+        mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional
+            Mask of the quadratic models to consider.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Curvature of the quadratic models of the nonlinear equality
+            functions along `v`.
+        """
+        if self._debug:
+            assert v.shape == (self.n,), "The shape of `v` is not valid."
+            assert mask is None or mask.shape == (
+                self.m_nonlinear_eq,
+            ), "The shape of `mask` is not valid."
+        return np.array(
+            [model.curv(v, self.interpolation)
+             for model in self._get_ceq(mask)]
+        )
+
+    def reset_models(self):
+        """
+        Set the quadratic models of the objective function, nonlinear
+        inequality constraints, and nonlinear equality constraints to the
+        alternative quadratic models.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the interpolation system is ill-defined.
+        """
+        self._fun = Quadratic(self.interpolation, self.fun_val, self._debug)
+        for i in range(self.m_nonlinear_ub):
+            self._cub[i] = Quadratic(
+                self.interpolation,
+                self.cub_val[:, i],
+                self._debug,
+            )
+        for i in range(self.m_nonlinear_eq):
+            self._ceq[i] = Quadratic(
+                self.interpolation,
+                self.ceq_val[:, i],
+                self._debug,
+            )
+        if self._debug:
+            self._check_interpolation_conditions()
+
+    def update_interpolation(self, k_new, x_new, fun_val, cub_val, ceq_val):
+        """
+        Update the interpolation set.
+
+        This method updates the interpolation set by replacing the `knew`-th
+        interpolation point with `xnew`. It also updates the function values
+        and the quadratic models.
+
+        Parameters
+        ----------
+        k_new : int
+            Index of the updated interpolation point.
+        x_new : `numpy.ndarray`, shape (n,)
+            New interpolation point. Its value is interpreted as relative to
+            the origin, not the base point.
+        fun_val : float
+            Value of the objective function at `x_new`.
+            Objective function value at `x_new`.
+        cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,)
+            Values of the nonlinear inequality constraints at `x_new`.
+        ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,)
+            Values of the nonlinear equality constraints at `x_new`.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the interpolation system is ill-defined.
+        """
+        if self._debug:
+            assert 0 <= k_new < self.npt, "The index `k_new` is not valid."
+            assert x_new.shape == (self.n,), \
+                "The shape of `x_new` is not valid."
+            assert isinstance(fun_val, float), \
+                "The function value is not valid."
+            assert cub_val.shape == (
+                self.m_nonlinear_ub,
+            ), "The shape of `cub_val` is not valid."
+            assert ceq_val.shape == (
+                self.m_nonlinear_eq,
+            ), "The shape of `ceq_val` is not valid."
+
+        # Compute the updates in the interpolation conditions.
+        fun_diff = np.zeros(self.npt)
+        cub_diff = np.zeros(self.cub_val.shape)
+        ceq_diff = np.zeros(self.ceq_val.shape)
+        fun_diff[k_new] = fun_val - self.fun(x_new)
+        cub_diff[k_new, :] = cub_val - self.cub(x_new)
+        ceq_diff[k_new, :] = ceq_val - self.ceq(x_new)
+
+        # Update the function values.
+        self.fun_val[k_new] = fun_val
+        self.cub_val[k_new, :] = cub_val
+        self.ceq_val[k_new, :] = ceq_val
+
+        # Update the interpolation set.
+        dir_old = np.copy(self.interpolation.xpt[:, k_new])
+        self.interpolation.xpt[:, k_new] = x_new - self.interpolation.x_base
+
+        # Update the quadratic models.
+        ill_conditioned = self._fun.update(
+            self.interpolation,
+            k_new,
+            dir_old,
+            fun_diff,
+        )
+        for i in range(self.m_nonlinear_ub):
+            ill_conditioned = ill_conditioned or self._cub[i].update(
+                self.interpolation,
+                k_new,
+                dir_old,
+                cub_diff[:, i],
+            )
+        for i in range(self.m_nonlinear_eq):
+            ill_conditioned = ill_conditioned or self._ceq[i].update(
+                self.interpolation,
+                k_new,
+                dir_old,
+                ceq_diff[:, i],
+            )
+        if self._debug:
+            self._check_interpolation_conditions()
+        return ill_conditioned
+
+    def determinants(self, x_new, k_new=None):
+        """
+        Compute the normalized determinants of the new interpolation systems.
+
+        Parameters
+        ----------
+        x_new : `numpy.ndarray`, shape (n,)
+            New interpolation point. Its value is interpreted as relative to
+            the origin, not the base point.
+        k_new : int, optional
+            Index of the updated interpolation point. If `k_new` is not
+            specified, all the possible determinants are computed.
+
+        Returns
+        -------
+        {float, `numpy.ndarray`, shape (npt,)}
+            Determinant(s) of the new interpolation system.
+
+        Raises
+        ------
+        `numpy.linalg.LinAlgError`
+            If the interpolation system is ill-defined.
+
+        Notes
+        -----
+        The determinants are normalized by the determinant of the current
+        interpolation system. For stability reasons, the calculations are done
+        using the formula (2.12) in [1]_.
+
+        References
+        ----------
+        .. [1] M. J. D. Powell. On updating the inverse of a KKT matrix.
+           Technical Report DAMTP 2004/NA01, Department of Applied Mathematics
+           and Theoretical Physics, University of Cambridge, Cambridge, UK,
+           2004.
+        """
+        if self._debug:
+            assert x_new.shape == (self.n,), \
+                "The shape of `x_new` is not valid."
+            assert (
+                k_new is None or 0 <= k_new < self.npt
+            ), "The index `k_new` is not valid."
+
+        # Compute the values independent of k_new.
+        shift = x_new - self.interpolation.x_base
+        new_col = np.empty((self.npt + self.n + 1, 1))
+        new_col[: self.npt, 0] = (
+                0.5 * (self.interpolation.xpt.T @ shift) ** 2.0)
+        new_col[self.npt, 0] = 1.0
+        new_col[self.npt + 1:, 0] = shift
+        inv_new_col = Quadratic.solve_systems(self.interpolation, new_col)[0]
+        beta = 0.5 * (shift @ shift) ** 2.0 - new_col[:, 0] @ inv_new_col[:, 0]
+
+        # Compute the values that depend on k.
+        if k_new is None:
+            coord_vec = np.eye(self.npt + self.n + 1, self.npt)
+            alpha = np.diag(
+                Quadratic.solve_systems(
+                    self.interpolation,
+                    coord_vec,
+                )[0]
+            )
+            tau = inv_new_col[: self.npt, 0]
+        else:
+            coord_vec = np.eye(self.npt + self.n + 1, 1, -k_new)
+            alpha = Quadratic.solve_systems(
+                self.interpolation,
+                coord_vec,
+            )[
+                0
+            ][k_new, 0]
+            tau = inv_new_col[k_new, 0]
+        return alpha * beta + tau**2.0
+
+    def shift_x_base(self, new_x_base, options):
+        """
+        Shift the base point without changing the interpolation set.
+
+        Parameters
+        ----------
+        new_x_base : `numpy.ndarray`, shape (n,)
+            New base point.
+        options : dict
+            Options of the solver.
+        """
+        if self._debug:
+            assert new_x_base.shape == (
+                self.n,
+            ), "The shape of `new_x_base` is not valid."
+
+        # Update the models.
+        self._fun.shift_x_base(self.interpolation, new_x_base)
+        for model in self._cub:
+            model.shift_x_base(self.interpolation, new_x_base)
+        for model in self._ceq:
+            model.shift_x_base(self.interpolation, new_x_base)
+
+        # Update the base point and the interpolation points.
+        shift = new_x_base - self.interpolation.x_base
+        self.interpolation.x_base += shift
+        self.interpolation.xpt -= shift[:, np.newaxis]
+        if options[Options.DEBUG]:
+            self._check_interpolation_conditions()
+
+    def _get_cub(self, mask=None):
+        """
+        Get the quadratic models of the nonlinear inequality constraints.
+
+        Parameters
+        ----------
+        mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional
+            Mask of the quadratic models to return.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Quadratic models of the nonlinear inequality constraints.
+        """
+        return self._cub if mask is None else self._cub[mask]
+
+    def _get_ceq(self, mask=None):
+        """
+        Get the quadratic models of the nonlinear equality constraints.
+
+        Parameters
+        ----------
+        mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional
+            Mask of the quadratic models to return.
+
+        Returns
+        -------
+        `numpy.ndarray`
+            Quadratic models of the nonlinear equality constraints.
+        """
+        return self._ceq if mask is None else self._ceq[mask]
+
+    def _check_interpolation_conditions(self):
+        """
+        Check the interpolation conditions of all quadratic models.
+        """
+        error_fun = 0.0
+        error_cub = 0.0
+        error_ceq = 0.0
+        for k in range(self.npt):
+            error_fun = np.max(
+                [
+                    error_fun,
+                    np.abs(
+                        self.fun(self.interpolation.point(k)) - self.fun_val[k]
+                    ),
+                ]
+            )
+            error_cub = np.max(
+                np.abs(
+                    self.cub(self.interpolation.point(k)) - self.cub_val[k, :]
+                ),
+                initial=error_cub,
+            )
+            error_ceq = np.max(
+                np.abs(
+                    self.ceq(self.interpolation.point(k)) - self.ceq_val[k, :]
+                ),
+                initial=error_ceq,
+            )
+        tol = 10.0 * np.sqrt(EPS) * max(self.n, self.npt)
+        if error_fun > tol * np.max(np.abs(self.fun_val), initial=1.0):
+            warnings.warn(
+                "The interpolation conditions for the objective function are "
+                "not satisfied.",
+                RuntimeWarning,
+                2,
+            )
+        if error_cub > tol * np.max(np.abs(self.cub_val), initial=1.0):
+            warnings.warn(
+                "The interpolation conditions for the inequality constraint "
+                "function are not satisfied.",
+                RuntimeWarning,
+                2,
+            )
+        if error_ceq > tol * np.max(np.abs(self.ceq_val), initial=1.0):
+            warnings.warn(
+                "The interpolation conditions for the equality constraint "
+                "function are not satisfied.",
+                RuntimeWarning,
+                2,
+            )
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/problem.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/problem.py
new file mode 100644
index 0000000000000000000000000000000000000000..2dbebce3a48067e97da2b75bd2cdd609e01029b2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/problem.py
@@ -0,0 +1,1296 @@
+from contextlib import suppress
+from inspect import signature
+import copy
+
+import numpy as np
+from scipy.optimize import (
+    Bounds,
+    LinearConstraint,
+    NonlinearConstraint,
+    OptimizeResult,
+)
+from scipy.optimize._constraints import PreparedConstraint
+
+
+from .settings import PRINT_OPTIONS, BARRIER
+from .utils import CallbackSuccess, get_arrays_tol
+from .utils import exact_1d_array
+
+
+class ObjectiveFunction:
+    """
+    Real-valued objective function.
+    """
+
+    def __init__(self, fun, verbose, debug, *args):
+        """
+        Initialize the objective function.
+
+        Parameters
+        ----------
+        fun : {callable, None}
+            Function to evaluate, or None.
+
+                ``fun(x, *args) -> float``
+
+            where ``x`` is an array with shape (n,) and `args` is a tuple.
+        verbose : bool
+            Whether to print the function evaluations.
+        debug : bool
+            Whether to make debugging tests during the execution.
+        *args : tuple
+            Additional arguments to be passed to the function.
+        """
+        if debug:
+            assert fun is None or callable(fun)
+            assert isinstance(verbose, bool)
+            assert isinstance(debug, bool)
+
+        self._fun = fun
+        self._verbose = verbose
+        self._args = args
+        self._n_eval = 0
+
+    def __call__(self, x):
+        """
+        Evaluate the objective function.
+
+        Parameters
+        ----------
+        x : array_like, shape (n,)
+            Point at which the objective function is evaluated.
+
+        Returns
+        -------
+        float
+            Function value at `x`.
+        """
+        x = np.array(x, dtype=float)
+        if self._fun is None:
+            f = 0.0
+        else:
+            f = float(np.squeeze(self._fun(x, *self._args)))
+            self._n_eval += 1
+            if self._verbose:
+                with np.printoptions(**PRINT_OPTIONS):
+                    print(f"{self.name}({x}) = {f}")
+        return f
+
+    @property
+    def n_eval(self):
+        """
+        Number of function evaluations.
+
+        Returns
+        -------
+        int
+            Number of function evaluations.
+        """
+        return self._n_eval
+
+    @property
+    def name(self):
+        """
+        Name of the objective function.
+
+        Returns
+        -------
+        str
+            Name of the objective function.
+        """
+        name = ""
+        if self._fun is not None:
+            try:
+                name = self._fun.__name__
+            except AttributeError:
+                name = "fun"
+        return name
+
+
+class BoundConstraints:
+    """
+    Bound constraints ``xl <= x <= xu``.
+    """
+
+    def __init__(self, bounds):
+        """
+        Initialize the bound constraints.
+
+        Parameters
+        ----------
+        bounds : scipy.optimize.Bounds
+            Bound constraints.
+        """
+        self._xl = np.array(bounds.lb, float)
+        self._xu = np.array(bounds.ub, float)
+
+        # Remove the ill-defined bounds.
+        self.xl[np.isnan(self.xl)] = -np.inf
+        self.xu[np.isnan(self.xu)] = np.inf
+
+        self.is_feasible = (
+            np.all(self.xl <= self.xu)
+            and np.all(self.xl < np.inf)
+            and np.all(self.xu > -np.inf)
+        )
+        self.m = np.count_nonzero(self.xl > -np.inf) + np.count_nonzero(
+            self.xu < np.inf
+        )
+        self.pcs = PreparedConstraint(bounds, np.ones(bounds.lb.size))
+
+    @property
+    def xl(self):
+        """
+        Lower bound.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Lower bound.
+        """
+        return self._xl
+
+    @property
+    def xu(self):
+        """
+        Upper bound.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Upper bound.
+        """
+        return self._xu
+
+    def maxcv(self, x):
+        """
+        Evaluate the maximum constraint violation.
+
+        Parameters
+        ----------
+        x : array_like, shape (n,)
+            Point at which the maximum constraint violation is evaluated.
+
+        Returns
+        -------
+        float
+            Maximum constraint violation at `x`.
+        """
+        x = np.asarray(x, dtype=float)
+        return self.violation(x)
+
+    def violation(self, x):
+        # shortcut for no bounds
+        if self.is_feasible:
+            return np.array([0])
+        else:
+            return self.pcs.violation(x)
+
+    def project(self, x):
+        """
+        Project a point onto the feasible set.
+
+        Parameters
+        ----------
+        x : array_like, shape (n,)
+            Point to be projected.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Projection of `x` onto the feasible set.
+        """
+        return np.clip(x, self.xl, self.xu) if self.is_feasible else x
+
+
+class LinearConstraints:
+    """
+    Linear constraints ``a_ub @ x <= b_ub`` and ``a_eq @ x == b_eq``.
+    """
+
+    def __init__(self, constraints, n, debug):
+        """
+        Initialize the linear constraints.
+
+        Parameters
+        ----------
+        constraints : list of LinearConstraint
+            Linear constraints.
+        n : int
+            Number of variables.
+        debug : bool
+            Whether to make debugging tests during the execution.
+        """
+        if debug:
+            assert isinstance(constraints, list)
+            for constraint in constraints:
+                assert isinstance(constraint, LinearConstraint)
+            assert isinstance(debug, bool)
+
+        self._a_ub = np.empty((0, n))
+        self._b_ub = np.empty(0)
+        self._a_eq = np.empty((0, n))
+        self._b_eq = np.empty(0)
+        for constraint in constraints:
+            is_equality = np.abs(
+                constraint.ub - constraint.lb
+            ) <= get_arrays_tol(constraint.lb, constraint.ub)
+            if np.any(is_equality):
+                self._a_eq = np.vstack((self.a_eq, constraint.A[is_equality]))
+                self._b_eq = np.concatenate(
+                    (
+                        self.b_eq,
+                        0.5
+                        * (
+                            constraint.lb[is_equality]
+                            + constraint.ub[is_equality]
+                        ),
+                    )
+                )
+            if not np.all(is_equality):
+                self._a_ub = np.vstack(
+                    (
+                        self.a_ub,
+                        constraint.A[~is_equality],
+                        -constraint.A[~is_equality],
+                    )
+                )
+                self._b_ub = np.concatenate(
+                    (
+                        self.b_ub,
+                        constraint.ub[~is_equality],
+                        -constraint.lb[~is_equality],
+                    )
+                )
+
+        # Remove the ill-defined constraints.
+        self.a_ub[np.isnan(self.a_ub)] = 0.0
+        self.a_eq[np.isnan(self.a_eq)] = 0.0
+        undef_ub = np.isnan(self.b_ub) | np.isinf(self.b_ub)
+        undef_eq = np.isnan(self.b_eq)
+        self._a_ub = self.a_ub[~undef_ub, :]
+        self._b_ub = self.b_ub[~undef_ub]
+        self._a_eq = self.a_eq[~undef_eq, :]
+        self._b_eq = self.b_eq[~undef_eq]
+        self.pcs = [
+            PreparedConstraint(c, np.ones(n)) for c in constraints if c.A.size
+        ]
+
+    @property
+    def a_ub(self):
+        """
+        Left-hand side matrix of the linear inequality constraints.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m, n)
+            Left-hand side matrix of the linear inequality constraints.
+        """
+        return self._a_ub
+
+    @property
+    def b_ub(self):
+        """
+        Right-hand side vector of the linear inequality constraints.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m, n)
+            Right-hand side vector of the linear inequality constraints.
+        """
+        return self._b_ub
+
+    @property
+    def a_eq(self):
+        """
+        Left-hand side matrix of the linear equality constraints.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m, n)
+            Left-hand side matrix of the linear equality constraints.
+        """
+        return self._a_eq
+
+    @property
+    def b_eq(self):
+        """
+        Right-hand side vector of the linear equality constraints.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m, n)
+            Right-hand side vector of the linear equality constraints.
+        """
+        return self._b_eq
+
+    @property
+    def m_ub(self):
+        """
+        Number of linear inequality constraints.
+
+        Returns
+        -------
+        int
+            Number of linear inequality constraints.
+        """
+        return self.b_ub.size
+
+    @property
+    def m_eq(self):
+        """
+        Number of linear equality constraints.
+
+        Returns
+        -------
+        int
+            Number of linear equality constraints.
+        """
+        return self.b_eq.size
+
+    def maxcv(self, x):
+        """
+        Evaluate the maximum constraint violation.
+
+        Parameters
+        ----------
+        x : array_like, shape (n,)
+            Point at which the maximum constraint violation is evaluated.
+
+        Returns
+        -------
+        float
+            Maximum constraint violation at `x`.
+        """
+        return np.max(self.violation(x), initial=0.0)
+
+    def violation(self, x):
+        if len(self.pcs):
+            return np.concatenate([pc.violation(x) for pc in self.pcs])
+        return np.array([])
+
+
+class NonlinearConstraints:
+    """
+    Nonlinear constraints ``c_ub(x) <= 0`` and ``c_eq(x) == b_eq``.
+    """
+
+    def __init__(self, constraints, verbose, debug):
+        """
+        Initialize the nonlinear constraints.
+
+        Parameters
+        ----------
+        constraints : list
+            Nonlinear constraints.
+        verbose : bool
+            Whether to print the function evaluations.
+        debug : bool
+            Whether to make debugging tests during the execution.
+        """
+        if debug:
+            assert isinstance(constraints, list)
+            for constraint in constraints:
+                assert isinstance(constraint, NonlinearConstraint)
+            assert isinstance(verbose, bool)
+            assert isinstance(debug, bool)
+
+        self._constraints = constraints
+        self.pcs = []
+        self._verbose = verbose
+
+        # map of indexes for equality and inequality constraints
+        self._map_ub = None
+        self._map_eq = None
+        self._m_ub = self._m_eq = None
+
+    def __call__(self, x):
+        """
+        Calculates the residual (slack) for the constraints.
+
+        Parameters
+        ----------
+        x : array_like, shape (n,)
+            Point at which the constraints are evaluated.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (m_nonlinear_ub,)
+            Nonlinear inequality constraint slack values.
+        `numpy.ndarray`, shape (m_nonlinear_eq,)
+            Nonlinear equality constraint slack values.
+        """
+        if not len(self._constraints):
+            self._m_eq = self._m_ub = 0
+            return np.array([]), np.array([])
+
+        x = np.array(x, dtype=float)
+        # first time around the constraints haven't been prepared
+        if not len(self.pcs):
+            self._map_ub = []
+            self._map_eq = []
+            self._m_eq = 0
+            self._m_ub = 0
+
+            for constraint in self._constraints:
+                if not callable(constraint.jac):
+                    # having a callable constraint function prevents
+                    # constraint.fun from being evaluated when preparing
+                    # constraint
+                    c = copy.copy(constraint)
+                    c.jac = lambda x0: x0
+                    c.hess = lambda x0, v: 0.0
+                    pc = PreparedConstraint(c, x)
+                else:
+                    pc = PreparedConstraint(constraint, x)
+                # we're going to be using the same x value again immediately
+                # after this initialisation
+                pc.fun.f_updated = True
+
+                self.pcs.append(pc)
+                idx = np.arange(pc.fun.m)
+
+                # figure out equality and inequality maps
+                lb, ub = pc.bounds[0], pc.bounds[1]
+                arr_tol = get_arrays_tol(lb, ub)
+                is_equality = np.abs(ub - lb) <= arr_tol
+                self._map_eq.append(idx[is_equality])
+                self._map_ub.append(idx[~is_equality])
+
+                # these values will be corrected to their proper values later
+                self._m_eq += np.count_nonzero(is_equality)
+                self._m_ub += np.count_nonzero(~is_equality)
+
+        c_ub = []
+        c_eq = []
+        for i, pc in enumerate(self.pcs):
+            val = pc.fun.fun(x)
+            if self._verbose:
+                with np.printoptions(**PRINT_OPTIONS):
+                    with suppress(AttributeError):
+                        fun_name = self._constraints[i].fun.__name__
+                        print(f"{fun_name}({x}) = {val}")
+
+            # separate violations into c_eq and c_ub
+            eq_idx = self._map_eq[i]
+            ub_idx = self._map_ub[i]
+
+            ub_val = val[ub_idx]
+            if len(ub_idx):
+                xl = pc.bounds[0][ub_idx]
+                xu = pc.bounds[1][ub_idx]
+
+                # calculate slack within lower bound
+                finite_xl = xl > -np.inf
+                _v = xl[finite_xl] - ub_val[finite_xl]
+                c_ub.append(_v)
+
+                # calculate slack within lower bound
+                finite_xu = xu < np.inf
+                _v = ub_val[finite_xu] - xu[finite_xu]
+                c_ub.append(_v)
+
+            # equality constraints taken from midpoint between lb and ub
+            eq_val = val[eq_idx]
+            if len(eq_idx):
+                midpoint = 0.5 * (pc.bounds[1][eq_idx] + pc.bounds[0][eq_idx])
+                eq_val -= midpoint
+            c_eq.append(eq_val)
+
+        if self._m_eq:
+            c_eq = np.concatenate(c_eq)
+        else:
+            c_eq = np.array([])
+
+        if self._m_ub:
+            c_ub = np.concatenate(c_ub)
+        else:
+            c_ub = np.array([])
+
+        self._m_ub = c_ub.size
+        self._m_eq = c_eq.size
+
+        return c_ub, c_eq
+
+    @property
+    def m_ub(self):
+        """
+        Number of nonlinear inequality constraints.
+
+        Returns
+        -------
+        int
+            Number of nonlinear inequality constraints.
+
+        Raises
+        ------
+        ValueError
+            If the number of nonlinear inequality constraints is unknown.
+        """
+        if self._m_ub is None:
+            raise ValueError(
+                "The number of nonlinear inequality constraints is unknown."
+            )
+        else:
+            return self._m_ub
+
+    @property
+    def m_eq(self):
+        """
+        Number of nonlinear equality constraints.
+
+        Returns
+        -------
+        int
+            Number of nonlinear equality constraints.
+
+        Raises
+        ------
+        ValueError
+            If the number of nonlinear equality constraints is unknown.
+        """
+        if self._m_eq is None:
+            raise ValueError(
+                "The number of nonlinear equality constraints is unknown."
+            )
+        else:
+            return self._m_eq
+
+    @property
+    def n_eval(self):
+        """
+        Number of function evaluations.
+
+        Returns
+        -------
+        int
+            Number of function evaluations.
+        """
+        if len(self.pcs):
+            return self.pcs[0].fun.nfev
+        else:
+            return 0
+
+    def maxcv(self, x, cub_val=None, ceq_val=None):
+        """
+        Evaluate the maximum constraint violation.
+
+        Parameters
+        ----------
+        x : array_like, shape (n,)
+            Point at which the maximum constraint violation is evaluated.
+        cub_val : array_like, shape (m_nonlinear_ub,), optional
+            Values of the nonlinear inequality constraints. If not provided,
+            the nonlinear inequality constraints are evaluated at `x`.
+        ceq_val : array_like, shape (m_nonlinear_eq,), optional
+            Values of the nonlinear equality constraints. If not provided,
+            the nonlinear equality constraints are evaluated at `x`.
+
+        Returns
+        -------
+        float
+            Maximum constraint violation at `x`.
+        """
+        return np.max(
+            self.violation(x, cub_val=cub_val, ceq_val=ceq_val), initial=0.0
+        )
+
+    def violation(self, x, cub_val=None, ceq_val=None):
+        return np.concatenate([pc.violation(x) for pc in self.pcs])
+
+
+class Problem:
+    """
+    Optimization problem.
+    """
+
+    def __init__(
+        self,
+        obj,
+        x0,
+        bounds,
+        linear,
+        nonlinear,
+        callback,
+        feasibility_tol,
+        scale,
+        store_history,
+        history_size,
+        filter_size,
+        debug,
+    ):
+        """
+        Initialize the nonlinear problem.
+
+        The problem is preprocessed to remove all the variables that are fixed
+        by the bound constraints.
+
+        Parameters
+        ----------
+        obj : ObjectiveFunction
+            Objective function.
+        x0 : array_like, shape (n,)
+            Initial guess.
+        bounds : BoundConstraints
+            Bound constraints.
+        linear : LinearConstraints
+            Linear constraints.
+        nonlinear : NonlinearConstraints
+            Nonlinear constraints.
+        callback : {callable, None}
+            Callback function.
+        feasibility_tol : float
+            Tolerance on the constraint violation.
+        scale : bool
+            Whether to scale the problem according to the bounds.
+        store_history : bool
+            Whether to store the function evaluations.
+        history_size : int
+            Maximum number of function evaluations to store.
+        filter_size : int
+            Maximum number of points in the filter.
+        debug : bool
+            Whether to make debugging tests during the execution.
+        """
+        if debug:
+            assert isinstance(obj, ObjectiveFunction)
+            assert isinstance(bounds, BoundConstraints)
+            assert isinstance(linear, LinearConstraints)
+            assert isinstance(nonlinear, NonlinearConstraints)
+            assert isinstance(feasibility_tol, float)
+            assert isinstance(scale, bool)
+            assert isinstance(store_history, bool)
+            assert isinstance(history_size, int)
+            if store_history:
+                assert history_size > 0
+            assert isinstance(filter_size, int)
+            assert filter_size > 0
+            assert isinstance(debug, bool)
+
+        self._obj = obj
+        self._linear = linear
+        self._nonlinear = nonlinear
+        if callback is not None:
+            if not callable(callback):
+                raise TypeError("The callback must be a callable function.")
+        self._callback = callback
+
+        # Check the consistency of the problem.
+        x0 = exact_1d_array(x0, "The initial guess must be a vector.")
+        n = x0.size
+        if bounds.xl.size != n:
+            raise ValueError(f"The bounds must have {n} elements.")
+        if linear.a_ub.shape[1] != n:
+            raise ValueError(
+                f"The left-hand side matrices of the linear constraints must "
+                f"have {n} columns."
+            )
+
+        # Check which variables are fixed.
+        tol = get_arrays_tol(bounds.xl, bounds.xu)
+        self._fixed_idx = (bounds.xl <= bounds.xu) & (
+            np.abs(bounds.xl - bounds.xu) < tol
+        )
+        self._fixed_val = 0.5 * (
+            bounds.xl[self._fixed_idx] + bounds.xu[self._fixed_idx]
+        )
+        self._fixed_val = np.clip(
+            self._fixed_val,
+            bounds.xl[self._fixed_idx],
+            bounds.xu[self._fixed_idx],
+        )
+
+        # Set the bound constraints.
+        self._orig_bounds = bounds
+        self._bounds = BoundConstraints(
+            Bounds(bounds.xl[~self._fixed_idx], bounds.xu[~self._fixed_idx])
+        )
+
+        # Set the initial guess.
+        self._x0 = self._bounds.project(x0[~self._fixed_idx])
+
+        # Set the linear constraints.
+        b_eq = linear.b_eq - linear.a_eq[:, self._fixed_idx] @ self._fixed_val
+        self._linear = LinearConstraints(
+            [
+                LinearConstraint(
+                    linear.a_ub[:, ~self._fixed_idx],
+                    -np.inf,
+                    linear.b_ub
+                    - linear.a_ub[:, self._fixed_idx] @ self._fixed_val,
+                ),
+                LinearConstraint(linear.a_eq[:, ~self._fixed_idx], b_eq, b_eq),
+            ],
+            self.n,
+            debug,
+        )
+
+        # Scale the problem if necessary.
+        scale = (
+            scale
+            and self._bounds.is_feasible
+            and np.all(np.isfinite(self._bounds.xl))
+            and np.all(np.isfinite(self._bounds.xu))
+        )
+        if scale:
+            self._scaling_factor = 0.5 * (self._bounds.xu - self._bounds.xl)
+            self._scaling_shift = 0.5 * (self._bounds.xu + self._bounds.xl)
+            self._bounds = BoundConstraints(
+                Bounds(-np.ones(self.n), np.ones(self.n))
+            )
+            b_eq = self._linear.b_eq - self._linear.a_eq @ self._scaling_shift
+            self._linear = LinearConstraints(
+                [
+                    LinearConstraint(
+                        self._linear.a_ub @ np.diag(self._scaling_factor),
+                        -np.inf,
+                        self._linear.b_ub
+                        - self._linear.a_ub @ self._scaling_shift,
+                    ),
+                    LinearConstraint(
+                        self._linear.a_eq @ np.diag(self._scaling_factor),
+                        b_eq,
+                        b_eq,
+                    ),
+                ],
+                self.n,
+                debug,
+            )
+            self._x0 = (self._x0 - self._scaling_shift) / self._scaling_factor
+        else:
+            self._scaling_factor = np.ones(self.n)
+            self._scaling_shift = np.zeros(self.n)
+
+        # Set the initial filter.
+        self._feasibility_tol = feasibility_tol
+        self._filter_size = filter_size
+        self._fun_filter = []
+        self._maxcv_filter = []
+        self._x_filter = []
+
+        # Set the initial history.
+        self._store_history = store_history
+        self._history_size = history_size
+        self._fun_history = []
+        self._maxcv_history = []
+        self._x_history = []
+
+    def __call__(self, x, penalty=0.0):
+        """
+        Evaluate the objective and nonlinear constraint functions.
+
+        Parameters
+        ----------
+        x : array_like, shape (n,)
+            Point at which the functions are evaluated.
+        penalty : float, optional
+            Penalty parameter used to select the point in the filter to forward
+            to the callback function.
+
+        Returns
+        -------
+        float
+            Objective function value.
+        `numpy.ndarray`, shape (m_nonlinear_ub,)
+            Nonlinear inequality constraint function values.
+        `numpy.ndarray`, shape (m_nonlinear_eq,)
+            Nonlinear equality constraint function values.
+
+        Raises
+        ------
+        `cobyqa.utils.CallbackSuccess`
+            If the callback function raises a ``StopIteration``.
+        """
+        # Evaluate the objective and nonlinear constraint functions.
+        x = np.asarray(x, dtype=float)
+        x_full = self.build_x(x)
+        fun_val = self._obj(x_full)
+        cub_val, ceq_val = self._nonlinear(x_full)
+        maxcv_val = self.maxcv(x, cub_val, ceq_val)
+        if self._store_history:
+            self._fun_history.append(fun_val)
+            self._maxcv_history.append(maxcv_val)
+            self._x_history.append(x)
+            if len(self._fun_history) > self._history_size:
+                self._fun_history.pop(0)
+                self._maxcv_history.pop(0)
+                self._x_history.pop(0)
+
+        # Add the point to the filter if it is not dominated by any point.
+        if np.isnan(fun_val) and np.isnan(maxcv_val):
+            include_point = len(self._fun_filter) == 0
+        elif np.isnan(fun_val):
+            include_point = all(
+                np.isnan(fun_filter)
+                and maxcv_val < maxcv_filter
+                or np.isnan(maxcv_filter)
+                for fun_filter, maxcv_filter in zip(
+                    self._fun_filter,
+                    self._maxcv_filter,
+                )
+            )
+        elif np.isnan(maxcv_val):
+            include_point = all(
+                np.isnan(maxcv_filter)
+                and fun_val < fun_filter
+                or np.isnan(fun_filter)
+                for fun_filter, maxcv_filter in zip(
+                    self._fun_filter,
+                    self._maxcv_filter,
+                )
+            )
+        else:
+            include_point = all(
+                fun_val < fun_filter or maxcv_val < maxcv_filter
+                for fun_filter, maxcv_filter in zip(
+                    self._fun_filter,
+                    self._maxcv_filter,
+                )
+            )
+        if include_point:
+            self._fun_filter.append(fun_val)
+            self._maxcv_filter.append(maxcv_val)
+            self._x_filter.append(x)
+
+            # Remove the points in the filter that are dominated by the new
+            # point. We must iterate in reverse order to avoid problems when
+            # removing elements from the list.
+            for k in range(len(self._fun_filter) - 2, -1, -1):
+                if np.isnan(fun_val):
+                    remove_point = np.isnan(self._fun_filter[k])
+                elif np.isnan(maxcv_val):
+                    remove_point = np.isnan(self._maxcv_filter[k])
+                else:
+                    remove_point = (
+                        np.isnan(self._fun_filter[k])
+                        or np.isnan(self._maxcv_filter[k])
+                        or fun_val <= self._fun_filter[k]
+                        and maxcv_val <= self._maxcv_filter[k]
+                    )
+                if remove_point:
+                    self._fun_filter.pop(k)
+                    self._maxcv_filter.pop(k)
+                    self._x_filter.pop(k)
+
+            # Keep only the most recent points in the filter.
+            if len(self._fun_filter) > self._filter_size:
+                self._fun_filter.pop(0)
+                self._maxcv_filter.pop(0)
+                self._x_filter.pop(0)
+
+        # Evaluate the callback function after updating the filter to ensure
+        # that the current point can be returned by the method.
+        if self._callback is not None:
+            sig = signature(self._callback)
+            try:
+                x_best, fun_best, _ = self.best_eval(penalty)
+                x_best = self.build_x(x_best)
+                if set(sig.parameters) == {"intermediate_result"}:
+                    intermediate_result = OptimizeResult(
+                        x=x_best,
+                        fun=fun_best,
+                        # maxcv=maxcv_best,
+                    )
+                    self._callback(intermediate_result=intermediate_result)
+                else:
+                    self._callback(x_best)
+            except StopIteration as exc:
+                raise CallbackSuccess from exc
+
+        # Apply the extreme barriers and return.
+        if np.isnan(fun_val):
+            fun_val = BARRIER
+        cub_val[np.isnan(cub_val)] = BARRIER
+        ceq_val[np.isnan(ceq_val)] = BARRIER
+        fun_val = max(min(fun_val, BARRIER), -BARRIER)
+        cub_val = np.maximum(np.minimum(cub_val, BARRIER), -BARRIER)
+        ceq_val = np.maximum(np.minimum(ceq_val, BARRIER), -BARRIER)
+        return fun_val, cub_val, ceq_val
+
+    @property
+    def n(self):
+        """
+        Number of variables.
+
+        Returns
+        -------
+        int
+            Number of variables.
+        """
+        return self.x0.size
+
+    @property
+    def n_orig(self):
+        """
+        Number of variables in the original problem (with fixed variables).
+
+        Returns
+        -------
+        int
+            Number of variables in the original problem (with fixed variables).
+        """
+        return self._fixed_idx.size
+
+    @property
+    def x0(self):
+        """
+        Initial guess.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Initial guess.
+        """
+        return self._x0
+
+    @property
+    def n_eval(self):
+        """
+        Number of function evaluations.
+
+        Returns
+        -------
+        int
+            Number of function evaluations.
+        """
+        return self._obj.n_eval
+
+    @property
+    def fun_name(self):
+        """
+        Name of the objective function.
+
+        Returns
+        -------
+        str
+            Name of the objective function.
+        """
+        return self._obj.name
+
+    @property
+    def bounds(self):
+        """
+        Bound constraints.
+
+        Returns
+        -------
+        BoundConstraints
+            Bound constraints.
+        """
+        return self._bounds
+
+    @property
+    def linear(self):
+        """
+        Linear constraints.
+
+        Returns
+        -------
+        LinearConstraints
+            Linear constraints.
+        """
+        return self._linear
+
+    @property
+    def m_bounds(self):
+        """
+        Number of bound constraints.
+
+        Returns
+        -------
+        int
+            Number of bound constraints.
+        """
+        return self.bounds.m
+
+    @property
+    def m_linear_ub(self):
+        """
+        Number of linear inequality constraints.
+
+        Returns
+        -------
+        int
+            Number of linear inequality constraints.
+        """
+        return self.linear.m_ub
+
+    @property
+    def m_linear_eq(self):
+        """
+        Number of linear equality constraints.
+
+        Returns
+        -------
+        int
+            Number of linear equality constraints.
+        """
+        return self.linear.m_eq
+
+    @property
+    def m_nonlinear_ub(self):
+        """
+        Number of nonlinear inequality constraints.
+
+        Returns
+        -------
+        int
+            Number of nonlinear inequality constraints.
+
+        Raises
+        ------
+        ValueError
+            If the number of nonlinear inequality constraints is not known.
+        """
+        return self._nonlinear.m_ub
+
+    @property
+    def m_nonlinear_eq(self):
+        """
+        Number of nonlinear equality constraints.
+
+        Returns
+        -------
+        int
+            Number of nonlinear equality constraints.
+
+        Raises
+        ------
+        ValueError
+            If the number of nonlinear equality constraints is not known.
+        """
+        return self._nonlinear.m_eq
+
+    @property
+    def fun_history(self):
+        """
+        History of objective function evaluations.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n_eval,)
+            History of objective function evaluations.
+        """
+        return np.array(self._fun_history, dtype=float)
+
+    @property
+    def maxcv_history(self):
+        """
+        History of maximum constraint violations.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n_eval,)
+            History of maximum constraint violations.
+        """
+        return np.array(self._maxcv_history, dtype=float)
+
+    @property
+    def type(self):
+        """
+        Type of the problem.
+
+        The problem can be either 'unconstrained', 'bound-constrained',
+        'linearly constrained', or 'nonlinearly constrained'.
+
+        Returns
+        -------
+        str
+            Type of the problem.
+        """
+        try:
+            if self.m_nonlinear_ub > 0 or self.m_nonlinear_eq > 0:
+                return "nonlinearly constrained"
+            elif self.m_linear_ub > 0 or self.m_linear_eq > 0:
+                return "linearly constrained"
+            elif self.m_bounds > 0:
+                return "bound-constrained"
+            else:
+                return "unconstrained"
+        except ValueError:
+            # The number of nonlinear constraints is not known. It may be zero
+            # if the user provided a nonlinear inequality and/or equality
+            # constraint function that returns an empty array. However, as this
+            # is not known before the first call to the function, we assume
+            # that the problem is nonlinearly constrained.
+            return "nonlinearly constrained"
+
+    @property
+    def is_feasibility(self):
+        """
+        Whether the problem is a feasibility problem.
+
+        Returns
+        -------
+        bool
+            Whether the problem is a feasibility problem.
+        """
+        return self.fun_name == ""
+
+    def build_x(self, x):
+        """
+        Build the full vector of variables from the reduced vector.
+
+        Parameters
+        ----------
+        x : array_like, shape (n,)
+            Reduced vector of variables.
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n_orig,)
+            Full vector of variables.
+        """
+        x_full = np.empty(self.n_orig)
+        x_full[self._fixed_idx] = self._fixed_val
+        x_full[~self._fixed_idx] = (x * self._scaling_factor
+                                    + self._scaling_shift)
+        return self._orig_bounds.project(x_full)
+
+    def maxcv(self, x, cub_val=None, ceq_val=None):
+        """
+        Evaluate the maximum constraint violation.
+
+        Parameters
+        ----------
+        x : array_like, shape (n,)
+            Point at which the maximum constraint violation is evaluated.
+        cub_val : array_like, shape (m_nonlinear_ub,), optional
+            Values of the nonlinear inequality constraints. If not provided,
+            the nonlinear inequality constraints are evaluated at `x`.
+        ceq_val : array_like, shape (m_nonlinear_eq,), optional
+            Values of the nonlinear equality constraints. If not provided,
+            the nonlinear equality constraints are evaluated at `x`.
+
+        Returns
+        -------
+        float
+            Maximum constraint violation at `x`.
+        """
+        violation = self.violation(x, cub_val=cub_val, ceq_val=ceq_val)
+        if np.count_nonzero(violation):
+            return np.max(violation, initial=0.0)
+        else:
+            return 0.0
+
+    def violation(self, x, cub_val=None, ceq_val=None):
+        violation = []
+        if not self.bounds.is_feasible:
+            b = self.bounds.violation(x)
+            violation.append(b)
+
+        if len(self.linear.pcs):
+            lc = self.linear.violation(x)
+            violation.append(lc)
+        if len(self._nonlinear.pcs):
+            nlc = self._nonlinear.violation(x, cub_val, ceq_val)
+            violation.append(nlc)
+
+        if len(violation):
+            return np.concatenate(violation)
+
+    def best_eval(self, penalty):
+        """
+        Return the best point in the filter and the corresponding objective and
+        nonlinear constraint function evaluations.
+
+        Parameters
+        ----------
+        penalty : float
+            Penalty parameter
+
+        Returns
+        -------
+        `numpy.ndarray`, shape (n,)
+            Best point.
+        float
+            Corresponding objective function value.
+        float
+            Corresponding maximum constraint violation.
+        """
+        # If the filter is empty, i.e., if no function evaluation has been
+        # performed, we evaluate the objective and nonlinear constraint
+        # functions at the initial guess.
+        if len(self._fun_filter) == 0:
+            self(self.x0)
+
+        # Find the best point in the filter.
+        fun_filter = np.array(self._fun_filter)
+        maxcv_filter = np.array(self._maxcv_filter)
+        x_filter = np.array(self._x_filter)
+        finite_idx = np.isfinite(maxcv_filter)
+        if np.any(finite_idx):
+            # At least one point has a finite maximum constraint violation.
+            feasible_idx = maxcv_filter <= self._feasibility_tol
+            if np.any(feasible_idx) and not np.all(
+                np.isnan(fun_filter[feasible_idx])
+            ):
+                # At least one point is feasible and has a well-defined
+                # objective function value. We select the point with the least
+                # objective function value. If there is a tie, we select the
+                # point with the least maximum constraint violation. If there
+                # is still a tie, we select the most recent point.
+                fun_min_idx = feasible_idx & (
+                    fun_filter <= np.nanmin(fun_filter[feasible_idx])
+                )
+                if np.count_nonzero(fun_min_idx) > 1:
+                    fun_min_idx &= maxcv_filter <= np.min(
+                        maxcv_filter[fun_min_idx]
+                    )
+                i = np.flatnonzero(fun_min_idx)[-1]
+            elif np.any(feasible_idx):
+                # At least one point is feasible but no feasible point has a
+                # well-defined objective function value. We select the most
+                # recent feasible point.
+                i = np.flatnonzero(feasible_idx)[-1]
+            else:
+                # No point is feasible. We first compute the merit function
+                # value for each point.
+                merit_filter = np.full_like(fun_filter, np.nan)
+                merit_filter[finite_idx] = (
+                    fun_filter[finite_idx] + penalty * maxcv_filter[finite_idx]
+                )
+                if np.all(np.isnan(merit_filter)):
+                    # No point has a well-defined merit function value. In
+                    # other words, among the points with a well-defined maximum
+                    # constraint violation, none has a well-defined objective
+                    # function value. We select the point with the least
+                    # maximum constraint violation. If there is a tie, we
+                    # select the most recent point.
+                    min_maxcv_idx = maxcv_filter <= np.nanmin(maxcv_filter)
+                    i = np.flatnonzero(min_maxcv_idx)[-1]
+                else:
+                    # At least one point has a well-defined merit function
+                    # value. We select the point with the least merit function
+                    # value. If there is a tie, we select the point with the
+                    # least maximum constraint violation. If there is still a
+                    # tie, we select the point with the least objective
+                    # function value. If there is still a tie, we select the
+                    # most recent point.
+                    merit_min_idx = merit_filter <= np.nanmin(merit_filter)
+                    if np.count_nonzero(merit_min_idx) > 1:
+                        merit_min_idx &= maxcv_filter <= np.min(
+                            maxcv_filter[merit_min_idx]
+                        )
+
+                    if np.count_nonzero(merit_min_idx) > 1:
+                        merit_min_idx &= fun_filter <= np.min(
+                            fun_filter[merit_min_idx]
+                        )
+                    i = np.flatnonzero(merit_min_idx)[-1]
+        elif not np.all(np.isnan(fun_filter)):
+            # No maximum constraint violation is well-defined but at least one
+            # point has a well-defined objective function value. We select the
+            # point with the least objective function value. If there is a tie,
+            # we select the most recent point.
+            fun_min_idx = fun_filter <= np.nanmin(fun_filter)
+            i = np.flatnonzero(fun_min_idx)[-1]
+        else:
+            # No point has a well-defined maximum constraint violation or
+            # objective function value. We select the most recent point.
+            i = len(fun_filter) - 1
+        return (
+            self.bounds.project(x_filter[i, :]),
+            fun_filter[i],
+            maxcv_filter[i],
+        )
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/settings.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/settings.py
new file mode 100644
index 0000000000000000000000000000000000000000..6394822826e094a803a485556a298e342bf260ac
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/settings.py
@@ -0,0 +1,132 @@
+import sys
+from enum import Enum
+
+import numpy as np
+
+
+# Exit status.
+class ExitStatus(Enum):
+    """
+    Exit statuses.
+    """
+
+    RADIUS_SUCCESS = 0
+    TARGET_SUCCESS = 1
+    FIXED_SUCCESS = 2
+    CALLBACK_SUCCESS = 3
+    FEASIBLE_SUCCESS = 4
+    MAX_EVAL_WARNING = 5
+    MAX_ITER_WARNING = 6
+    INFEASIBLE_ERROR = -1
+    LINALG_ERROR = -2
+
+
+class Options(str, Enum):
+    """
+    Options.
+    """
+
+    DEBUG = "debug"
+    FEASIBILITY_TOL = "feasibility_tol"
+    FILTER_SIZE = "filter_size"
+    HISTORY_SIZE = "history_size"
+    MAX_EVAL = "maxfev"
+    MAX_ITER = "maxiter"
+    NPT = "nb_points"
+    RHOBEG = "radius_init"
+    RHOEND = "radius_final"
+    SCALE = "scale"
+    STORE_HISTORY = "store_history"
+    TARGET = "target"
+    VERBOSE = "disp"
+
+
+class Constants(str, Enum):
+    """
+    Constants.
+    """
+
+    DECREASE_RADIUS_FACTOR = "decrease_radius_factor"
+    INCREASE_RADIUS_FACTOR = "increase_radius_factor"
+    INCREASE_RADIUS_THRESHOLD = "increase_radius_threshold"
+    DECREASE_RADIUS_THRESHOLD = "decrease_radius_threshold"
+    DECREASE_RESOLUTION_FACTOR = "decrease_resolution_factor"
+    LARGE_RESOLUTION_THRESHOLD = "large_resolution_threshold"
+    MODERATE_RESOLUTION_THRESHOLD = "moderate_resolution_threshold"
+    LOW_RATIO = "low_ratio"
+    HIGH_RATIO = "high_ratio"
+    VERY_LOW_RATIO = "very_low_ratio"
+    PENALTY_INCREASE_THRESHOLD = "penalty_increase_threshold"
+    PENALTY_INCREASE_FACTOR = "penalty_increase_factor"
+    SHORT_STEP_THRESHOLD = "short_step_threshold"
+    LOW_RADIUS_FACTOR = "low_radius_factor"
+    BYRD_OMOJOKUN_FACTOR = "byrd_omojokun_factor"
+    THRESHOLD_RATIO_CONSTRAINTS = "threshold_ratio_constraints"
+    LARGE_SHIFT_FACTOR = "large_shift_factor"
+    LARGE_GRADIENT_FACTOR = "large_gradient_factor"
+    RESOLUTION_FACTOR = "resolution_factor"
+    IMPROVE_TCG = "improve_tcg"
+
+
+# Default options.
+DEFAULT_OPTIONS = {
+    Options.DEBUG.value: False,
+    Options.FEASIBILITY_TOL.value: np.sqrt(np.finfo(float).eps),
+    Options.FILTER_SIZE.value: sys.maxsize,
+    Options.HISTORY_SIZE.value: sys.maxsize,
+    Options.MAX_EVAL.value: lambda n: 500 * n,
+    Options.MAX_ITER.value: lambda n: 1000 * n,
+    Options.NPT.value: lambda n: 2 * n + 1,
+    Options.RHOBEG.value: 1.0,
+    Options.RHOEND.value: 1e-6,
+    Options.SCALE.value: False,
+    Options.STORE_HISTORY.value: False,
+    Options.TARGET.value: -np.inf,
+    Options.VERBOSE.value: False,
+}
+
+# Default constants.
+DEFAULT_CONSTANTS = {
+    Constants.DECREASE_RADIUS_FACTOR.value: 0.5,
+    Constants.INCREASE_RADIUS_FACTOR.value: np.sqrt(2.0),
+    Constants.INCREASE_RADIUS_THRESHOLD.value: 2.0,
+    Constants.DECREASE_RADIUS_THRESHOLD.value: 1.4,
+    Constants.DECREASE_RESOLUTION_FACTOR.value: 0.1,
+    Constants.LARGE_RESOLUTION_THRESHOLD.value: 250.0,
+    Constants.MODERATE_RESOLUTION_THRESHOLD.value: 16.0,
+    Constants.LOW_RATIO.value: 0.1,
+    Constants.HIGH_RATIO.value: 0.7,
+    Constants.VERY_LOW_RATIO.value: 0.01,
+    Constants.PENALTY_INCREASE_THRESHOLD.value: 1.5,
+    Constants.PENALTY_INCREASE_FACTOR.value: 2.0,
+    Constants.SHORT_STEP_THRESHOLD.value: 0.5,
+    Constants.LOW_RADIUS_FACTOR.value: 0.1,
+    Constants.BYRD_OMOJOKUN_FACTOR.value: 0.8,
+    Constants.THRESHOLD_RATIO_CONSTRAINTS.value: 2.0,
+    Constants.LARGE_SHIFT_FACTOR.value: 10.0,
+    Constants.LARGE_GRADIENT_FACTOR.value: 10.0,
+    Constants.RESOLUTION_FACTOR.value: 2.0,
+    Constants.IMPROVE_TCG.value: True,
+}
+
+# Printing options.
+PRINT_OPTIONS = {
+    "threshold": 6,
+    "edgeitems": 2,
+    "linewidth": sys.maxsize,
+    "formatter": {
+        "float_kind": lambda x: np.format_float_scientific(
+            x,
+            precision=3,
+            unique=False,
+            pad_left=2,
+        )
+    },
+}
+
+# Constants.
+BARRIER = 2.0 ** min(
+    100,
+    np.finfo(float).maxexp // 2,
+    -np.finfo(float).minexp // 2,
+)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/._optim.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/._optim.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..01a1ad3c6f4cb5c0c9b99d1ce35fea92e7618ff5
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/__init__.py
@@ -0,0 +1,14 @@
+from .geometry import cauchy_geometry, spider_geometry
+from .optim import (
+    tangential_byrd_omojokun,
+    constrained_tangential_byrd_omojokun,
+    normal_byrd_omojokun,
+)
+
+__all__ = [
+    "cauchy_geometry",
+    "spider_geometry",
+    "tangential_byrd_omojokun",
+    "constrained_tangential_byrd_omojokun",
+    "normal_byrd_omojokun",
+]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/geometry.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/geometry.py
new file mode 100644
index 0000000000000000000000000000000000000000..7b67fd7c813ee493b18720d1daf71324d72330b6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/geometry.py
@@ -0,0 +1,387 @@
+import inspect
+
+import numpy as np
+
+from ..utils import get_arrays_tol
+
+
+TINY = np.finfo(float).tiny
+
+
+def cauchy_geometry(const, grad, curv, xl, xu, delta, debug):
+    r"""
+    Maximize approximately the absolute value of a quadratic function subject
+    to bound constraints in a trust region.
+
+    This function solves approximately
+
+    .. math::
+
+        \max_{s \in \mathbb{R}^n} \quad \bigg\lvert c + g^{\mathsf{T}} s +
+        \frac{1}{2} s^{\mathsf{T}} H s \bigg\rvert \quad \text{s.t.} \quad
+        \left\{ \begin{array}{l}
+            l \le s \le u,\\
+            \lVert s \rVert \le \Delta,
+        \end{array} \right.
+
+    by maximizing the objective function along the constrained Cauchy
+    direction.
+
+    Parameters
+    ----------
+    const : float
+        Constant :math:`c` as shown above.
+    grad : `numpy.ndarray`, shape (n,)
+        Gradient :math:`g` as shown above.
+    curv : callable
+        Curvature of :math:`H` along any vector.
+
+            ``curv(s) -> float``
+
+        returns :math:`s^{\mathsf{T}} H s`.
+    xl : `numpy.ndarray`, shape (n,)
+        Lower bounds :math:`l` as shown above.
+    xu : `numpy.ndarray`, shape (n,)
+        Upper bounds :math:`u` as shown above.
+    delta : float
+        Trust-region radius :math:`\Delta` as shown above.
+    debug : bool
+        Whether to make debugging tests during the execution.
+
+    Returns
+    -------
+    `numpy.ndarray`, shape (n,)
+        Approximate solution :math:`s`.
+
+    Notes
+    -----
+    This function is described as the first alternative in Section 6.5 of [1]_.
+    It is assumed that the origin is feasible with respect to the bound
+    constraints and that `delta` is finite and positive.
+
+    References
+    ----------
+    .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods
+       and Software*. PhD thesis, Department of Applied Mathematics, The Hong
+       Kong Polytechnic University, Hong Kong, China, 2022. URL:
+       https://theses.lib.polyu.edu.hk/handle/200/12294.
+    """
+    if debug:
+        assert isinstance(const, float)
+        assert isinstance(grad, np.ndarray) and grad.ndim == 1
+        assert inspect.signature(curv).bind(grad)
+        assert isinstance(xl, np.ndarray) and xl.shape == grad.shape
+        assert isinstance(xu, np.ndarray) and xu.shape == grad.shape
+        assert isinstance(delta, float)
+        assert isinstance(debug, bool)
+        tol = get_arrays_tol(xl, xu)
+        assert np.all(xl <= tol)
+        assert np.all(xu >= -tol)
+        assert np.isfinite(delta) and delta > 0.0
+    xl = np.minimum(xl, 0.0)
+    xu = np.maximum(xu, 0.0)
+
+    # To maximize the absolute value of a quadratic function, we maximize the
+    # function itself or its negative, and we choose the solution that provides
+    # the largest function value.
+    step1, q_val1 = _cauchy_geom(const, grad, curv, xl, xu, delta, debug)
+    step2, q_val2 = _cauchy_geom(
+        -const,
+        -grad,
+        lambda x: -curv(x),
+        xl,
+        xu,
+        delta,
+        debug,
+    )
+    step = step1 if abs(q_val1) >= abs(q_val2) else step2
+
+    if debug:
+        assert np.all(xl <= step)
+        assert np.all(step <= xu)
+        assert np.linalg.norm(step) < 1.1 * delta
+    return step
+
+
+def spider_geometry(const, grad, curv, xpt, xl, xu, delta, debug):
+    r"""
+    Maximize approximately the absolute value of a quadratic function subject
+    to bound constraints in a trust region.
+
+    This function solves approximately
+
+    .. math::
+
+        \max_{s \in \mathbb{R}^n} \quad \bigg\lvert c + g^{\mathsf{T}} s +
+        \frac{1}{2} s^{\mathsf{T}} H s \bigg\rvert \quad \text{s.t.} \quad
+        \left\{ \begin{array}{l}
+            l \le s \le u,\\
+            \lVert s \rVert \le \Delta,
+        \end{array} \right.
+
+    by maximizing the objective function along given straight lines.
+
+    Parameters
+    ----------
+    const : float
+        Constant :math:`c` as shown above.
+    grad : `numpy.ndarray`, shape (n,)
+        Gradient :math:`g` as shown above.
+    curv : callable
+        Curvature of :math:`H` along any vector.
+
+            ``curv(s) -> float``
+
+        returns :math:`s^{\mathsf{T}} H s`.
+    xpt : `numpy.ndarray`, shape (n, npt)
+        Points defining the straight lines. The straight lines considered are
+        the ones passing through the origin and the points in `xpt`.
+    xl : `numpy.ndarray`, shape (n,)
+        Lower bounds :math:`l` as shown above.
+    xu : `numpy.ndarray`, shape (n,)
+        Upper bounds :math:`u` as shown above.
+    delta : float
+        Trust-region radius :math:`\Delta` as shown above.
+    debug : bool
+        Whether to make debugging tests during the execution.
+
+    Returns
+    -------
+    `numpy.ndarray`, shape (n,)
+        Approximate solution :math:`s`.
+
+    Notes
+    -----
+    This function is described as the second alternative in Section 6.5 of
+    [1]_. It is assumed that the origin is feasible with respect to the bound
+    constraints and that `delta` is finite and positive.
+
+    References
+    ----------
+    .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods
+       and Software*. PhD thesis, Department of Applied Mathematics, The Hong
+       Kong Polytechnic University, Hong Kong, China, 2022. URL:
+       https://theses.lib.polyu.edu.hk/handle/200/12294.
+    """
+    if debug:
+        assert isinstance(const, float)
+        assert isinstance(grad, np.ndarray) and grad.ndim == 1
+        assert inspect.signature(curv).bind(grad)
+        assert (
+            isinstance(xpt, np.ndarray)
+            and xpt.ndim == 2
+            and xpt.shape[0] == grad.size
+        )
+        assert isinstance(xl, np.ndarray) and xl.shape == grad.shape
+        assert isinstance(xu, np.ndarray) and xu.shape == grad.shape
+        assert isinstance(delta, float)
+        assert isinstance(debug, bool)
+        tol = get_arrays_tol(xl, xu)
+        assert np.all(xl <= tol)
+        assert np.all(xu >= -tol)
+        assert np.isfinite(delta) and delta > 0.0
+    xl = np.minimum(xl, 0.0)
+    xu = np.maximum(xu, 0.0)
+
+    # Iterate through the straight lines.
+    step = np.zeros_like(grad)
+    q_val = const
+    s_norm = np.linalg.norm(xpt, axis=0)
+
+    # Set alpha_xl to the step size for the lower-bound constraint and
+    # alpha_xu to the step size for the upper-bound constraint.
+
+    # xl.shape = (N,)
+    # xpt.shape = (N, M)
+    # i_xl_pos.shape = (M, N)
+    i_xl_pos = (xl > -np.inf) & (xpt.T > -TINY * xl)
+    i_xl_neg = (xl > -np.inf) & (xpt.T < TINY * xl)
+    i_xu_pos = (xu < np.inf) & (xpt.T > TINY * xu)
+    i_xu_neg = (xu < np.inf) & (xpt.T < -TINY * xu)
+
+    # (M, N)
+    alpha_xl_pos = np.atleast_2d(
+        np.broadcast_to(xl, i_xl_pos.shape)[i_xl_pos] / xpt.T[i_xl_pos]
+    )
+    # (M,)
+    alpha_xl_pos = np.max(alpha_xl_pos, axis=1, initial=-np.inf)
+    # make sure it's (M,)
+    alpha_xl_pos = np.broadcast_to(np.atleast_1d(alpha_xl_pos), xpt.shape[1])
+
+    alpha_xl_neg = np.atleast_2d(
+        np.broadcast_to(xl, i_xl_neg.shape)[i_xl_neg] / xpt.T[i_xl_neg]
+    )
+    alpha_xl_neg = np.max(alpha_xl_neg, axis=1, initial=np.inf)
+    alpha_xl_neg = np.broadcast_to(np.atleast_1d(alpha_xl_neg), xpt.shape[1])
+
+    alpha_xu_neg = np.atleast_2d(
+        np.broadcast_to(xu, i_xu_neg.shape)[i_xu_neg] / xpt.T[i_xu_neg]
+    )
+    alpha_xu_neg = np.max(alpha_xu_neg, axis=1, initial=-np.inf)
+    alpha_xu_neg = np.broadcast_to(np.atleast_1d(alpha_xu_neg), xpt.shape[1])
+
+    alpha_xu_pos = np.atleast_2d(
+        np.broadcast_to(xu, i_xu_pos.shape)[i_xu_pos] / xpt.T[i_xu_pos]
+    )
+    alpha_xu_pos = np.max(alpha_xu_pos, axis=1, initial=np.inf)
+    alpha_xu_pos = np.broadcast_to(np.atleast_1d(alpha_xu_pos), xpt.shape[1])
+
+    for k in range(xpt.shape[1]):
+        # Set alpha_tr to the step size for the trust-region constraint.
+        if s_norm[k] > TINY * delta:
+            alpha_tr = max(delta / s_norm[k], 0.0)
+        else:
+            # The current straight line is basically zero.
+            continue
+
+        alpha_bd_pos = max(min(alpha_xu_pos[k], alpha_xl_neg[k]), 0.0)
+        alpha_bd_neg = min(max(alpha_xl_pos[k], alpha_xu_neg[k]), 0.0)
+
+        # Set alpha_quad_pos and alpha_quad_neg to the step size to the extrema
+        # of the quadratic function along the positive and negative directions.
+        grad_step = grad @ xpt[:, k]
+        curv_step = curv(xpt[:, k])
+        if (
+            grad_step >= 0.0
+            and curv_step < -TINY * grad_step
+            or grad_step <= 0.0
+            and curv_step > -TINY * grad_step
+        ):
+            alpha_quad_pos = max(-grad_step / curv_step, 0.0)
+        else:
+            alpha_quad_pos = np.inf
+        if (
+            grad_step >= 0.0
+            and curv_step > TINY * grad_step
+            or grad_step <= 0.0
+            and curv_step < TINY * grad_step
+        ):
+            alpha_quad_neg = min(-grad_step / curv_step, 0.0)
+        else:
+            alpha_quad_neg = -np.inf
+
+        # Select the step that provides the largest value of the objective
+        # function if it improves the current best. The best positive step is
+        # either the one that reaches the constraints or the one that reaches
+        # the extremum of the objective function along the current direction
+        # (only possible if the resulting step is feasible). We test both, and
+        # we perform similar calculations along the negative step.
+        # N.B.: we select the largest possible step among all the ones that
+        # maximize the objective function. This is to avoid returning the zero
+        # step in some extreme cases.
+        alpha_pos = min(alpha_tr, alpha_bd_pos)
+        alpha_neg = max(-alpha_tr, alpha_bd_neg)
+        q_val_pos = (
+            const + alpha_pos * grad_step + 0.5 * alpha_pos**2.0 * curv_step
+        )
+        q_val_neg = (
+            const + alpha_neg * grad_step + 0.5 * alpha_neg**2.0 * curv_step
+        )
+        if alpha_quad_pos < alpha_pos:
+            q_val_quad_pos = (
+                const
+                + alpha_quad_pos * grad_step
+                + 0.5 * alpha_quad_pos**2.0 * curv_step
+            )
+            if abs(q_val_quad_pos) > abs(q_val_pos):
+                alpha_pos = alpha_quad_pos
+                q_val_pos = q_val_quad_pos
+        if alpha_quad_neg > alpha_neg:
+            q_val_quad_neg = (
+                const
+                + alpha_quad_neg * grad_step
+                + 0.5 * alpha_quad_neg**2.0 * curv_step
+            )
+            if abs(q_val_quad_neg) > abs(q_val_neg):
+                alpha_neg = alpha_quad_neg
+                q_val_neg = q_val_quad_neg
+        if abs(q_val_pos) >= abs(q_val_neg) and abs(q_val_pos) > abs(q_val):
+            step = np.clip(alpha_pos * xpt[:, k], xl, xu)
+            q_val = q_val_pos
+        elif abs(q_val_neg) > abs(q_val_pos) and abs(q_val_neg) > abs(q_val):
+            step = np.clip(alpha_neg * xpt[:, k], xl, xu)
+            q_val = q_val_neg
+
+    if debug:
+        assert np.all(xl <= step)
+        assert np.all(step <= xu)
+        assert np.linalg.norm(step) < 1.1 * delta
+    return step
+
+
+def _cauchy_geom(const, grad, curv, xl, xu, delta, debug):
+    """
+    Same as `bound_constrained_cauchy_step` without the absolute value.
+    """
+    # Calculate the initial active set.
+    fixed_xl = (xl < 0.0) & (grad > 0.0)
+    fixed_xu = (xu > 0.0) & (grad < 0.0)
+
+    # Calculate the Cauchy step.
+    cauchy_step = np.zeros_like(grad)
+    cauchy_step[fixed_xl] = xl[fixed_xl]
+    cauchy_step[fixed_xu] = xu[fixed_xu]
+    if np.linalg.norm(cauchy_step) > delta:
+        working = fixed_xl | fixed_xu
+        while True:
+            # Calculate the Cauchy step for the directions in the working set.
+            g_norm = np.linalg.norm(grad[working])
+            delta_reduced = np.sqrt(
+                delta**2.0 - cauchy_step[~working] @ cauchy_step[~working]
+            )
+            if g_norm > TINY * abs(delta_reduced):
+                mu = max(delta_reduced / g_norm, 0.0)
+            else:
+                break
+            cauchy_step[working] = mu * grad[working]
+
+            # Update the working set.
+            fixed_xl = working & (cauchy_step < xl)
+            fixed_xu = working & (cauchy_step > xu)
+            if not np.any(fixed_xl) and not np.any(fixed_xu):
+                # Stop the calculations as the Cauchy step is now feasible.
+                break
+            cauchy_step[fixed_xl] = xl[fixed_xl]
+            cauchy_step[fixed_xu] = xu[fixed_xu]
+            working = working & ~(fixed_xl | fixed_xu)
+
+    # Calculate the step that maximizes the quadratic along the Cauchy step.
+    grad_step = grad @ cauchy_step
+    if grad_step >= 0.0:
+        # Set alpha_tr to the step size for the trust-region constraint.
+        s_norm = np.linalg.norm(cauchy_step)
+        if s_norm > TINY * delta:
+            alpha_tr = max(delta / s_norm, 0.0)
+        else:
+            # The Cauchy step is basically zero.
+            alpha_tr = 0.0
+
+        # Set alpha_quad to the step size for the maximization problem.
+        curv_step = curv(cauchy_step)
+        if curv_step < -TINY * grad_step:
+            alpha_quad = max(-grad_step / curv_step, 0.0)
+        else:
+            alpha_quad = np.inf
+
+        # Set alpha_bd to the step size for the bound constraints.
+        i_xl = (xl > -np.inf) & (cauchy_step < TINY * xl)
+        i_xu = (xu < np.inf) & (cauchy_step > TINY * xu)
+        alpha_xl = np.min(xl[i_xl] / cauchy_step[i_xl], initial=np.inf)
+        alpha_xu = np.min(xu[i_xu] / cauchy_step[i_xu], initial=np.inf)
+        alpha_bd = min(alpha_xl, alpha_xu)
+
+        # Calculate the solution and the corresponding function value.
+        alpha = min(alpha_tr, alpha_quad, alpha_bd)
+        step = np.clip(alpha * cauchy_step, xl, xu)
+        q_val = const + alpha * grad_step + 0.5 * alpha**2.0 * curv_step
+    else:
+        # This case is never reached in exact arithmetic. It prevents this
+        # function to return a step that decreases the objective function.
+        step = np.zeros_like(grad)
+        q_val = const
+
+    if debug:
+        assert np.all(xl <= step)
+        assert np.all(step <= xu)
+        assert np.linalg.norm(step) < 1.1 * delta
+    return step, q_val
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/optim.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/optim.py
new file mode 100644
index 0000000000000000000000000000000000000000..c4a960396fb2e992cf76bac0baf171b5af9b7717
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/optim.py
@@ -0,0 +1,1203 @@
+import inspect
+
+import numpy as np
+from scipy.linalg import qr
+
+from ..utils import get_arrays_tol
+
+
+TINY = np.finfo(float).tiny
+EPS = np.finfo(float).eps
+
+
+def tangential_byrd_omojokun(grad, hess_prod, xl, xu, delta, debug, **kwargs):
+    r"""
+    Minimize approximately a quadratic function subject to bound constraints in
+    a trust region.
+
+    This function solves approximately
+
+    .. math::
+
+        \min_{s \in \mathbb{R}^n} \quad g^{\mathsf{T}} s + \frac{1}{2}
+        s^{\mathsf{T}} H s \quad \text{s.t.} \quad
+        \left\{ \begin{array}{l}
+            l \le s \le u\\
+            \lVert s \rVert \le \Delta,
+        \end{array} \right.
+
+    using an active-set variation of the truncated conjugate gradient method.
+
+    Parameters
+    ----------
+    grad : `numpy.ndarray`, shape (n,)
+        Gradient :math:`g` as shown above.
+    hess_prod : callable
+        Product of the Hessian matrix :math:`H` with any vector.
+
+            ``hess_prod(s) -> `numpy.ndarray`, shape (n,)``
+
+        returns the product :math:`H s`.
+    xl : `numpy.ndarray`, shape (n,)
+        Lower bounds :math:`l` as shown above.
+    xu : `numpy.ndarray`, shape (n,)
+        Upper bounds :math:`u` as shown above.
+    delta : float
+        Trust-region radius :math:`\Delta` as shown above.
+    debug : bool
+        Whether to make debugging tests during the execution.
+
+    Returns
+    -------
+    `numpy.ndarray`, shape (n,)
+        Approximate solution :math:`s`.
+
+    Other Parameters
+    ----------------
+    improve_tcg : bool, optional
+        If True, a solution generated by the truncated conjugate gradient
+        method that is on the boundary of the trust region is improved by
+        moving around the trust-region boundary on the two-dimensional space
+        spanned by the solution and the gradient of the quadratic function at
+        the solution (default is True).
+
+    Notes
+    -----
+    This function implements Algorithm 6.2 of [1]_. It is assumed that the
+    origin is feasible with respect to the bound constraints and that `delta`
+    is finite and positive.
+
+    References
+    ----------
+    .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods
+       and Software*. PhD thesis, Department of Applied Mathematics, The Hong
+       Kong Polytechnic University, Hong Kong, China, 2022. URL:
+       https://theses.lib.polyu.edu.hk/handle/200/12294.
+    """
+    if debug:
+        assert isinstance(grad, np.ndarray) and grad.ndim == 1
+        assert inspect.signature(hess_prod).bind(grad)
+        assert isinstance(xl, np.ndarray) and xl.shape == grad.shape
+        assert isinstance(xu, np.ndarray) and xu.shape == grad.shape
+        assert isinstance(delta, float)
+        assert isinstance(debug, bool)
+        tol = get_arrays_tol(xl, xu)
+        assert np.all(xl <= tol)
+        assert np.all(xu >= -tol)
+        assert np.isfinite(delta) and delta > 0.0
+    xl = np.minimum(xl, 0.0)
+    xu = np.maximum(xu, 0.0)
+
+    # Copy the arrays that may be modified by the code below.
+    n = grad.size
+    grad = np.copy(grad)
+    grad_orig = np.copy(grad)
+
+    # Calculate the initial active set.
+    free_bd = ((xl < 0.0) | (grad < 0.0)) & ((xu > 0.0) | (grad > 0.0))
+
+    # Set the initial iterate and the initial search direction.
+    step = np.zeros_like(grad)
+    sd = np.zeros_like(step)
+    sd[free_bd] = -grad[free_bd]
+
+    k = 0
+    reduct = 0.0
+    boundary_reached = False
+    while k < np.count_nonzero(free_bd):
+        # Stop the computations if sd is not a descent direction.
+        grad_sd = grad @ sd
+        if grad_sd >= -10.0 * EPS * n * max(1.0, np.linalg.norm(grad)):
+            break
+
+        # Set alpha_tr to the step size for the trust-region constraint.
+        try:
+            alpha_tr = _alpha_tr(step, sd, delta)
+        except ZeroDivisionError:
+            break
+
+        # Stop the computations if a step along sd is expected to give a
+        # relatively small reduction in the objective function.
+        if -alpha_tr * grad_sd <= 1e-8 * reduct:
+            break
+
+        # Set alpha_quad to the step size for the minimization problem.
+        hess_sd = hess_prod(sd)
+        curv_sd = sd @ hess_sd
+        if curv_sd > TINY * abs(grad_sd):
+            alpha_quad = max(-grad_sd / curv_sd, 0.0)
+        else:
+            alpha_quad = np.inf
+
+        # Stop the computations if the reduction in the objective function
+        # provided by an unconstrained step is small.
+        alpha = min(alpha_tr, alpha_quad)
+        if -alpha * (grad_sd + 0.5 * alpha * curv_sd) <= 1e-8 * reduct:
+            break
+
+        # Set alpha_bd to the step size for the bound constraints.
+        i_xl = (xl > -np.inf) & (sd < -TINY * np.abs(xl - step))
+        i_xu = (xu < np.inf) & (sd > TINY * np.abs(xu - step))
+        all_alpha_xl = np.full_like(step, np.inf)
+        all_alpha_xu = np.full_like(step, np.inf)
+        all_alpha_xl[i_xl] = np.maximum(
+            (xl[i_xl] - step[i_xl]) / sd[i_xl],
+            0.0,
+        )
+        all_alpha_xu[i_xu] = np.maximum(
+            (xu[i_xu] - step[i_xu]) / sd[i_xu],
+            0.0,
+        )
+        alpha_xl = np.min(all_alpha_xl)
+        alpha_xu = np.min(all_alpha_xu)
+        alpha_bd = min(alpha_xl, alpha_xu)
+
+        # Update the iterate.
+        alpha = min(alpha, alpha_bd)
+        if alpha > 0.0:
+            step[free_bd] = np.clip(
+                step[free_bd] + alpha * sd[free_bd],
+                xl[free_bd],
+                xu[free_bd],
+            )
+            grad += alpha * hess_sd
+            reduct -= alpha * (grad_sd + 0.5 * alpha * curv_sd)
+
+        if alpha < min(alpha_tr, alpha_bd):
+            # The current iteration is a conjugate gradient iteration. Update
+            # the search direction so that it is conjugate (with respect to H)
+            # to all the previous search directions.
+            beta = (grad[free_bd] @ hess_sd[free_bd]) / curv_sd
+            sd[free_bd] = beta * sd[free_bd] - grad[free_bd]
+            sd[~free_bd] = 0.0
+            k += 1
+        elif alpha < alpha_tr:
+            # The iterate is restricted by a bound constraint. Add this bound
+            # constraint to the active set, and restart the calculations.
+            if alpha_xl <= alpha:
+                i_new = np.argmin(all_alpha_xl)
+                step[i_new] = xl[i_new]
+            else:
+                i_new = np.argmin(all_alpha_xu)
+                step[i_new] = xu[i_new]
+            free_bd[i_new] = False
+            sd[free_bd] = -grad[free_bd]
+            sd[~free_bd] = 0.0
+            k = 0
+        else:
+            # The current iterate is on the trust-region boundary. Add all the
+            # active bounds to the working set to prepare for the improvement
+            # of the solution, and stop the iterations.
+            if alpha_xl <= alpha:
+                i_new = _argmin(all_alpha_xl)
+                step[i_new] = xl[i_new]
+                free_bd[i_new] = False
+            if alpha_xu <= alpha:
+                i_new = _argmin(all_alpha_xu)
+                step[i_new] = xu[i_new]
+                free_bd[i_new] = False
+            boundary_reached = True
+            break
+
+    # Attempt to improve the solution on the trust-region boundary.
+    if kwargs.get("improve_tcg", True) and boundary_reached:
+        step_base = np.copy(step)
+        step_comparator = grad_orig @ step_base + 0.5 * step_base @ hess_prod(
+            step_base
+        )
+
+        while np.count_nonzero(free_bd) > 0:
+            # Check whether a substantial reduction in the objective function
+            # is possible, and set the search direction.
+            step_sq = step[free_bd] @ step[free_bd]
+            grad_sq = grad[free_bd] @ grad[free_bd]
+            grad_step = grad[free_bd] @ step[free_bd]
+            grad_sd = -np.sqrt(max(step_sq * grad_sq - grad_step**2.0, 0.0))
+            sd[free_bd] = grad_step * step[free_bd] - step_sq * grad[free_bd]
+            sd[~free_bd] = 0.0
+            if grad_sd >= -1e-8 * reduct or np.any(
+                grad_sd >= -TINY * np.abs(sd[free_bd])
+            ):
+                break
+            sd[free_bd] /= -grad_sd
+
+            # Calculate an upper bound for the tangent of half the angle theta
+            # of this alternative iteration. The step will be updated as:
+            # step = cos(theta) * step + sin(theta) * sd.
+            temp_xl = np.zeros(n)
+            temp_xu = np.zeros(n)
+            temp_xl[free_bd] = (
+                step[free_bd] ** 2.0 + sd[free_bd] ** 2.0 - xl[free_bd] ** 2.0
+            )
+            temp_xu[free_bd] = (
+                step[free_bd] ** 2.0 + sd[free_bd] ** 2.0 - xu[free_bd] ** 2.0
+            )
+            temp_xl[temp_xl > 0.0] = (
+                np.sqrt(temp_xl[temp_xl > 0.0]) - sd[temp_xl > 0.0]
+            )
+            temp_xu[temp_xu > 0.0] = (
+                np.sqrt(temp_xu[temp_xu > 0.0]) + sd[temp_xu > 0.0]
+            )
+            dist_xl = np.maximum(step - xl, 0.0)
+            dist_xu = np.maximum(xu - step, 0.0)
+            i_xl = temp_xl > TINY * dist_xl
+            i_xu = temp_xu > TINY * dist_xu
+            all_t_xl = np.ones(n)
+            all_t_xu = np.ones(n)
+            all_t_xl[i_xl] = np.minimum(
+                all_t_xl[i_xl],
+                dist_xl[i_xl] / temp_xl[i_xl],
+            )
+            all_t_xu[i_xu] = np.minimum(
+                all_t_xu[i_xu],
+                dist_xu[i_xu] / temp_xu[i_xu],
+            )
+            t_xl = np.min(all_t_xl)
+            t_xu = np.min(all_t_xu)
+            t_bd = min(t_xl, t_xu)
+
+            # Calculate some curvature information.
+            hess_step = hess_prod(step)
+            hess_sd = hess_prod(sd)
+            curv_step = step @ hess_step
+            curv_sd = sd @ hess_sd
+            curv_step_sd = step @ hess_sd
+
+            # For a range of equally spaced values of tan(0.5 * theta),
+            # calculate the reduction in the objective function that would be
+            # obtained by accepting the corresponding angle.
+            n_samples = 20
+            n_samples = int((n_samples - 3) * t_bd + 3)
+            t_samples = np.linspace(t_bd / n_samples, t_bd, n_samples)
+            sin_values = 2.0 * t_samples / (1.0 + t_samples**2.0)
+            all_reduct = sin_values * (
+                grad_step * t_samples
+                - grad_sd
+                - t_samples * curv_step
+                + sin_values
+                * (t_samples * curv_step_sd - 0.5 * (curv_sd - curv_step))
+            )
+            if np.all(all_reduct <= 0.0):
+                # No reduction in the objective function is obtained.
+                break
+
+            # Accept the angle that provides the largest reduction in the
+            # objective function, and update the iterate.
+            i_max = np.argmax(all_reduct)
+            cos_value = (1.0 - t_samples[i_max] ** 2.0) / (
+                1.0 + t_samples[i_max] ** 2.0
+            )
+            step[free_bd] = (
+                cos_value * step[free_bd] + sin_values[i_max] * sd[free_bd]
+            )
+            grad += (cos_value - 1.0) * hess_step + sin_values[i_max] * hess_sd
+            reduct += all_reduct[i_max]
+
+            # If the above angle is restricted by bound constraints, add them
+            # to the working set, and restart the alternative iteration.
+            # Otherwise, the calculations are terminated.
+            if t_bd < 1.0 and i_max == n_samples - 1:
+                if t_xl <= t_bd:
+                    i_new = _argmin(all_t_xl)
+                    step[i_new] = xl[i_new]
+                    free_bd[i_new] = False
+                if t_xu <= t_bd:
+                    i_new = _argmin(all_t_xu)
+                    step[i_new] = xu[i_new]
+                    free_bd[i_new] = False
+            else:
+                break
+
+        # Ensure that the alternative iteration improves the objective
+        # function.
+        if grad_orig @ step + 0.5 * step @ hess_prod(step) > step_comparator:
+            step = step_base
+
+    if debug:
+        assert np.all(xl <= step)
+        assert np.all(step <= xu)
+        assert np.linalg.norm(step) < 1.1 * delta
+    return step
+
+
+def constrained_tangential_byrd_omojokun(
+    grad,
+    hess_prod,
+    xl,
+    xu,
+    aub,
+    bub,
+    aeq,
+    delta,
+    debug,
+    **kwargs,
+):
+    r"""
+    Minimize approximately a quadratic function subject to bound and linear
+    constraints in a trust region.
+
+    This function solves approximately
+
+    .. math::
+
+        \min_{s \in \mathbb{R}^n} \quad g^{\mathsf{T}} s + \frac{1}{2}
+        s^{\mathsf{T}} H s \quad \text{s.t.} \quad
+        \left\{ \begin{array}{l}
+            l \le s \le u,\\
+            A_{\scriptscriptstyle I} s \le b_{\scriptscriptstyle I},\\
+            A_{\scriptscriptstyle E} s = 0,\\
+            \lVert s \rVert \le \Delta,
+        \end{array} \right.
+
+    using an active-set variation of the truncated conjugate gradient method.
+
+    Parameters
+    ----------
+    grad : `numpy.ndarray`, shape (n,)
+        Gradient :math:`g` as shown above.
+    hess_prod : callable
+        Product of the Hessian matrix :math:`H` with any vector.
+
+            ``hess_prod(s) -> `numpy.ndarray`, shape (n,)``
+
+        returns the product :math:`H s`.
+    xl : `numpy.ndarray`, shape (n,)
+        Lower bounds :math:`l` as shown above.
+    xu : `numpy.ndarray`, shape (n,)
+        Upper bounds :math:`u` as shown above.
+    aub : `numpy.ndarray`, shape (m_linear_ub, n)
+        Coefficient matrix :math:`A_{\scriptscriptstyle I}` as shown above.
+    bub : `numpy.ndarray`, shape (m_linear_ub,)
+        Right-hand side :math:`b_{\scriptscriptstyle I}` as shown above.
+    aeq : `numpy.ndarray`, shape (m_linear_eq, n)
+        Coefficient matrix :math:`A_{\scriptscriptstyle E}` as shown above.
+    delta : float
+        Trust-region radius :math:`\Delta` as shown above.
+    debug : bool
+        Whether to make debugging tests during the execution.
+
+    Returns
+    -------
+    `numpy.ndarray`, shape (n,)
+        Approximate solution :math:`s`.
+
+    Other Parameters
+    ----------------
+    improve_tcg : bool, optional
+        If True, a solution generated by the truncated conjugate gradient
+        method that is on the boundary of the trust region is improved by
+        moving around the trust-region boundary on the two-dimensional space
+        spanned by the solution and the gradient of the quadratic function at
+        the solution (default is True).
+
+    Notes
+    -----
+    This function implements Algorithm 6.3 of [1]_. It is assumed that the
+    origin is feasible with respect to the bound and linear constraints, and
+    that `delta` is finite and positive.
+
+    References
+    ----------
+    .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods
+       and Software*. PhD thesis, Department of Applied Mathematics, The Hong
+       Kong Polytechnic University, Hong Kong, China, 2022. URL:
+       https://theses.lib.polyu.edu.hk/handle/200/12294.
+    """
+    if debug:
+        assert isinstance(grad, np.ndarray) and grad.ndim == 1
+        assert inspect.signature(hess_prod).bind(grad)
+        assert isinstance(xl, np.ndarray) and xl.shape == grad.shape
+        assert isinstance(xu, np.ndarray) and xu.shape == grad.shape
+        assert (
+            isinstance(aub, np.ndarray)
+            and aub.ndim == 2
+            and aub.shape[1] == grad.size
+        )
+        assert (
+            isinstance(bub, np.ndarray)
+            and bub.ndim == 1
+            and bub.size == aub.shape[0]
+        )
+        assert (
+            isinstance(aeq, np.ndarray)
+            and aeq.ndim == 2
+            and aeq.shape[1] == grad.size
+        )
+        assert isinstance(delta, float)
+        assert isinstance(debug, bool)
+        tol = get_arrays_tol(xl, xu)
+        assert np.all(xl <= tol)
+        assert np.all(xu >= -tol)
+        assert np.all(bub >= -tol)
+        assert np.isfinite(delta) and delta > 0.0
+    xl = np.minimum(xl, 0.0)
+    xu = np.maximum(xu, 0.0)
+    bub = np.maximum(bub, 0.0)
+
+    # Copy the arrays that may be modified by the code below.
+    n = grad.size
+    grad = np.copy(grad)
+    grad_orig = np.copy(grad)
+
+    # Calculate the initial active set.
+    free_xl = (xl < 0.0) | (grad < 0.0)
+    free_xu = (xu > 0.0) | (grad > 0.0)
+    free_ub = (bub > 0.0) | (aub @ grad > 0.0)
+    n_act, q = qr_tangential_byrd_omojokun(aub, aeq, free_xl, free_xu, free_ub)
+
+    # Set the initial iterate and the initial search direction.
+    step = np.zeros_like(grad)
+    sd = -q[:, n_act:] @ (q[:, n_act:].T @ grad)
+    resid = np.copy(bub)
+
+    k = 0
+    reduct = 0.0
+    boundary_reached = False
+    while k < n - n_act:
+        # Stop the computations if sd is not a descent direction.
+        grad_sd = grad @ sd
+        if grad_sd >= -10.0 * EPS * n * max(1.0, np.linalg.norm(grad)):
+            break
+
+        # Set alpha_tr to the step size for the trust-region constraint.
+        try:
+            alpha_tr = _alpha_tr(step, sd, delta)
+        except ZeroDivisionError:
+            break
+
+        # Stop the computations if a step along sd is expected to give a
+        # relatively small reduction in the objective function.
+        if -alpha_tr * grad_sd <= 1e-8 * reduct:
+            break
+
+        # Set alpha_quad to the step size for the minimization problem.
+        hess_sd = hess_prod(sd)
+        curv_sd = sd @ hess_sd
+        if curv_sd > TINY * abs(grad_sd):
+            alpha_quad = max(-grad_sd / curv_sd, 0.0)
+        else:
+            alpha_quad = np.inf
+
+        # Stop the computations if the reduction in the objective function
+        # provided by an unconstrained step is small.
+        alpha = min(alpha_tr, alpha_quad)
+        if -alpha * (grad_sd + 0.5 * alpha * curv_sd) <= 1e-8 * reduct:
+            break
+
+        # Set alpha_bd to the step size for the bound constraints.
+        i_xl = free_xl & (xl > -np.inf) & (sd < -TINY * np.abs(xl - step))
+        i_xu = free_xu & (xu < np.inf) & (sd > TINY * np.abs(xu - step))
+        all_alpha_xl = np.full_like(step, np.inf)
+        all_alpha_xu = np.full_like(step, np.inf)
+        all_alpha_xl[i_xl] = np.maximum(
+            (xl[i_xl] - step[i_xl]) / sd[i_xl],
+            0.0,
+        )
+        all_alpha_xu[i_xu] = np.maximum(
+            (xu[i_xu] - step[i_xu]) / sd[i_xu],
+            0.0,
+        )
+        alpha_xl = np.min(all_alpha_xl)
+        alpha_xu = np.min(all_alpha_xu)
+        alpha_bd = min(alpha_xl, alpha_xu)
+
+        # Set alpha_ub to the step size for the linear constraints.
+        aub_sd = aub @ sd
+        i_ub = free_ub & (aub_sd > TINY * np.abs(resid))
+        all_alpha_ub = np.full_like(bub, np.inf)
+        all_alpha_ub[i_ub] = resid[i_ub] / aub_sd[i_ub]
+        alpha_ub = np.min(all_alpha_ub, initial=np.inf)
+
+        # Update the iterate.
+        alpha = min(alpha, alpha_bd, alpha_ub)
+        if alpha > 0.0:
+            step = np.clip(step + alpha * sd, xl, xu)
+            grad += alpha * hess_sd
+            resid = np.maximum(0.0, resid - alpha * aub_sd)
+            reduct -= alpha * (grad_sd + 0.5 * alpha * curv_sd)
+
+        if alpha < min(alpha_tr, alpha_bd, alpha_ub):
+            # The current iteration is a conjugate gradient iteration. Update
+            # the search direction so that it is conjugate (with respect to H)
+            # to all the previous search directions.
+            grad_proj = q[:, n_act:] @ (q[:, n_act:].T @ grad)
+            beta = (grad_proj @ hess_sd) / curv_sd
+            sd = beta * sd - grad_proj
+            k += 1
+        elif alpha < alpha_tr:
+            # The iterate is restricted by a bound/linear constraint. Add this
+            # constraint to the active set, and restart the calculations.
+            if alpha_xl <= alpha:
+                i_new = np.argmin(all_alpha_xl)
+                step[i_new] = xl[i_new]
+                free_xl[i_new] = False
+            elif alpha_xu <= alpha:
+                i_new = np.argmin(all_alpha_xu)
+                step[i_new] = xu[i_new]
+                free_xu[i_new] = False
+            else:
+                i_new = np.argmin(all_alpha_ub)
+                free_ub[i_new] = False
+            n_act, q = qr_tangential_byrd_omojokun(
+                aub,
+                aeq,
+                free_xl,
+                free_xu,
+                free_ub,
+            )
+            sd = -q[:, n_act:] @ (q[:, n_act:].T @ grad)
+            k = 0
+        else:
+            # The current iterate is on the trust-region boundary. Add all the
+            # active bound/linear constraints to the working set to prepare for
+            # the improvement of the solution, and stop the iterations.
+            if alpha_xl <= alpha:
+                i_new = _argmin(all_alpha_xl)
+                step[i_new] = xl[i_new]
+                free_xl[i_new] = False
+            if alpha_xu <= alpha:
+                i_new = _argmin(all_alpha_xu)
+                step[i_new] = xu[i_new]
+                free_xu[i_new] = False
+            if alpha_ub <= alpha:
+                i_new = _argmin(all_alpha_ub)
+                free_ub[i_new] = False
+            n_act, q = qr_tangential_byrd_omojokun(
+                aub,
+                aeq,
+                free_xl,
+                free_xu,
+                free_ub,
+            )
+            boundary_reached = True
+            break
+
+    # Attempt to improve the solution on the trust-region boundary.
+    if kwargs.get("improve_tcg", True) and boundary_reached and n_act < n:
+        step_base = np.copy(step)
+        while n_act < n:
+            # Check whether a substantial reduction in the objective function
+            # is possible, and set the search direction.
+            step_proj = q[:, n_act:] @ (q[:, n_act:].T @ step)
+            grad_proj = q[:, n_act:] @ (q[:, n_act:].T @ grad)
+            step_sq = step_proj @ step_proj
+            grad_sq = grad_proj @ grad_proj
+            grad_step = grad_proj @ step_proj
+            grad_sd = -np.sqrt(max(step_sq * grad_sq - grad_step**2.0, 0.0))
+            sd = q[:, n_act:] @ (
+                q[:, n_act:].T @ (grad_step * step - step_sq * grad)
+            )
+            if grad_sd >= -1e-8 * reduct or np.any(
+                grad_sd >= -TINY * np.abs(sd)
+            ):
+                break
+            sd /= -grad_sd
+
+            # Calculate an upper bound for the tangent of half the angle theta
+            # of this alternative iteration for the bound constraints. The step
+            # will be updated as:
+            # step += (cos(theta) - 1) * step_proj + sin(theta) * sd.
+            temp_xl = np.zeros(n)
+            temp_xu = np.zeros(n)
+            dist_xl = np.maximum(step - xl, 0.0)
+            dist_xu = np.maximum(xu - step, 0.0)
+            temp_xl[free_xl] = sd[free_xl] ** 2.0 - dist_xl[free_xl] * (
+                dist_xl[free_xl] - 2.0 * step_proj[free_xl]
+            )
+            temp_xu[free_xu] = sd[free_xu] ** 2.0 - dist_xu[free_xu] * (
+                dist_xu[free_xu] + 2.0 * step_proj[free_xu]
+            )
+            temp_xl[temp_xl > 0.0] = (
+                np.sqrt(temp_xl[temp_xl > 0.0]) - sd[temp_xl > 0.0]
+            )
+            temp_xu[temp_xu > 0.0] = (
+                np.sqrt(temp_xu[temp_xu > 0.0]) + sd[temp_xu > 0.0]
+            )
+            i_xl = temp_xl > TINY * dist_xl
+            i_xu = temp_xu > TINY * dist_xu
+            all_t_xl = np.ones(n)
+            all_t_xu = np.ones(n)
+            all_t_xl[i_xl] = np.minimum(
+                all_t_xl[i_xl],
+                dist_xl[i_xl] / temp_xl[i_xl],
+            )
+            all_t_xu[i_xu] = np.minimum(
+                all_t_xu[i_xu],
+                dist_xu[i_xu] / temp_xu[i_xu],
+            )
+            t_xl = np.min(all_t_xl)
+            t_xu = np.min(all_t_xu)
+            t_bd = min(t_xl, t_xu)
+
+            # Calculate an upper bound for the tangent of half the angle theta
+            # of this alternative iteration for the linear constraints.
+            temp_ub = np.zeros_like(resid)
+            aub_step = aub @ step_proj
+            aub_sd = aub @ sd
+            temp_ub[free_ub] = aub_sd[free_ub] ** 2.0 - resid[free_ub] * (
+                resid[free_ub] + 2.0 * aub_step[free_ub]
+            )
+            temp_ub[temp_ub > 0.0] = (
+                np.sqrt(temp_ub[temp_ub > 0.0]) + aub_sd[temp_ub > 0.0]
+            )
+            i_ub = temp_ub > TINY * resid
+            all_t_ub = np.ones_like(resid)
+            all_t_ub[i_ub] = np.minimum(
+                all_t_ub[i_ub],
+                resid[i_ub] / temp_ub[i_ub],
+            )
+            t_ub = np.min(all_t_ub, initial=1.0)
+            t_min = min(t_bd, t_ub)
+
+            # Calculate some curvature information.
+            hess_step = hess_prod(step_proj)
+            hess_sd = hess_prod(sd)
+            curv_step = step_proj @ hess_step
+            curv_sd = sd @ hess_sd
+            curv_step_sd = step_proj @ hess_sd
+
+            # For a range of equally spaced values of tan(0.5 * theta),
+            # calculate the reduction in the objective function that would be
+            # obtained by accepting the corresponding angle.
+            n_samples = 20
+            n_samples = int((n_samples - 3) * t_min + 3)
+            t_samples = np.linspace(t_min / n_samples, t_min, n_samples)
+            sin_values = 2.0 * t_samples / (1.0 + t_samples**2.0)
+            all_reduct = sin_values * (
+                grad_step * t_samples
+                - grad_sd
+                - sin_values
+                * (
+                    0.5 * t_samples**2.0 * curv_step
+                    - 2.0 * t_samples * curv_step_sd
+                    + 0.5 * curv_sd
+                )
+            )
+            if np.all(all_reduct <= 0.0):
+                # No reduction in the objective function is obtained.
+                break
+
+            # Accept the angle that provides the largest reduction in the
+            # objective function, and update the iterate.
+            i_max = np.argmax(all_reduct)
+            cos_value = (1.0 - t_samples[i_max] ** 2.0) / (
+                1.0 + t_samples[i_max] ** 2.0
+            )
+            step = np.clip(
+                step + (cos_value - 1.0) * step_proj + sin_values[i_max] * sd,
+                xl,
+                xu,
+            )
+            grad += (cos_value - 1.0) * hess_step + sin_values[i_max] * hess_sd
+            resid = np.maximum(
+                0.0,
+                resid
+                - (cos_value - 1.0) * aub_step
+                - sin_values[i_max] * aub_sd,
+            )
+            reduct += all_reduct[i_max]
+
+            # If the above angle is restricted by bound constraints, add them
+            # to the working set, and restart the alternative iteration.
+            # Otherwise, the calculations are terminated.
+            if t_min < 1.0 and i_max == n_samples - 1:
+                if t_xl <= t_min:
+                    i_new = _argmin(all_t_xl)
+                    step[i_new] = xl[i_new]
+                    free_xl[i_new] = False
+                if t_xu <= t_min:
+                    i_new = _argmin(all_t_xu)
+                    step[i_new] = xu[i_new]
+                    free_xl[i_new] = False
+                if t_ub <= t_min:
+                    i_new = _argmin(all_t_ub)
+                    free_ub[i_new] = False
+                n_act, q = qr_tangential_byrd_omojokun(
+                    aub,
+                    aeq,
+                    free_xl,
+                    free_xu,
+                    free_ub,
+                )
+            else:
+                break
+
+        # Ensure that the alternative iteration improves the objective
+        # function.
+        if grad_orig @ step + 0.5 * step @ hess_prod(
+            step
+        ) > grad_orig @ step_base + 0.5 * step_base @ hess_prod(step_base):
+            step = step_base
+
+    if debug:
+        tol = get_arrays_tol(xl, xu)
+        assert np.all(xl <= step)
+        assert np.all(step <= xu)
+        assert np.all(aub @ step <= bub + tol)
+        assert np.all(np.abs(aeq @ step) <= tol)
+        assert np.linalg.norm(step) < 1.1 * delta
+    return step
+
+
+def normal_byrd_omojokun(aub, bub, aeq, beq, xl, xu, delta, debug, **kwargs):
+    r"""
+    Minimize approximately a linear constraint violation subject to bound
+    constraints in a trust region.
+
+    This function solves approximately
+
+    .. math::
+
+        \min_{s \in \mathbb{R}^n} \quad \frac{1}{2} \big( \lVert \max \{
+        A_{\scriptscriptstyle I} s - b_{\scriptscriptstyle I}, 0 \} \rVert^2 +
+        \lVert A_{\scriptscriptstyle E} s - b_{\scriptscriptstyle E} \rVert^2
+        \big) \quad \text{s.t.}
+        \quad
+        \left\{ \begin{array}{l}
+            l \le s \le u,\\
+            \lVert s \rVert \le \Delta,
+        \end{array} \right.
+
+    using a variation of the truncated conjugate gradient method.
+
+    Parameters
+    ----------
+    aub : `numpy.ndarray`, shape (m_linear_ub, n)
+        Matrix :math:`A_{\scriptscriptstyle I}` as shown above.
+    bub : `numpy.ndarray`, shape (m_linear_ub,)
+        Vector :math:`b_{\scriptscriptstyle I}` as shown above.
+    aeq : `numpy.ndarray`, shape (m_linear_eq, n)
+        Matrix :math:`A_{\scriptscriptstyle E}` as shown above.
+    beq : `numpy.ndarray`, shape (m_linear_eq,)
+        Vector :math:`b_{\scriptscriptstyle E}` as shown above.
+    xl : `numpy.ndarray`, shape (n,)
+        Lower bounds :math:`l` as shown above.
+    xu : `numpy.ndarray`, shape (n,)
+        Upper bounds :math:`u` as shown above.
+    delta : float
+        Trust-region radius :math:`\Delta` as shown above.
+    debug : bool
+        Whether to make debugging tests during the execution.
+
+    Returns
+    -------
+    `numpy.ndarray`, shape (n,)
+        Approximate solution :math:`s`.
+
+    Other Parameters
+    ----------------
+    improve_tcg : bool, optional
+        If True, a solution generated by the truncated conjugate gradient
+        method that is on the boundary of the trust region is improved by
+        moving around the trust-region boundary on the two-dimensional space
+        spanned by the solution and the gradient of the quadratic function at
+        the solution (default is True).
+
+    Notes
+    -----
+    This function implements Algorithm 6.4 of [1]_. It is assumed that the
+    origin is feasible with respect to the bound constraints and that `delta`
+    is finite and positive.
+
+    References
+    ----------
+    .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods
+       and Software*. PhD thesis, Department of Applied Mathematics, The Hong
+       Kong Polytechnic University, Hong Kong, China, 2022. URL:
+       https://theses.lib.polyu.edu.hk/handle/200/12294.
+    """
+    if debug:
+        assert isinstance(aub, np.ndarray) and aub.ndim == 2
+        assert (
+            isinstance(bub, np.ndarray)
+            and bub.ndim == 1
+            and bub.size == aub.shape[0]
+        )
+        assert (
+            isinstance(aeq, np.ndarray)
+            and aeq.ndim == 2
+            and aeq.shape[1] == aub.shape[1]
+        )
+        assert (
+            isinstance(beq, np.ndarray)
+            and beq.ndim == 1
+            and beq.size == aeq.shape[0]
+        )
+        assert isinstance(xl, np.ndarray) and xl.shape == (aub.shape[1],)
+        assert isinstance(xu, np.ndarray) and xu.shape == (aub.shape[1],)
+        assert isinstance(delta, float)
+        assert isinstance(debug, bool)
+        tol = get_arrays_tol(xl, xu)
+        assert np.all(xl <= tol)
+        assert np.all(xu >= -tol)
+        assert np.isfinite(delta) and delta > 0.0
+    xl = np.minimum(xl, 0.0)
+    xu = np.maximum(xu, 0.0)
+
+    # Calculate the initial active set.
+    m_linear_ub, n = aub.shape
+    grad = np.r_[aeq.T @ -beq, np.maximum(0.0, -bub)]
+    free_xl = (xl < 0.0) | (grad[:n] < 0.0)
+    free_xu = (xu > 0.0) | (grad[:n] > 0.0)
+    free_slack = bub < 0.0
+    free_ub = (bub > 0.0) | (aub @ grad[:n] - grad[n:] > 0.0)
+    n_act, q = qr_normal_byrd_omojokun(
+        aub,
+        free_xl,
+        free_xu,
+        free_slack,
+        free_ub,
+    )
+
+    # Calculate an upper bound on the norm of the slack variables. It is not
+    # used in the original algorithm, but it may prevent undesired behaviors
+    # engendered by computer rounding errors.
+    delta_slack = np.sqrt(beq @ beq + grad[n:] @ grad[n:])
+
+    # Set the initial iterate and the initial search direction.
+    step = np.zeros(n)
+    sd = -q[:, n_act:] @ (q[:, n_act:].T @ grad)
+    resid = bub + grad[n:]
+
+    k = 0
+    reduct = 0.0
+    boundary_reached = False
+    while k < n + m_linear_ub - n_act:
+        # Stop the computations if sd is not a descent direction.
+        grad_sd = grad @ sd
+        if grad_sd >= -10.0 * EPS * n * max(1.0, np.linalg.norm(grad)):
+            break
+
+        # Set alpha_tr to the step size for the trust-region constraint.
+        try:
+            alpha_tr = _alpha_tr(step, sd[:n], delta)
+        except ZeroDivisionError:
+            alpha_tr = np.inf
+
+        # Prevent undesired behaviors engendered by computer rounding errors by
+        # considering the trust-region constraint on the slack variables.
+        try:
+            alpha_tr = min(alpha_tr, _alpha_tr(grad[n:], sd[n:], delta_slack))
+        except ZeroDivisionError:
+            pass
+
+        # Stop the computations if a step along sd is expected to give a
+        # relatively small reduction in the objective function.
+        if -alpha_tr * grad_sd <= 1e-8 * reduct:
+            break
+
+        # Set alpha_quad to the step size for the minimization problem.
+        hess_sd = np.r_[aeq.T @ (aeq @ sd[:n]), sd[n:]]
+        curv_sd = sd @ hess_sd
+        if curv_sd > TINY * abs(grad_sd):
+            alpha_quad = max(-grad_sd / curv_sd, 0.0)
+        else:
+            alpha_quad = np.inf
+
+        # Stop the computations if the reduction in the objective function
+        # provided by an unconstrained step is small.
+        alpha = min(alpha_tr, alpha_quad)
+        if -alpha * (grad_sd + 0.5 * alpha * curv_sd) <= 1e-8 * reduct:
+            break
+
+        # Set alpha_bd to the step size for the bound constraints.
+        i_xl = free_xl & (xl > -np.inf) & (sd[:n] < -TINY * np.abs(xl - step))
+        i_xu = free_xu & (xu < np.inf) & (sd[:n] > TINY * np.abs(xu - step))
+        i_slack = free_slack & (sd[n:] < -TINY * np.abs(grad[n:]))
+        all_alpha_xl = np.full_like(step, np.inf)
+        all_alpha_xu = np.full_like(step, np.inf)
+        all_alpha_slack = np.full_like(bub, np.inf)
+        all_alpha_xl[i_xl] = np.maximum(
+            (xl[i_xl] - step[i_xl]) / sd[:n][i_xl],
+            0.0,
+        )
+        all_alpha_xu[i_xu] = np.maximum(
+            (xu[i_xu] - step[i_xu]) / sd[:n][i_xu],
+            0.0,
+        )
+        all_alpha_slack[i_slack] = np.maximum(
+            -grad[n:][i_slack] / sd[n:][i_slack],
+            0.0,
+        )
+        alpha_xl = np.min(all_alpha_xl)
+        alpha_xu = np.min(all_alpha_xu)
+        alpha_slack = np.min(all_alpha_slack, initial=np.inf)
+        alpha_bd = min(alpha_xl, alpha_xu, alpha_slack)
+
+        # Set alpha_ub to the step size for the linear constraints.
+        aub_sd = aub @ sd[:n] - sd[n:]
+        i_ub = free_ub & (aub_sd > TINY * np.abs(resid))
+        all_alpha_ub = np.full_like(bub, np.inf)
+        all_alpha_ub[i_ub] = resid[i_ub] / aub_sd[i_ub]
+        alpha_ub = np.min(all_alpha_ub, initial=np.inf)
+
+        # Update the iterate.
+        alpha = min(alpha, alpha_bd, alpha_ub)
+        if alpha > 0.0:
+            step = np.clip(step + alpha * sd[:n], xl, xu)
+            grad += alpha * hess_sd
+            resid = np.maximum(0.0, resid - alpha * aub_sd)
+            reduct -= alpha * (grad_sd + 0.5 * alpha * curv_sd)
+
+        if alpha < min(alpha_tr, alpha_bd, alpha_ub):
+            # The current iteration is a conjugate gradient iteration. Update
+            # the search direction so that it is conjugate (with respect to H)
+            # to all the previous search directions.
+            grad_proj = q[:, n_act:] @ (q[:, n_act:].T @ grad)
+            beta = (grad_proj @ hess_sd) / curv_sd
+            sd = beta * sd - grad_proj
+            k += 1
+        elif alpha < alpha_tr:
+            # The iterate is restricted by a bound/linear constraint. Add this
+            # constraint to the active set, and restart the calculations.
+            if alpha_xl <= alpha:
+                i_new = np.argmin(all_alpha_xl)
+                step[i_new] = xl[i_new]
+                free_xl[i_new] = False
+            elif alpha_xu <= alpha:
+                i_new = np.argmin(all_alpha_xu)
+                step[i_new] = xu[i_new]
+                free_xu[i_new] = False
+            elif alpha_slack <= alpha:
+                i_new = np.argmin(all_alpha_slack)
+                free_slack[i_new] = False
+            else:
+                i_new = np.argmin(all_alpha_ub)
+                free_ub[i_new] = False
+            n_act, q = qr_normal_byrd_omojokun(
+                aub, free_xl, free_xu, free_slack, free_ub
+            )
+            sd = -q[:, n_act:] @ (q[:, n_act:].T @ grad)
+            k = 0
+        else:
+            # The current iterate is on the trust-region boundary. Add all the
+            # active bound constraints to the working set to prepare for the
+            # improvement of the solution, and stop the iterations.
+            if alpha_xl <= alpha:
+                i_new = _argmin(all_alpha_xl)
+                step[i_new] = xl[i_new]
+                free_xl[i_new] = False
+            if alpha_xu <= alpha:
+                i_new = _argmin(all_alpha_xu)
+                step[i_new] = xu[i_new]
+                free_xu[i_new] = False
+            boundary_reached = True
+            break
+
+    # Attempt to improve the solution on the trust-region boundary.
+    if kwargs.get("improve_tcg", True) and boundary_reached:
+        step_base = np.copy(step)
+        free_bd = free_xl & free_xu
+        grad = aub.T @ np.maximum(aub @ step - bub, 0.0) + aeq.T @ (
+            aeq @ step - beq
+        )
+        sd = np.zeros(n)
+        while np.count_nonzero(free_bd) > 0:
+            # Check whether a substantial reduction in the objective function
+            # is possible, and set the search direction.
+            step_sq = step[free_bd] @ step[free_bd]
+            grad_sq = grad[free_bd] @ grad[free_bd]
+            grad_step = grad[free_bd] @ step[free_bd]
+            grad_sd = -np.sqrt(max(step_sq * grad_sq - grad_step**2.0, 0.0))
+            sd[free_bd] = grad_step * step[free_bd] - step_sq * grad[free_bd]
+            sd[~free_bd] = 0.0
+            if grad_sd >= -1e-8 * reduct or np.any(
+                grad_sd >= -TINY * np.abs(sd[free_bd])
+            ):
+                break
+            sd[free_bd] /= -grad_sd
+
+            # Calculate an upper bound for the tangent of half the angle theta
+            # of this alternative iteration. The step will be updated as:
+            # step = cos(theta) * step + sin(theta) * sd.
+            temp_xl = np.zeros(n)
+            temp_xu = np.zeros(n)
+            temp_xl[free_bd] = (
+                step[free_bd] ** 2.0 + sd[free_bd] ** 2.0 - xl[free_bd] ** 2.0
+            )
+            temp_xu[free_bd] = (
+                step[free_bd] ** 2.0 + sd[free_bd] ** 2.0 - xu[free_bd] ** 2.0
+            )
+            temp_xl[temp_xl > 0.0] = (
+                np.sqrt(temp_xl[temp_xl > 0.0]) - sd[temp_xl > 0.0]
+            )
+            temp_xu[temp_xu > 0.0] = (
+                np.sqrt(temp_xu[temp_xu > 0.0]) + sd[temp_xu > 0.0]
+            )
+            dist_xl = np.maximum(step - xl, 0.0)
+            dist_xu = np.maximum(xu - step, 0.0)
+            i_xl = temp_xl > TINY * dist_xl
+            i_xu = temp_xu > TINY * dist_xu
+            all_t_xl = np.ones(n)
+            all_t_xu = np.ones(n)
+            all_t_xl[i_xl] = np.minimum(
+                all_t_xl[i_xl],
+                dist_xl[i_xl] / temp_xl[i_xl],
+            )
+            all_t_xu[i_xu] = np.minimum(
+                all_t_xu[i_xu],
+                dist_xu[i_xu] / temp_xu[i_xu],
+            )
+            t_xl = np.min(all_t_xl)
+            t_xu = np.min(all_t_xu)
+            t_bd = min(t_xl, t_xu)
+
+            # For a range of equally spaced values of tan(0.5 * theta),
+            # calculate the reduction in the objective function that would be
+            # obtained by accepting the corresponding angle.
+            n_samples = 20
+            n_samples = int((n_samples - 3) * t_bd + 3)
+            t_samples = np.linspace(t_bd / n_samples, t_bd, n_samples)
+            resid_ub = np.maximum(aub @ step - bub, 0.0)
+            resid_eq = aeq @ step - beq
+            step_proj = np.copy(step)
+            step_proj[~free_bd] = 0.0
+            all_reduct = np.empty(n_samples)
+            for i in range(n_samples):
+                sin_value = 2.0 * t_samples[i] / (1.0 + t_samples[i] ** 2.0)
+                step_alt = np.clip(
+                    step + sin_value * (sd - t_samples[i] * step_proj),
+                    xl,
+                    xu,
+                )
+                resid_ub_alt = np.maximum(aub @ step_alt - bub, 0.0)
+                resid_eq_alt = aeq @ step_alt - beq
+                all_reduct[i] = 0.5 * (
+                    resid_ub @ resid_ub
+                    + resid_eq @ resid_eq
+                    - resid_ub_alt @ resid_ub_alt
+                    - resid_eq_alt @ resid_eq_alt
+                )
+            if np.all(all_reduct <= 0.0):
+                # No reduction in the objective function is obtained.
+                break
+
+            # Accept the angle that provides the largest reduction in the
+            # objective function, and update the iterate.
+            i_max = np.argmax(all_reduct)
+            cos_value = (1.0 - t_samples[i_max] ** 2.0) / (
+                1.0 + t_samples[i_max] ** 2.0
+            )
+            sin_value = (2.0 * t_samples[i_max]
+                         / (1.0 + t_samples[i_max] ** 2.0))
+            step[free_bd] = cos_value * step[free_bd] + sin_value * sd[free_bd]
+            grad = aub.T @ np.maximum(aub @ step - bub, 0.0) + aeq.T @ (
+                aeq @ step - beq
+            )
+            reduct += all_reduct[i_max]
+
+            # If the above angle is restricted by bound constraints, add them
+            # to the working set, and restart the alternative iteration.
+            # Otherwise, the calculations are terminated.
+            if t_bd < 1.0 and i_max == n_samples - 1:
+                if t_xl <= t_bd:
+                    i_new = _argmin(all_t_xl)
+                    step[i_new] = xl[i_new]
+                    free_bd[i_new] = False
+                if t_xu <= t_bd:
+                    i_new = _argmin(all_t_xu)
+                    step[i_new] = xu[i_new]
+                    free_bd[i_new] = False
+            else:
+                break
+
+        # Ensure that the alternative iteration improves the objective
+        # function.
+        resid_ub = np.maximum(aub @ step - bub, 0.0)
+        resid_ub_base = np.maximum(aub @ step_base - bub, 0.0)
+        resid_eq = aeq @ step - beq
+        resid_eq_base = aeq @ step_base - beq
+        if (
+            resid_ub @ resid_ub + resid_eq @ resid_eq
+            > resid_ub_base @ resid_ub_base + resid_eq_base @ resid_eq_base
+        ):
+            step = step_base
+
+    if debug:
+        assert np.all(xl <= step)
+        assert np.all(step <= xu)
+        assert np.linalg.norm(step) < 1.1 * delta
+    return step
+
+
+def qr_tangential_byrd_omojokun(aub, aeq, free_xl, free_xu, free_ub):
+    n = free_xl.size
+    identity = np.eye(n)
+    q, r, _ = qr(
+        np.block(
+            [
+                [aeq],
+                [aub[~free_ub, :]],
+                [-identity[~free_xl, :]],
+                [identity[~free_xu, :]],
+            ]
+        ).T,
+        pivoting=True,
+    )
+    n_act = np.count_nonzero(
+        np.abs(np.diag(r))
+        >= 10.0
+        * EPS
+        * n
+        * np.linalg.norm(r[: np.min(r.shape), : np.min(r.shape)], axis=0)
+    )
+    return n_act, q
+
+
+def qr_normal_byrd_omojokun(aub, free_xl, free_xu, free_slack, free_ub):
+    m_linear_ub, n = aub.shape
+    identity_n = np.eye(n)
+    identity_m = np.eye(m_linear_ub)
+    q, r, _ = qr(
+        np.block(
+            [
+                [
+                    aub[~free_ub, :],
+                    -identity_m[~free_ub, :],
+                ],
+                [
+                    np.zeros((m_linear_ub - np.count_nonzero(free_slack), n)),
+                    -identity_m[~free_slack, :],
+                ],
+                [
+                    -identity_n[~free_xl, :],
+                    np.zeros((n - np.count_nonzero(free_xl), m_linear_ub)),
+                ],
+                [
+                    identity_n[~free_xu, :],
+                    np.zeros((n - np.count_nonzero(free_xu), m_linear_ub)),
+                ],
+            ]
+        ).T,
+        pivoting=True,
+    )
+    n_act = np.count_nonzero(
+        np.abs(np.diag(r))
+        >= 10.0
+        * EPS
+        * (n + m_linear_ub)
+        * np.linalg.norm(r[: np.min(r.shape), : np.min(r.shape)], axis=0)
+    )
+    return n_act, q
+
+
+def _alpha_tr(step, sd, delta):
+    step_sd = step @ sd
+    sd_sq = sd @ sd
+    dist_tr_sq = delta**2.0 - step @ step
+    temp = np.sqrt(max(step_sd**2.0 + sd_sq * dist_tr_sq, 0.0))
+    if step_sd <= 0.0 and sd_sq > TINY * abs(temp - step_sd):
+        alpha_tr = max((temp - step_sd) / sd_sq, 0.0)
+    elif abs(temp + step_sd) > TINY * dist_tr_sq:
+        alpha_tr = max(dist_tr_sq / (temp + step_sd), 0.0)
+    else:
+        raise ZeroDivisionError
+    return alpha_tr
+
+
+def _argmax(x):
+    return np.flatnonzero(x >= np.max(x))
+
+
+def _argmin(x):
+    return np.flatnonzero(x <= np.min(x))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/._versions.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/._versions.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..fe6b4841ddff3a04bda5cbff744e30681b6963b9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/__init__.py
@@ -0,0 +1,18 @@
+from .exceptions import (
+    MaxEvalError,
+    TargetSuccess,
+    CallbackSuccess,
+    FeasibleSuccess,
+)
+from .math import get_arrays_tol, exact_1d_array
+from .versions import show_versions
+
+__all__ = [
+    "MaxEvalError",
+    "TargetSuccess",
+    "CallbackSuccess",
+    "FeasibleSuccess",
+    "get_arrays_tol",
+    "exact_1d_array",
+    "show_versions",
+]
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/exceptions.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/exceptions.py
new file mode 100644
index 0000000000000000000000000000000000000000..c85094894f378a8e3934ad109ea6166e33e4366b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/exceptions.py
@@ -0,0 +1,22 @@
+class MaxEvalError(Exception):
+    """
+    Exception raised when the maximum number of evaluations is reached.
+    """
+
+
+class TargetSuccess(Exception):
+    """
+    Exception raised when the target value is reached.
+    """
+
+
+class CallbackSuccess(StopIteration):
+    """
+    Exception raised when the callback function raises a ``StopIteration``.
+    """
+
+
+class FeasibleSuccess(Exception):
+    """
+    Exception raised when a feasible point of a feasible problem is found.
+    """
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/math.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/math.py
new file mode 100644
index 0000000000000000000000000000000000000000..1b16ae98a0df38752815f5a69d56da20f856f9f9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/math.py
@@ -0,0 +1,77 @@
+import numpy as np
+
+
+EPS = np.finfo(float).eps
+
+
+def get_arrays_tol(*arrays):
+    """
+    Get a relative tolerance for a set of arrays.
+
+    Parameters
+    ----------
+    *arrays: tuple
+        Set of `numpy.ndarray` to get the tolerance for.
+
+    Returns
+    -------
+    float
+        Relative tolerance for the set of arrays.
+
+    Raises
+    ------
+    ValueError
+        If no array is provided.
+    """
+    if len(arrays) == 0:
+        raise ValueError("At least one array must be provided.")
+    size = max(array.size for array in arrays)
+    weight = max(
+        np.max(np.abs(array[np.isfinite(array)]), initial=1.0)
+        for array in arrays
+    )
+    return 10.0 * EPS * max(size, 1.0) * weight
+
+
+def exact_1d_array(x, message):
+    """
+    Preprocess a 1-dimensional array.
+
+    Parameters
+    ----------
+    x : array_like
+        Array to be preprocessed.
+    message : str
+        Error message if `x` cannot be interpreter as a 1-dimensional array.
+
+    Returns
+    -------
+    `numpy.ndarray`
+        Preprocessed array.
+    """
+    x = np.atleast_1d(np.squeeze(x)).astype(float)
+    if x.ndim != 1:
+        raise ValueError(message)
+    return x
+
+
+def exact_2d_array(x, message):
+    """
+    Preprocess a 2-dimensional array.
+
+    Parameters
+    ----------
+    x : array_like
+        Array to be preprocessed.
+    message : str
+        Error message if `x` cannot be interpreter as a 2-dimensional array.
+
+    Returns
+    -------
+    `numpy.ndarray`
+        Preprocessed array.
+    """
+    x = np.atleast_2d(x).astype(float)
+    if x.ndim != 2:
+        raise ValueError(message)
+    return x
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/versions.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/versions.py
new file mode 100644
index 0000000000000000000000000000000000000000..94a0f8f5cef626354f40901cbe06a84287291c1c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/cobyqa/utils/versions.py
@@ -0,0 +1,67 @@
+import os
+import platform
+import sys
+from importlib.metadata import PackageNotFoundError, version
+
+
+def _get_sys_info():
+    """
+    Get useful system information.
+
+    Returns
+    -------
+    dict
+        Useful system information.
+    """
+    return {
+        "python": sys.version.replace(os.linesep, " "),
+        "executable": sys.executable,
+        "machine": platform.platform(),
+    }
+
+
+def _get_deps_info():
+    """
+    Get the versions of the dependencies.
+
+    Returns
+    -------
+    dict
+        Versions of the dependencies.
+    """
+    deps = ["cobyqa", "numpy", "scipy", "setuptools", "pip"]
+    deps_info = {}
+    for module in deps:
+        try:
+            deps_info[module] = version(module)
+        except PackageNotFoundError:
+            deps_info[module] = None
+    return deps_info
+
+
+def show_versions():
+    """
+    Display useful system and dependencies information.
+
+    When reporting issues, please include this information.
+    """
+    print("System settings")
+    print("---------------")
+    sys_info = _get_sys_info()
+    print(
+        "\n".join(
+            f"{k:>{max(map(len, sys_info.keys())) + 1}}: {v}"
+            for k, v in sys_info.items()
+        )
+    )
+
+    print()
+    print("Python dependencies")
+    print("-------------------")
+    deps_info = _get_deps_info()
+    print(
+        "\n".join(
+            f"{k:>{max(map(len, deps_info.keys())) + 1}}: {v}"
+            for k, v in deps_info.items()
+        )
+    )
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/deprecation.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/deprecation.py
new file mode 100644
index 0000000000000000000000000000000000000000..ea60d3809bf9b11309f8a6613caffb6aaab7e667
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/deprecation.py
@@ -0,0 +1,274 @@
+from inspect import Parameter, signature
+import functools
+import warnings
+from importlib import import_module
+from scipy._lib._docscrape import FunctionDoc
+
+
+__all__ = ["_deprecated"]
+
+
+# Object to use as default value for arguments to be deprecated. This should
+# be used over 'None' as the user could parse 'None' as a positional argument
+_NoValue = object()
+
+def _sub_module_deprecation(*, sub_package, module, private_modules, all,
+                            attribute, correct_module=None, dep_version="1.16.0"):
+    """Helper function for deprecating modules that are public but were
+    intended to be private.
+
+    Parameters
+    ----------
+    sub_package : str
+        Subpackage the module belongs to eg. stats
+    module : str
+        Public but intended private module to deprecate
+    private_modules : list
+        Private replacement(s) for `module`; should contain the
+        content of ``all``, possibly spread over several modules.
+    all : list
+        ``__all__`` belonging to `module`
+    attribute : str
+        The attribute in `module` being accessed
+    correct_module : str, optional
+        Module in `sub_package` that `attribute` should be imported from.
+        Default is that `attribute` should be imported from ``scipy.sub_package``.
+    dep_version : str, optional
+        Version in which deprecated attributes will be removed.
+    """
+    if correct_module is not None:
+        correct_import = f"scipy.{sub_package}.{correct_module}"
+    else:
+        correct_import = f"scipy.{sub_package}"
+
+    if attribute not in all:
+        raise AttributeError(
+            f"`scipy.{sub_package}.{module}` has no attribute `{attribute}`; "
+            f"furthermore, `scipy.{sub_package}.{module}` is deprecated "
+            f"and will be removed in SciPy 2.0.0."
+        )
+
+    attr = getattr(import_module(correct_import), attribute, None)
+
+    if attr is not None:
+        message = (
+            f"Please import `{attribute}` from the `{correct_import}` namespace; "
+            f"the `scipy.{sub_package}.{module}` namespace is deprecated "
+            f"and will be removed in SciPy 2.0.0."
+        )
+    else:
+        message = (
+            f"`scipy.{sub_package}.{module}.{attribute}` is deprecated along with "
+            f"the `scipy.{sub_package}.{module}` namespace. "
+            f"`scipy.{sub_package}.{module}.{attribute}` will be removed "
+            f"in SciPy {dep_version}, and the `scipy.{sub_package}.{module}` namespace "
+            f"will be removed in SciPy 2.0.0."
+        )
+
+    warnings.warn(message, category=DeprecationWarning, stacklevel=3)
+
+    for module in private_modules:
+        try:
+            return getattr(import_module(f"scipy.{sub_package}.{module}"), attribute)
+        except AttributeError as e:
+            # still raise an error if the attribute isn't in any of the expected
+            # private modules
+            if module == private_modules[-1]:
+                raise e
+            continue
+    
+
+def _deprecated(msg, stacklevel=2):
+    """Deprecate a function by emitting a warning on use."""
+    def wrap(fun):
+        if isinstance(fun, type):
+            warnings.warn(
+                f"Trying to deprecate class {fun!r}",
+                category=RuntimeWarning, stacklevel=2)
+            return fun
+
+        @functools.wraps(fun)
+        def call(*args, **kwargs):
+            warnings.warn(msg, category=DeprecationWarning,
+                          stacklevel=stacklevel)
+            return fun(*args, **kwargs)
+        call.__doc__ = fun.__doc__
+        return call
+
+    return wrap
+
+
+class _DeprecationHelperStr:
+    """
+    Helper class used by deprecate_cython_api
+    """
+    def __init__(self, content, message):
+        self._content = content
+        self._message = message
+
+    def __hash__(self):
+        return hash(self._content)
+
+    def __eq__(self, other):
+        res = (self._content == other)
+        if res:
+            warnings.warn(self._message, category=DeprecationWarning,
+                          stacklevel=2)
+        return res
+
+
+def deprecate_cython_api(module, routine_name, new_name=None, message=None):
+    """
+    Deprecate an exported cdef function in a public Cython API module.
+
+    Only functions can be deprecated; typedefs etc. cannot.
+
+    Parameters
+    ----------
+    module : module
+        Public Cython API module (e.g. scipy.linalg.cython_blas).
+    routine_name : str
+        Name of the routine to deprecate. May also be a fused-type
+        routine (in which case its all specializations are deprecated).
+    new_name : str
+        New name to include in the deprecation warning message
+    message : str
+        Additional text in the deprecation warning message
+
+    Examples
+    --------
+    Usually, this function would be used in the top-level of the
+    module ``.pyx`` file:
+
+    >>> from scipy._lib.deprecation import deprecate_cython_api
+    >>> import scipy.linalg.cython_blas as mod
+    >>> deprecate_cython_api(mod, "dgemm", "dgemm_new",
+    ...                      message="Deprecated in Scipy 1.5.0")
+    >>> del deprecate_cython_api, mod
+
+    After this, Cython modules that use the deprecated function emit a
+    deprecation warning when they are imported.
+
+    """
+    old_name = f"{module.__name__}.{routine_name}"
+
+    if new_name is None:
+        depdoc = f"`{old_name}` is deprecated!"
+    else:
+        depdoc = f"`{old_name}` is deprecated, use `{new_name}` instead!"
+
+    if message is not None:
+        depdoc += "\n" + message
+
+    d = module.__pyx_capi__
+
+    # Check if the function is a fused-type function with a mangled name
+    j = 0
+    has_fused = False
+    while True:
+        fused_name = f"__pyx_fuse_{j}{routine_name}"
+        if fused_name in d:
+            has_fused = True
+            d[_DeprecationHelperStr(fused_name, depdoc)] = d.pop(fused_name)
+            j += 1
+        else:
+            break
+
+    # If not, apply deprecation to the named routine
+    if not has_fused:
+        d[_DeprecationHelperStr(routine_name, depdoc)] = d.pop(routine_name)
+
+
+# taken from scikit-learn, see
+# https://github.com/scikit-learn/scikit-learn/blob/1.3.0/sklearn/utils/validation.py#L38
+def _deprecate_positional_args(func=None, *, version=None,
+                               deprecated_args=None, custom_message=""):
+    """Decorator for methods that issues warnings for positional arguments.
+
+    Using the keyword-only argument syntax in pep 3102, arguments after the
+    * will issue a warning when passed as a positional argument.
+
+    Parameters
+    ----------
+    func : callable, default=None
+        Function to check arguments on.
+    version : callable, default=None
+        The version when positional arguments will result in error.
+    deprecated_args : set of str, optional
+        Arguments to deprecate - whether passed by position or keyword.
+    custom_message : str, optional
+        Custom message to add to deprecation warning and documentation.
+    """
+    if version is None:
+        msg = "Need to specify a version where signature will be changed"
+        raise ValueError(msg)
+
+    deprecated_args = set() if deprecated_args is None else set(deprecated_args)
+
+    def _inner_deprecate_positional_args(f):
+        sig = signature(f)
+        kwonly_args = []
+        all_args = []
+
+        for name, param in sig.parameters.items():
+            if param.kind == Parameter.POSITIONAL_OR_KEYWORD:
+                all_args.append(name)
+            elif param.kind == Parameter.KEYWORD_ONLY:
+                kwonly_args.append(name)
+
+        def warn_deprecated_args(kwargs):
+            intersection = deprecated_args.intersection(kwargs)
+            if intersection:
+                message = (f"Arguments {intersection} are deprecated, whether passed "
+                           "by position or keyword. They will be removed in SciPy "
+                           f"{version}. ")
+                message += custom_message
+                warnings.warn(message, category=DeprecationWarning, stacklevel=3)
+
+        @functools.wraps(f)
+        def inner_f(*args, **kwargs):
+
+            extra_args = len(args) - len(all_args)
+            if extra_args <= 0:
+                warn_deprecated_args(kwargs)
+                return f(*args, **kwargs)
+
+            # extra_args > 0
+            kwonly_extra_args = set(kwonly_args[:extra_args]) - deprecated_args
+            args_msg = ", ".join(kwonly_extra_args)
+            warnings.warn(
+                (
+                    f"You are passing as positional arguments: {args_msg}. "
+                    "Please change your invocation to use keyword arguments. "
+                    f"From SciPy {version}, passing these as positional "
+                    "arguments will result in an error."
+                ),
+                DeprecationWarning,
+                stacklevel=2,
+            )
+            kwargs.update(zip(sig.parameters, args))
+            warn_deprecated_args(kwargs)
+            return f(**kwargs)
+
+        doc = FunctionDoc(inner_f)
+        kwonly_extra_args = set(kwonly_args) - deprecated_args
+        admonition = f"""
+.. deprecated:: {version}
+    Use of argument(s) ``{kwonly_extra_args}`` by position is deprecated; beginning in 
+    SciPy {version}, these will be keyword-only. """
+        if deprecated_args:
+            admonition += (f"Argument(s) ``{deprecated_args}`` are deprecated, whether "
+                           "passed by position or keyword; they will be removed in "
+                           f"SciPy {version}. ")
+        admonition += custom_message
+        doc['Extended Summary'] += [admonition]
+
+        doc = str(doc).split("\n", 1)[1].lstrip(" \n")  # remove signature
+        inner_f.__doc__ = str(doc)
+
+        return inner_f
+
+    if func is not None:
+        return _inner_deprecate_positional_args(func)
+
+    return _inner_deprecate_positional_args
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/doccer.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/doccer.py
new file mode 100644
index 0000000000000000000000000000000000000000..7fd8fef0b4c49a60fdd71427d134528aee00a216
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/doccer.py
@@ -0,0 +1,366 @@
+"""Utilities to allow inserting docstring fragments for common
+parameters into function and method docstrings."""
+
+from collections.abc import Callable, Iterable, Mapping
+from typing import Protocol, TypeVar
+import sys
+
+__all__ = [
+    "docformat",
+    "inherit_docstring_from",
+    "indentcount_lines",
+    "filldoc",
+    "unindent_dict",
+    "unindent_string",
+    "extend_notes_in_docstring",
+    "replace_notes_in_docstring",
+    "doc_replace",
+]
+
+_F = TypeVar("_F", bound=Callable[..., object])
+
+
+class Decorator(Protocol):
+    """A decorator of a function."""
+
+    def __call__(self, func: _F, /) -> _F: ...
+
+
+def docformat(docstring: str, docdict: Mapping[str, str] | None = None) -> str:
+    """Fill a function docstring from variables in dictionary.
+
+    Adapt the indent of the inserted docs
+
+    Parameters
+    ----------
+    docstring : str
+        A docstring from a function, possibly with dict formatting strings.
+    docdict : dict[str, str], optional
+        A dictionary with keys that match the dict formatting strings
+        and values that are docstring fragments to be inserted. The
+        indentation of the inserted docstrings is set to match the
+        minimum indentation of the ``docstring`` by adding this
+        indentation to all lines of the inserted string, except the
+        first.
+
+    Returns
+    -------
+    docstring : str
+        string with requested ``docdict`` strings inserted.
+
+    Examples
+    --------
+    >>> docformat(' Test string with %(value)s', {'value':'inserted value'})
+    ' Test string with inserted value'
+    >>> docstring = 'First line\\n    Second line\\n    %(value)s'
+    >>> inserted_string = "indented\\nstring"
+    >>> docdict = {'value': inserted_string}
+    >>> docformat(docstring, docdict)
+    'First line\\n    Second line\\n    indented\\n    string'
+    """
+    if not docstring:
+        return docstring
+    if docdict is None:
+        docdict = {}
+    if not docdict:
+        return docstring
+    lines = docstring.expandtabs().splitlines()
+    # Find the minimum indent of the main docstring, after first line
+    if len(lines) < 2:
+        icount = 0
+    else:
+        icount = indentcount_lines(lines[1:])
+    indent = " " * icount
+    # Insert this indent to dictionary docstrings
+    indented = {}
+    for name, dstr in docdict.items():
+        lines = dstr.expandtabs().splitlines()
+        indented[name] = ("\n" + indent).join(lines)
+    return docstring % indented
+
+
+def inherit_docstring_from(cls: object) -> Decorator:
+    """This decorator modifies the decorated function's docstring by
+    replacing occurrences of '%(super)s' with the docstring of the
+    method of the same name from the class `cls`.
+
+    If the decorated method has no docstring, it is simply given the
+    docstring of `cls`s method.
+
+    Parameters
+    ----------
+    cls : type or object
+        A class with a method with the same name as the decorated method.
+        The docstring of the method in this class replaces '%(super)s' in the
+        docstring of the decorated method.
+
+    Returns
+    -------
+    decfunc : function
+        The decorator function that modifies the __doc__ attribute
+        of its argument.
+
+    Examples
+    --------
+    In the following, the docstring for Bar.func created using the
+    docstring of `Foo.func`.
+
+    >>> class Foo:
+    ...     def func(self):
+    ...         '''Do something useful.'''
+    ...         return
+    ...
+    >>> class Bar(Foo):
+    ...     @inherit_docstring_from(Foo)
+    ...     def func(self):
+    ...         '''%(super)s
+    ...         Do it fast.
+    ...         '''
+    ...         return
+    ...
+    >>> b = Bar()
+    >>> b.func.__doc__
+    'Do something useful.\n        Do it fast.\n        '
+    """
+
+    def _doc(func: _F) -> _F:
+        cls_docstring = getattr(cls, func.__name__).__doc__
+        func_docstring = func.__doc__
+        if func_docstring is None:
+            func.__doc__ = cls_docstring
+        else:
+            new_docstring = func_docstring % dict(super=cls_docstring)
+            func.__doc__ = new_docstring
+        return func
+
+    return _doc
+
+
+def extend_notes_in_docstring(cls: object, notes: str) -> Decorator:
+    """This decorator replaces the decorated function's docstring
+    with the docstring from corresponding method in `cls`.
+    It extends the 'Notes' section of that docstring to include
+    the given `notes`.
+
+    Parameters
+    ----------
+    cls : type or object
+        A class with a method with the same name as the decorated method.
+        The docstring of the method in this class replaces the docstring of the
+        decorated method.
+    notes : str
+        Additional notes to append to the 'Notes' section of the docstring.
+
+    Returns
+    -------
+    decfunc : function
+        The decorator function that modifies the __doc__ attribute
+        of its argument.
+    """
+
+    def _doc(func: _F) -> _F:
+        cls_docstring = getattr(cls, func.__name__).__doc__
+        # If python is called with -OO option,
+        # there is no docstring
+        if cls_docstring is None:
+            return func
+        end_of_notes = cls_docstring.find("        References\n")
+        if end_of_notes == -1:
+            end_of_notes = cls_docstring.find("        Examples\n")
+            if end_of_notes == -1:
+                end_of_notes = len(cls_docstring)
+        func.__doc__ = (
+            cls_docstring[:end_of_notes] + notes + cls_docstring[end_of_notes:]
+        )
+        return func
+
+    return _doc
+
+
+def replace_notes_in_docstring(cls: object, notes: str) -> Decorator:
+    """This decorator replaces the decorated function's docstring
+    with the docstring from corresponding method in `cls`.
+    It replaces the 'Notes' section of that docstring with
+    the given `notes`.
+
+    Parameters
+    ----------
+    cls : type or object
+        A class with a method with the same name as the decorated method.
+        The docstring of the method in this class replaces the docstring of the
+        decorated method.
+    notes : str
+        The notes to replace the existing 'Notes' section with.
+
+    Returns
+    -------
+    decfunc : function
+        The decorator function that modifies the __doc__ attribute
+        of its argument.
+    """
+
+    def _doc(func: _F) -> _F:
+        cls_docstring = getattr(cls, func.__name__).__doc__
+        notes_header = "        Notes\n        -----\n"
+        # If python is called with -OO option,
+        # there is no docstring
+        if cls_docstring is None:
+            return func
+        start_of_notes = cls_docstring.find(notes_header)
+        end_of_notes = cls_docstring.find("        References\n")
+        if end_of_notes == -1:
+            end_of_notes = cls_docstring.find("        Examples\n")
+            if end_of_notes == -1:
+                end_of_notes = len(cls_docstring)
+        func.__doc__ = (
+            cls_docstring[: start_of_notes + len(notes_header)]
+            + notes
+            + cls_docstring[end_of_notes:]
+        )
+        return func
+
+    return _doc
+
+
+def indentcount_lines(lines: Iterable[str]) -> int:
+    """Minimum indent for all lines in line list
+
+    Parameters
+    ----------
+    lines : Iterable[str]
+        The lines to find the minimum indent of.
+
+    Returns
+    -------
+    indent : int
+        The minimum indent.
+
+
+    Examples
+    --------
+    >>> lines = [' one', '  two', '   three']
+    >>> indentcount_lines(lines)
+    1
+    >>> lines = []
+    >>> indentcount_lines(lines)
+    0
+    >>> lines = [' one']
+    >>> indentcount_lines(lines)
+    1
+    >>> indentcount_lines(['    '])
+    0
+    """
+    indentno = sys.maxsize
+    for line in lines:
+        stripped = line.lstrip()
+        if stripped:
+            indentno = min(indentno, len(line) - len(stripped))
+    if indentno == sys.maxsize:
+        return 0
+    return indentno
+
+
+def filldoc(docdict: Mapping[str, str], unindent_params: bool = True) -> Decorator:
+    """Return docstring decorator using docdict variable dictionary.
+
+    Parameters
+    ----------
+    docdict : dict[str, str]
+        A dictionary containing name, docstring fragment pairs.
+    unindent_params : bool, optional
+        If True, strip common indentation from all parameters in docdict.
+        Default is False.
+
+    Returns
+    -------
+    decfunc : function
+        The decorator function that applies dictionary to its
+        argument's __doc__ attribute.
+    """
+    if unindent_params:
+        docdict = unindent_dict(docdict)
+
+    def decorate(func: _F) -> _F:
+        # __doc__ may be None for optimized Python (-OO)
+        doc = func.__doc__ or ""
+        func.__doc__ = docformat(doc, docdict)
+        return func
+
+    return decorate
+
+
+def unindent_dict(docdict: Mapping[str, str]) -> dict[str, str]:
+    """Unindent all strings in a docdict.
+
+    Parameters
+    ----------
+    docdict : dict[str, str]
+        A dictionary with string values to unindent.
+
+    Returns
+    -------
+    docdict : dict[str, str]
+        The `docdict` dictionary but each of its string values are unindented.
+    """
+    can_dict: dict[str, str] = {}
+    for name, dstr in docdict.items():
+        can_dict[name] = unindent_string(dstr)
+    return can_dict
+
+
+def unindent_string(docstring: str) -> str:
+    """Set docstring to minimum indent for all lines, including first.
+
+    Parameters
+    ----------
+    docstring : str
+        The input docstring to unindent.
+
+    Returns
+    -------
+    docstring : str
+        The unindented docstring.
+
+    Examples
+    --------
+    >>> unindent_string(' two')
+    'two'
+    >>> unindent_string('  two\\n   three')
+    'two\\n three'
+    """
+    lines = docstring.expandtabs().splitlines()
+    icount = indentcount_lines(lines)
+    if icount == 0:
+        return docstring
+    return "\n".join([line[icount:] for line in lines])
+
+
+def doc_replace(obj: object, oldval: str, newval: str) -> Decorator:
+    """Decorator to take the docstring from obj, with oldval replaced by newval
+
+    Equivalent to ``func.__doc__ = obj.__doc__.replace(oldval, newval)``
+
+    Parameters
+    ----------
+    obj : object
+        A class or object whose docstring will be used as the basis for the
+        replacement operation.
+    oldval : str
+        The string to search for in the docstring.
+    newval : str
+        The string to replace `oldval` with in the docstring.
+
+    Returns
+    -------
+    decfunc : function
+        A decorator function that replaces occurrences of `oldval` with `newval`
+        in the docstring of the decorated function.
+    """
+    # __doc__ may be None for optimized Python (-OO)
+    doc = (obj.__doc__ or "").replace(oldval, newval)
+
+    def inner(func: _F) -> _F:
+        func.__doc__ = doc
+        return func
+
+    return inner
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/__init__.py
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/__init__.py
@@ -0,0 +1,212 @@
+# Bounds may appear unused in this file but we need to import it to make it available to the user
+from scipy.optimize import NonlinearConstraint, LinearConstraint, Bounds
+from .common._nonlinear_constraints import process_nl_constraints
+from .common._linear_constraints import (
+    combine_multiple_linear_constraints,
+    separate_LC_into_eq_and_ineq,
+)
+from .common._bounds import process_bounds
+from enum import Enum
+from .common._project import _project
+from .common.linalg import get_arrays_tol
+from .cobyla.cobyla import cobyla
+import numpy as np
+from collections.abc import Iterable
+
+
+class ConstraintType(Enum):
+    LINEAR_OBJECT = 5
+    NONLINEAR_OBJECT = 10
+    LINEAR_DICT = 15
+    NONLINEAR_DICT = 20
+
+
+def get_constraint_type(constraint):
+    if isinstance(constraint, dict) and ("A" in constraint) and ("lb" in constraint) and ("ub" in constraint):
+        return ConstraintType.LINEAR_DICT
+    elif isinstance(constraint, dict) and ("fun" in constraint) and ("lb" in constraint) and ("ub" in constraint):
+        return ConstraintType.NONLINEAR_DICT
+    elif hasattr(constraint, "A") and hasattr(constraint, "lb") and hasattr(constraint, "ub"):
+        return ConstraintType.LINEAR_OBJECT
+    elif hasattr(constraint, "fun") and hasattr(constraint, "lb") and hasattr(constraint, "ub"):
+        return ConstraintType.NONLINEAR_OBJECT
+    else:
+        raise ValueError(f"Constraint type {type(constraint)} not recognized")
+
+
+def process_constraints(constraints):
+    # First throw it back if it's an empty tuple
+    if not constraints:
+        return None, None
+    # Next figure out if it's a list of constraints or a single constraint
+    # If it's a single constraint, make it a list, and then the remaining logic
+    # doesn't have to change
+    if not isinstance(constraints, Iterable):
+        constraints = [constraints]
+
+    # Separate out the linear and nonlinear constraints
+    linear_constraints = []
+    nonlinear_constraints = []
+    for constraint in constraints:
+        constraint_type = get_constraint_type(constraint)
+        if constraint_type is ConstraintType.LINEAR_OBJECT:
+            linear_constraints.append(constraint)
+        elif constraint_type is ConstraintType.NONLINEAR_OBJECT:
+            nonlinear_constraints.append(constraint)
+        elif constraint_type == ConstraintType.LINEAR_DICT:
+            linear_constraints.append(LinearConstraint(constraint["A"], constraint["lb"], constraint["ub"]))
+        elif constraint_type == ConstraintType.NONLINEAR_DICT:
+            nonlinear_constraints.append(NonlinearConstraint(constraint["fun"], constraint["lb"], constraint["ub"]))
+        else:
+            raise ValueError("Constraint type not recognized")
+
+    if len(nonlinear_constraints) > 0:
+        nonlinear_constraint_function = process_nl_constraints(nonlinear_constraints)
+    else:
+        nonlinear_constraint_function = None
+
+    # Determine if we have multiple linear constraints, just 1, or none, and process accordingly
+    if len(linear_constraints) > 1:
+        linear_constraint = combine_multiple_linear_constraints(linear_constraints)
+    elif len(linear_constraints) == 1:
+        linear_constraint = linear_constraints[0]
+    else:
+        linear_constraint = None
+
+    return linear_constraint, nonlinear_constraint_function
+
+
+def minimize(fun, x0, args=(), method=None, bounds=None, constraints=(), callback=None, options=None):
+
+    linear_constraint, nonlinear_constraint_function = process_constraints(constraints)
+
+    options = {'quiet': True} if options is None else options
+    quiet = options.get("quiet", True)
+
+    if method is None:
+        if nonlinear_constraint_function is not None:
+            if not quiet: print("Nonlinear constraints detected, applying COBYLA")
+            method = "cobyla"
+        elif linear_constraint is not None:
+            if not quiet: print("Linear constraints detected without nonlinear constraints, applying LINCOA")
+            method = "lincoa"
+        elif bounds is not None:
+            if not quiet: print("Bounds without linear or nonlinear constraints detected, applying BOBYQA")
+            method = "bobyqa"
+        else:
+            if not quiet: print("No bounds or constraints detected, applying NEWUOA")
+            method = "newuoa"
+    else:
+        # Raise some errors if methods were called with inappropriate options
+        method = method.lower()
+        if method not in ('newuoa', 'uobyqa', 'bobyqa', 'cobyla', 'lincoa'):
+            raise ValueError(f"Method must be one of NEWUOA, UOBYQA, BOBYQA, COBYLA, or LINCOA, not '{method}'")
+        if method != "cobyla" and nonlinear_constraint_function is not None:
+            raise ValueError("Nonlinear constraints were provided for an algorithm that cannot handle them")
+        if method not in ("cobyla", "lincoa") and linear_constraint is not None:
+            raise ValueError("Linear constraints were provided for an algorithm that cannot handle them")
+        if method not in ("cobyla", "bobyqa", "lincoa") and bounds is not None:
+            raise ValueError("Bounds were provided for an algorithm that cannot handle them")
+
+    # Try to get the length of x0. If we can't that likely means it's a scalar, and
+    # in that case we turn it into an array and wrap the original function so that it
+    # can accept an array and return a scalar.
+    try:
+        lenx0 = len(x0)
+    except TypeError:
+        x0 = np.array([x0])
+        original_scalar_fun = fun
+        def scalar_fun(x):
+            return original_scalar_fun(x[0], *args)
+        fun = scalar_fun
+        lenx0 = 1
+
+    lb, ub = process_bounds(bounds, lenx0)
+
+    # Check which variables are fixed and eliminate them from the problem.
+    # Save the indices and values so that we can call the original function with
+    # an array of the appropriate size, and so that we can add the fixed values to the
+    # result when COBYLA returns.
+    tol = get_arrays_tol(lb, ub)
+    _fixed_idx = (
+        (lb <= ub)
+        & (np.abs(lb - ub) < tol)
+    )
+    if any(_fixed_idx):
+        _fixed_values = 0.5 * (
+            lb[_fixed_idx] + ub[_fixed_idx]
+        )
+        _fixed_values = np.clip(
+            _fixed_values,
+            lb[_fixed_idx],
+            ub[_fixed_idx],
+        )
+        x0 = x0[~_fixed_idx]
+        lb = lb[~_fixed_idx]
+        ub = ub[~_fixed_idx]
+        original_fun = fun
+        def fixed_fun(x):
+            newx = np.zeros(lenx0)
+            newx[_fixed_idx] = _fixed_values
+            newx[~_fixed_idx] = x
+            return original_fun(newx, *args)
+        fun = fixed_fun
+
+
+    # Project x0 onto the feasible set
+    if nonlinear_constraint_function is None:
+        result = _project(x0, lb, ub, {"linear": linear_constraint, "nonlinear": None})
+        x0 = result.x
+    
+    if linear_constraint is not None:
+        A_eq, b_eq, A_ineq, b_ineq = separate_LC_into_eq_and_ineq(linear_constraint)
+    else:
+        A_eq, b_eq, A_ineq, b_ineq = None, None, None, None
+
+    if nonlinear_constraint_function is not None:
+        # If there is a nonlinear constraint function, we will call COBYLA, which needs the number of nonlinear
+        # constraints (m_nlcon). In order to get this number we need to evaluate the constraint function at x0.
+        # The constraint value at x0 (nlconstr0) is not discarded but passed down to the Fortran backend, as its
+        # evaluation is assumed to be expensive. We also evaluate the objective function at x0 and pass the result
+        # (f0) down to the Fortran backend, which expects nlconstr0 and f0 to be provided in sync.
+        def calcfc(x):
+            f = fun(x, *args)
+            nlconstr = nonlinear_constraint_function(x)
+            return f, nlconstr
+    else:
+        def calcfc(x):
+            f = fun(x, *args)
+            constr = np.zeros(0)
+            return f, constr
+
+    f0, nlconstr0 = calcfc(x0)
+
+    if 'quiet' in options:
+        del options['quiet']
+
+    if 'maxfev' in options:
+        options['maxfun'] = options['maxfev']
+        del options['maxfev']
+
+    result = cobyla(
+        calcfc,
+        len(nlconstr0),
+        x0,
+        A_ineq,
+        b_ineq,
+        A_eq,
+        b_eq,
+        lb,
+        ub,
+        f0=f0,
+        nlconstr0=nlconstr0,
+        callback=callback,
+        **options
+    )
+
+    if any(_fixed_idx):
+        newx = np.zeros(lenx0)
+        newx[_fixed_idx] = _fixed_values
+        newx[~_fixed_idx] = result.x
+        result.x = newx
+    return result
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/cobyla.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/cobyla.py
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/cobyla.py
@@ -0,0 +1,559 @@
+'''
+This module provides Powell's COBYLA algorithm.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+
+N.B.:
+
+1. The modern-Fortran reference implementation in PRIMA contains bug fixes and improvements over the
+original Fortran 77 implementation by Powell. Consequently, the PRIMA implementation behaves differently
+from the original Fortran 77 implementation by Powell. Therefore, it is important to point out that
+you are using PRIMA rather than the original solvers if you want your results to be reproducible.
+
+2. Compared to Powell's Fortran 77 implementation, the modern-Fortran implementation and hence any
+faithful translation like this one generally produce better solutions with fewer function evaluations,
+making them preferable for applications with expensive function evaluations. However, if function
+evaluations are not the dominant cost in your application, the Fortran 77 solvers are likely to be
+faster, as they are more efficient in terms of memory usage and flops thanks to the careful and
+ingenious (but unmaintained and unmaintainable) implementation by Powell.
+
+See the PRIMA documentation (www.libprima.net) for more information.
+'''
+
+from ..common.evaluate import evaluate, moderatex, moderatef, moderatec
+from ..common.consts import (EPS, RHOBEG_DEFAULT, RHOEND_DEFAULT, CTOL_DEFAULT,
+                                   CWEIGHT_DEFAULT, FTARGET_DEFAULT, IPRINT_DEFAULT,
+                                   MAXFUN_DIM_DEFAULT, DEBUGGING, BOUNDMAX,
+                                   ETA1_DEFAULT, ETA2_DEFAULT, GAMMA1_DEFAULT,
+                                   GAMMA2_DEFAULT)
+from ..common.preproc import preproc
+from ..common.present import present
+from ..common.linalg import matprod
+from .cobylb import cobylb
+import numpy as np
+from dataclasses import dataclass
+from copy import copy
+
+
+@dataclass
+class COBYLAResult:
+    x: np.ndarray
+    f: float
+    constr: np.ndarray
+    cstrv: float
+    nf: int
+    xhist: np.ndarray | None
+    fhist: np.ndarray | None
+    chist: np.ndarray | None
+    conhist: np.ndarray | None
+    info: int
+
+
+def cobyla(calcfc, m_nlcon, x, Aineq=None, bineq=None, Aeq=None, beq=None,
+           xl=None, xu=None, f0=None, nlconstr0=None, rhobeg=None, rhoend=None,
+           ftarget=FTARGET_DEFAULT, ctol=CTOL_DEFAULT, cweight=CWEIGHT_DEFAULT,
+           maxfun=None, iprint=IPRINT_DEFAULT, eta1=None, eta2=None,
+           gamma1=GAMMA1_DEFAULT, gamma2=GAMMA2_DEFAULT, maxhist=None, maxfilt=2000,
+           callback=None):
+    """
+    Among all the arguments, only CALCFC, M_NLCON, and X are obligatory. The others are
+    OPTIONAL and you can neglect them unless you are familiar with the algorithm. Any
+    unspecified optional input will take the default value detailed below. For
+    instance, we may invoke the solver as follows.
+
+    # First define CALCFC, M_NLCON, and X, and then do the following.
+    result = cobyla(calcfc, m_nlcon, x)
+
+    or
+
+    # First define CALCFC, M_NLCON, X, Aineq, and Bineq, and then do the following.
+    result = cobyla(calcfc, m_nlcon, x, Aineq=Aineq, bineq=bineq, rhobeg=1.0e0,
+        rhoend=1.0e-6)
+
+    ####################################################################################
+    # IMPORTANT NOTICE: The user must set M_NLCON correctly to the number of nonlinear
+    # constraints, namely the size of NLCONSTR introduced below. Set it to 0 if there
+    # is no nonlinear constraint.
+    ####################################################################################
+
+    See examples/cobyla/cobyla_example.py for a concrete example.
+
+    A detailed introduction to the arguments is as follows.
+
+    ####################################################################################
+    # INPUTS
+    ####################################################################################
+
+    CALCFC
+      Input, function.
+      f, nlconstr = CALCFC(X) should evaluate the objective function and nonlinear
+      constraints at the given vector X; it should return a tuple consisting of the
+      objective function value and the nonlinear constraint value. It must be provided
+      by the user, and its definition must conform to the following interface:
+      #-------------------------------------------------------------------------#
+       def calcfc(x):
+           f = 0.0
+           nlconstr = np.zeros(m_nlcon)
+           return f, nlconstr
+      #-------------------------------------------------------------------------#
+
+    M_NLCON
+      Input, scalar.
+      M_NLCON must be set to the number of nonlinear constraints, namely the size of
+      NLCONSTR(X).
+      N.B.:
+      1. Why don't we define M_NLCON as optional and default it to 0 when it is absent?
+      This is because we need to allocate memory for CONSTR_LOC using M_NLCON. To
+      ensure that the size of CONSTR_LOC is correct, we require the user to specify
+      M_NLCON explicitly.
+
+    X
+      Input, vector.
+      As an input, X should be an N-dimensional vector that contains the starting
+      point, N being the dimension of the problem.
+
+    Aineq, Bineq
+      Input, matrix of size [Mineq, N] and vector of size Mineq unless they are both
+      empty, default: None and None.
+      Aineq and Bineq represent the linear inequality constraints: Aineq*X <= Bineq.
+
+    Aeq, Beq
+      Input, matrix of size [Meq, N] and vector of size Meq unless they are both
+      empty, default: None and None.
+      Aeq and Beq represent the linear equality constraints: Aeq*X = Beq.
+
+    XL, XU
+      Input, vectors of size N unless they are both None, default: None and None.
+      XL is the lower bound for X. If XL is None, X has no
+      lower bound. Any entry of XL that is NaN or below -BOUNDMAX will be taken as
+      -BOUNDMAX, which effectively means there is no lower bound for the corresponding
+      entry of X. The value of BOUNDMAX is 0.25*HUGE(X), which is about 8.6E37 for
+      single precision and 4.5E307 for double precision. XU is similar.
+
+    F0
+      Input, scalar.
+      F0, if present, should be set to the objective function value of the starting X.
+
+    NLCONSTR0
+      Input, vector.
+      NLCONSTR0, if present, should be set to the nonlinear constraint value at the
+      starting X; in addition, SIZE(NLCONSTR0) must be M_NLCON, or the solver will
+      abort.
+
+    RHOBEG, RHOEND
+      Inputs, scalars, default: RHOBEG = 1, RHOEND = 10^-6. RHOBEG and RHOEND must be
+      set to the initial and final values of a trust-region radius, both being positive
+      and RHOEND <= RHOBEG. Typically RHOBEG should be about one tenth of the greatest
+      expected change to a variable, and RHOEND should indicate the accuracy that is
+      required in the final values of the variables.
+
+    FTARGET
+      Input, scalar, default: -Inf.
+      FTARGET is the target function value. The algorithm will terminate when a
+      feasible point with a function value <= FTARGET is found.
+
+    CTOL
+      Input, scalar, default: sqrt(machine epsilon).
+      CTOL is the tolerance of constraint violation. X is considered feasible if
+      CSTRV(X) <= CTOL.
+      N.B.:
+        1. CTOL is absolute, not relative.
+        2. CTOL is used only when selecting the returned X. It does not affect the
+           iterations of the algorithm.
+
+    CWEIGHT
+      Input, scalar, default: CWEIGHT_DFT defined in common/consts.py.
+      CWEIGHT is the weight that the constraint violation takes in the selection of the
+      returned X.
+
+    MAXFUN
+      Input, integer scalar, default: MAXFUN_DIM_DFT*N with MAXFUN_DIM_DFT defined in
+      common/consts.py. MAXFUN is the maximal number of calls of CALCFC.
+
+    IPRINT
+      Input, integer scalar, default: 0.
+      The value of IPRINT should be set to 0, 1, -1, 2, -2, 3, or -3, which controls
+      how much information will be printed during the computation:
+      0: there will be no printing;
+      1: a message will be printed to the screen at the return, showing the best vector
+         of variables found and its objective function value;
+      2: in addition to 1, each new value of RHO is printed to the screen, with the
+         best vector of variables so far and its objective function value; each new
+         value of CPEN is also printed;
+      3: in addition to 2, each function evaluation with its variables will be printed
+         to the screen; -1, -2, -3: the same information as 1, 2, 3 will be printed,
+         not to the screen but to a file named COBYLA_output.txt; the file will be
+         created if it does not exist; the new output will be appended to the end of
+         this file if it already exists.
+      Note that IPRINT = +/-3 can be costly in terms of time and/or space.
+
+    ETA1, ETA2, GAMMA1, GAMMA2
+      Input, scalars, default: ETA1 = 0.1, ETA2 = 0.7, GAMMA1 = 0.5, and GAMMA2 = 2.
+      ETA1, ETA2, GAMMA1, and GAMMA2 are parameters in the updating scheme of the
+      trust-region radius detailed in the subroutine TRRAD in trustregion.py. Roughly
+      speaking, the trust-region radius is contracted by a factor of GAMMA1 when the
+      reduction ratio is below ETA1, and enlarged by a factor of GAMMA2 when the
+      reduction ratio is above ETA2. It is required that 0 < ETA1 <= ETA2 < 1 and
+      0 < GAMMA1 < 1 < GAMMA2. Normally, ETA1 <= 0.25. It is NOT advised to set
+      ETA1 >= 0.5.
+
+    MAXFILT
+      Input, scalar.
+      MAXFILT is a nonnegative integer indicating the maximal length of the filter used
+      for selecting the returned solution; default: MAXFILT_DFT (a value lower than
+      MIN_MAXFILT is not recommended);
+      see common/consts.py for the definitions of MAXFILT_DFT and MIN_MAXFILT.
+
+    CALLBACK
+      Input, function to report progress and optionally request termination.
+
+
+    ####################################################################################
+    # OUTPUTS
+    ####################################################################################
+
+    The output is a single data structure, COBYLAResult, with the following fields:
+
+    X
+      Output, vector.
+      As an output, X will be set to an approximate minimizer.
+
+    F
+      Output, scalar.
+      F will be set to the objective function value of X at exit.
+
+    CONSTR
+      Output, vector.
+      CONSTR will be set to the constraint value of X at exit.
+
+    CSTRV
+      Output, scalar.
+      CSTRV will be set to the constraint violation of X at exit, i.e.,
+      max([0, XL - X, X - XU, Aineq*X - Bineq, ABS(Aeq*X -Beq), NLCONSTR(X)]).
+
+    NF
+      Output, scalar.
+      NF will be set to the number of calls of CALCFC at exit.
+
+    XHIST, FHIST, CHIST, CONHIST, MAXHIST
+      XHIST: Output, rank 2 array;
+      FHIST: Output, rank 1 array;
+      CHIST: Output, rank 1 array;
+      CONHIST: Output, rank 2 array;
+      MAXHIST: Input, scalar, default: MAXFUN
+      XHIST, if present, will output the history of iterates; FHIST, if present, will
+      output the history function values; CHIST, if present, will output the history of
+      constraint violations; CONHIST, if present, will output the history of constraint
+      values; MAXHIST should be a nonnegative integer, and XHIST/FHIST/CHIST/CONHIST
+      will output only the history of the last MAXHIST iterations.
+      Therefore, MAXHIST= 0 means XHIST/FHIST/CONHIST/CHIST will output
+      nothing, while setting MAXHIST = MAXFUN requests XHIST/FHIST/CHIST/CONHIST to
+      output all the history. If XHIST is present, its size at exit will be
+      (N, min(NF, MAXHIST)); if FHIST is present, its size at exit will be
+      min(NF, MAXHIST); if CHIST is present, its size at exit will be min(NF, MAXHIST);
+      if CONHIST is present, its size at exit will be (M, min(NF, MAXHIST)).
+
+      IMPORTANT NOTICE:
+      Setting MAXHIST to a large value can be costly in terms of memory for large
+      problems.
+      MAXHIST will be reset to a smaller value if the memory needed exceeds MAXHISTMEM
+      defined in common/consts.py
+      Use *HIST with caution!!! (N.B.: the algorithm is NOT designed for large
+      problems).
+
+    INFO
+      Output, scalar.
+      INFO is the exit flag. It will be set to one of the following values defined in
+      common/infos.py:
+      SMALL_TR_RADIUS: the lower bound for the trust region radius is reached;
+      FTARGET_ACHIEVED: the target function value is reached;
+      MAXFUN_REACHED: the objective function has been evaluated MAXFUN times;
+      MAXTR_REACHED: the trust region iteration has been performed MAXTR times (MAXTR = 2*MAXFUN);
+      NAN_INF_X: NaN or Inf occurs in X;
+      DAMAGING_ROUNDING: rounding errors are becoming damaging.
+      #--------------------------------------------------------------------------#
+      The following case(s) should NEVER occur unless there is a bug.
+      NAN_INF_F: the objective function returns NaN or +Inf;
+      NAN_INF_MODEL: NaN or Inf occurs in the model;
+      TRSUBP_FAILED: a trust region step failed to reduce the model
+      #--------------------------------------------------------------------------#
+    """
+
+    # Local variables
+    solver = "COBYLA"
+    srname = "COBYLA"
+
+    # Sizes
+    mineq = len(bineq) if present(bineq) else 0
+    meq = len(beq) if present(beq) else 0
+    mxl = sum(xl > -BOUNDMAX) if present(xl) else 0
+    mxu = sum(xu < BOUNDMAX) if present(xu) else 0
+    mmm = mxu + mxl + 2*meq + mineq + m_nlcon
+    num_vars = len(x)
+
+    # Preconditions
+    if DEBUGGING:
+        assert m_nlcon >= 0, f'{srname} M_NLCON >= 0'
+        assert num_vars >= 1, f'{srname} N >= 1'
+
+        assert present(Aineq) == present(bineq), \
+            f'{srname} Aineq and Bineq are both present or both absent'
+        if (present(Aineq)):
+            assert Aineq.shape == (mineq, num_vars), f'{srname} SIZE(Aineq) == [Mineq, N]'
+
+        assert present(Aeq) == present(beq), \
+            f'{srname} Aeq and Beq are both present or both absent'
+        if (present(Aeq)):
+            assert Aeq.shape == (meq, num_vars), f'{srname} SIZE(Aeq) == [Meq, N]'
+
+        if (present(xl)):
+            assert len(xl) == num_vars, f'{srname} SIZE(XL) == N'
+        if (present(xu)):
+            assert len(xu) == num_vars, f'{srname} SIZE(XU) == N'
+
+
+        # N.B.: If NLCONSTR0 is present, then F0 must be present, and we assume that
+        # F(X0) = F0 even if F0 is NaN; if NLCONSTR0 is absent, then F0 must be either
+        # absent or NaN, both of which will be interpreted as F(X0) is not provided.
+        if present(nlconstr0):
+            assert present(f0), f'{srname} If NLCONSTR0 is present, then F0 is present'
+        if present(f0):
+            assert np.isnan(f0) or present(nlconstr0), \
+                f'{srname} If F0 is present and not NaN, then NLCONSTR0 is present'
+
+
+
+    # Exit if the size of NLCONSTR0 is inconsistent with M_NLCON.
+    if present(nlconstr0):
+        assert np.size(nlconstr0) == m_nlcon
+
+    # Read the inputs.
+
+    if xl is not None:
+      xl = copy(xl)
+      xl[np.isnan(xl)] = -BOUNDMAX
+      xl[xl < -BOUNDMAX] = -BOUNDMAX
+
+    if xu is not None:
+      xu = copy(xu)
+      xu[np.isnan(xu)] = BOUNDMAX
+      xu[xu > BOUNDMAX] = BOUNDMAX
+
+    # Wrap the linear and bound constraints into a single constraint: AMAT@X <= BVEC.
+    amat, bvec = get_lincon(Aeq, Aineq, beq, bineq, xl, xu)
+
+    # Create constraint vector
+    constr = np.zeros(mmm)
+
+    # Set [F_LOC, CONSTR_LOC] to [F(X0), CONSTR(X0)] after evaluating the latter if
+    # needed. In this way, COBYLB only needs one interface.
+    # N.B.: Due to the preconditions above, there are two possibilities for F0 and
+    # NLCONSTR0.
+    # If NLCONSTR0 is present, then F0 must be present, and we assume that F(X0) = F0
+    # even if F0 is NaN.
+    # If NLCONSTR0 is absent, then F0 must be either absent or NaN, both of which will
+    # be interpreted as F(X0) is not provided and we have to evaluate F(X0) and
+    # NLCONSTR(X0) now.
+    if (present(f0) and present(nlconstr0) and all(np.isfinite(x))):
+        f = moderatef(f0)
+        if amat is not None:
+          constr[:mmm - m_nlcon] = moderatec(matprod(amat, x) - bvec)
+        constr[mmm - m_nlcon:] = moderatec(nlconstr0)
+    else:
+        x = moderatex(x)
+        f, constr = evaluate(calcfc, x, m_nlcon, amat, bvec)
+        constr[:mmm - m_nlcon] = moderatec(constr[:mmm - m_nlcon])
+        # N.B.: Do NOT call FMSG, SAVEHIST, or SAVEFILT for the function/constraint evaluation at X0.
+        # They will be called during the initialization, which will read the function/constraint at X0.
+    cstrv = max(np.append(0, constr))
+
+
+    # If RHOBEG is present, use it; otherwise, RHOBEG takes the default value for
+    # RHOBEG, taking the value of RHOEND into account. Note that RHOEND is considered
+    # only if it is present and it is VALID (i.e., finite and positive). The other
+    # inputs are read similarly.
+    if present(rhobeg):
+        rhobeg = rhobeg
+    elif present(rhoend) and np.isfinite(rhoend) and rhoend > 0:
+        rhobeg = max(10 * rhoend, RHOBEG_DEFAULT)
+    else:
+        rhobeg = RHOBEG_DEFAULT
+
+    if present(rhoend):
+        rhoend = rhoend
+    elif rhobeg > 0:
+        rhoend = max(EPS, min(RHOEND_DEFAULT/RHOBEG_DEFAULT * rhobeg, RHOEND_DEFAULT))
+    else:
+        rhoend = RHOEND_DEFAULT
+
+    maxfun = maxfun if present(maxfun) else MAXFUN_DIM_DEFAULT * num_vars
+
+    if present(eta1):
+        eta1 = eta1
+    elif present(eta2) and 0 < eta2 < 1:
+        eta1 = max(EPS, eta2 / 7)
+    else:
+        eta1 = ETA1_DEFAULT
+
+    if present(eta2):
+        eta2 = eta2
+    elif 0 < eta1 < 1:
+        eta2 = (eta1 + 2) / 3
+    else:
+        eta2 = ETA2_DEFAULT
+
+    maxhist = (
+        maxhist
+        if present(maxhist)
+        else max(maxfun, num_vars + 2, MAXFUN_DIM_DEFAULT * num_vars)
+    )
+
+    # Preprocess the inputs in case some of them are invalid. It does nothing if all
+    # inputs are valid.
+    (
+        iprint,
+        maxfun,
+        maxhist,
+        ftarget,
+        rhobeg,
+        rhoend,
+        npt,  # Unused in COBYLA
+        maxfilt,
+        ctol,
+        cweight,
+        eta1,
+        eta2,
+        gamma1,
+        gamma2,
+        _x0,  # Unused in COBYLA
+    ) = preproc(
+        solver,
+        num_vars,
+        iprint,
+        maxfun,
+        maxhist,
+        ftarget,
+        rhobeg,
+        rhoend,
+        num_constraints=mmm,
+        maxfilt=maxfilt,
+        ctol=ctol,
+        cweight=cweight,
+        eta1=eta1,
+        eta2=eta2,
+        gamma1=gamma1,
+        gamma2=gamma2,
+        is_constrained=(mmm > 0),
+    )
+
+    # Further revise MAXHIST according to MAXHISTMEM, and allocate memory for the history.
+    # In MATLAB/Python/Julia/R implementation, we should simply set MAXHIST = MAXFUN and initialize
+    # CHIST = NaN(1, MAXFUN), CONHIST = NaN(M, MAXFUN), FHIST = NaN(1, MAXFUN), XHIST = NaN(N, MAXFUN)
+    # if they are requested; replace MAXFUN with 0 for the history that is not requested.
+    # prehist(maxhist, num_vars, present(xhist), xhist_loc, present(fhist), fhist_loc, &
+    #     & present(chist), chist_loc, m, present(conhist), conhist_loc)
+
+    # call cobylb, which performs the real calculations
+    x, f, constr, cstrv, nf, xhist, fhist, chist, conhist, info = cobylb(
+        calcfc,
+        iprint,
+        maxfilt,
+        maxfun,
+        amat,
+        bvec,
+        ctol,
+        cweight,
+        eta1,
+        eta2,
+        ftarget,
+        gamma1,
+        gamma2,
+        rhobeg,
+        rhoend,
+        constr,
+        f,
+        x,
+        maxhist,
+        callback
+    )
+
+    return COBYLAResult(x, f, constr, cstrv, nf, xhist, fhist, chist, conhist, info)
+
+
+def get_lincon(Aeq=None, Aineq=None, beq=None, bineq=None, xl=None, xu=None):
+    """
+    This subroutine wraps the linear and bound constraints into a single constraint:
+        AMAT*X <= BVEC.
+
+    N.B.:
+
+    LINCOA normalizes the linear constraints so that each constraint has a gradient
+    of norm 1. However, COBYLA does not do this.
+    """
+
+    # Sizes
+    if Aeq is not None:
+        num_vars = Aeq.shape[1]
+    elif Aineq is not None:
+        num_vars = Aineq.shape[1]
+    elif xl is not None:
+        num_vars = len(xl)
+    elif xu is not None:
+        num_vars = len(xu)
+    else:
+        return None, None
+
+    # Preconditions
+    if DEBUGGING:
+        assert Aineq is None or Aineq.shape == (len(bineq), num_vars)
+        assert Aeq is None or Aeq.shape == (len(beq), num_vars)
+        assert (xl is None or xu is None) or len(xl) == len(xu) == num_vars
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # Define the indices of the nontrivial bound constraints.
+    ixl = np.where(xl > -BOUNDMAX)[0] if xl is not None else None
+    ixu = np.where(xu < BOUNDMAX)[0] if xu is not None else None
+
+    # Wrap the linear constraints.
+    # The bound constraint XL <= X <= XU is handled as two constraints:
+    # -X <= -XL, X <= XU.
+    # The equality constraint Aeq*X = Beq is handled as two constraints:
+    # -Aeq*X <= -Beq, Aeq*X <= Beq.
+    # N.B.:
+    # 1. The treatment of the equality constraints is naive. One may choose to
+    #    eliminate them instead.
+    idmat = np.eye(num_vars)
+    amat = np.vstack([
+        -idmat[ixl, :] if ixl is not None else np.empty((0, num_vars)),
+        idmat[ixu, :] if ixu is not None else np.empty((0, num_vars)),
+        -Aeq if Aeq is not None else np.empty((0, num_vars)),
+        Aeq if Aeq is not None else np.empty((0, num_vars)),
+        Aineq if Aineq is not None else np.empty((0, num_vars))
+    ])
+    bvec = np.hstack([
+        -xl[ixl] if ixl is not None else np.empty(0),
+        xu[ixu] if ixu is not None else np.empty(0),
+        -beq if beq is not None else np.empty(0),
+        beq if beq is not None else np.empty(0),
+        bineq if bineq is not None else np.empty(0)
+    ])
+
+    amat = amat if amat.shape[0] > 0 else None
+    bvec = bvec if bvec.shape[0] > 0 else None
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert (amat is None and bvec is None) or amat.shape == (len(bvec), num_vars)
+
+    return amat, bvec
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/cobylb.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/cobylb.py
new file mode 100644
index 0000000000000000000000000000000000000000..91012c3b3b2bca1c8827db3c4e2b7245735d23c2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/cobylb.py
@@ -0,0 +1,714 @@
+'''
+This module performs the major calculations of COBYLA.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+import numpy as np
+from ..common.checkbreak import checkbreak_con
+from ..common.consts import REALMAX, EPS, DEBUGGING, MIN_MAXFILT
+from ..common.infos import INFO_DEFAULT, MAXTR_REACHED, DAMAGING_ROUNDING, \
+                    SMALL_TR_RADIUS, CALLBACK_TERMINATE
+from ..common.evaluate import evaluate
+from ..common.history import savehist
+from ..common.linalg import isinv, matprod, inprod, norm, primasum, primapow2
+from ..common.message import fmsg, retmsg, rhomsg
+from ..common.ratio import redrat
+from ..common.redrho import redrho
+from ..common.selectx import savefilt, selectx
+from .update import updatepole, findpole, updatexfc
+from .geometry import setdrop_tr, geostep
+from .trustregion import trstlp, trrad
+from .initialize import initxfc, initfilt
+
+
+def cobylb(calcfc, iprint, maxfilt, maxfun, amat, bvec, ctol, cweight, eta1, eta2,
+           ftarget, gamma1, gamma2, rhobeg, rhoend, constr, f, x, maxhist, callback):
+    '''
+    This subroutine performs the actual computations of COBYLA.
+    '''
+
+    # Outputs
+    xhist = []
+    fhist = []
+    chist = []
+    conhist = []
+
+    # Local variables
+    solver = 'COBYLA'
+    A = np.zeros((np.size(x), np.size(constr))) # A contains the approximate gradient for the constraints
+    distsq = np.zeros(np.size(x) + 1)
+    # CPENMIN is the minimum of the penalty parameter CPEN for the L-infinity
+    # constraint violation in the merit function. Note that CPENMIN = 0 in Powell's
+    # implementation, which allows CPEN to be 0. Here, we take CPENMIN > 0 so that CPEN
+    # is always positive. This avoids the situation where PREREM becomes 0 when
+    # PREREF = 0 = CPEN. It brings two advantages as follows.
+    # 1. If the trust-region subproblem solver works correctly and the trust-region
+    #    center is not optimal for the subproblem, then PREREM > 0 is guaranteed. This
+    #    is because, in theory, PREREC >= 0 and MAX(PREREC, PREREF) > 0, and the
+    #    definition of CPEN in GETCPEN ensures that PREREM > 0.
+    # 2. There is no need to revise ACTREM and PREREM when CPEN = 0 and F = FVAL(N+1)
+    #    as in lines 312--314 of Powell's cobylb.f code. Powell's code revises ACTREM
+    #    to CVAL(N + 1) - CSTRV and PREREM to PREREC in this case, which is crucial for
+    #    feasibility problems.
+    cpenmin = EPS
+
+    # Sizes
+    m_lcon = np.size(bvec) if bvec is not None else 0
+    num_constraints = np.size(constr)
+    m_nlcon = num_constraints - m_lcon
+    num_vars = np.size(x)
+
+    # Preconditions
+    if DEBUGGING:
+        assert abs(iprint) <= 3
+        assert num_constraints >= m_lcon and m_lcon >= 0
+        assert num_vars >= 1
+        assert maxfun >= num_vars + 2
+        assert rhobeg >= rhoend and rhoend > 0
+        assert all(np.isfinite(x))
+        assert 0 <= eta1 <= eta2 < 1
+        assert 0 < gamma1 < 1 < gamma2
+        assert 0 <= ctol
+        assert 0 <= cweight
+        assert 0 <= maxhist <= maxfun
+        assert amat is None or np.shape(amat) == (m_lcon, num_vars)
+        assert min(MIN_MAXFILT, maxfun) <= maxfilt <= maxfun
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # Initialize SIM, FVAL, CONMAT, and CVAL, together with the history.
+    # After the initialization, SIM[:, NUM_VARS] holds the vertex of the initial
+    # simplex with the smallest function value (regardless of the constraint
+    # violation), and SIM[:, :NUM_VARS] holds the displacements from the other vertices
+    # to SIM[:, NUM_VARS]. FVAL, CONMAT, and CVAL hold the function values, constraint
+    # values, and constraint violations on the vertices in the order corresponding to
+    # SIM.
+    evaluated, conmat, cval, sim, simi, fval, nf, subinfo = initxfc(calcfc, iprint,
+      maxfun, constr, amat, bvec, ctol, f, ftarget, rhobeg, x,
+      xhist, fhist, chist, conhist, maxhist)
+
+    # Initialize the filter, including xfilt, ffilt, confilt, cfilt, and nfilt.
+    # N.B.: The filter is used only when selecting which iterate to return. It does not
+    # interfere with the iterations. COBYLA is NOT a filter method but a trust-region
+    # method based on an L-infinity merit function. Powell's implementation does not
+    # use a filter to select the iterate, possibly returning a suboptimal iterate.
+    cfilt = np.zeros(np.minimum(np.maximum(maxfilt, 1), maxfun))
+    confilt = np.zeros((np.size(constr), np.size(cfilt)))
+    ffilt = np.zeros(np.size(cfilt))
+    xfilt = np.zeros((np.size(x), np.size(cfilt)))
+    nfilt = initfilt(conmat, ctol, cweight, cval, fval, sim, evaluated, cfilt, confilt,
+                     ffilt, xfilt)
+
+    # Check whether to return due to abnormal cases that may occur during the initialization.
+    if subinfo != INFO_DEFAULT:
+        info = subinfo
+        # Return the best calculated values of the variables
+        # N.B: Selectx and findpole choose X by different standards, one cannot replace the other
+        kopt = selectx(ffilt[:nfilt], cfilt[:nfilt], cweight, ctol)
+        x = xfilt[:, kopt]
+        f = ffilt[kopt]
+        constr = confilt[:, kopt]
+        cstrv = cfilt[kopt]
+        # print a return message according to IPRINT.
+        retmsg(solver, info, iprint, nf, f, x, cstrv, constr)
+        # Postconditions
+        if DEBUGGING:
+            assert nf <= maxfun
+            assert np.size(x) == num_vars and not any(np.isnan(x))
+            assert not (np.isnan(f) or np.isposinf(f))
+            # assert np.size(xhist, 0) == n and np.size(xhist, 1) == maxxhist
+            # assert not any(np.isnan(xhist(:, 1:min(nf, maxxhist))))
+            # The last calculated X can be Inf (finite + finite can be Inf numerically).
+            # assert np.size(fhist) == maxfhist
+            # assert not any(np.isnan(fhist(1:min(nf, maxfhist))) or np.isposinf(fhist(1:min(nf, maxfhist))))
+            # assert np.size(conhist, 0) == m and np.size(conhist, 1) == maxconhist
+            # assert not any(np.isnan(conhist(:, 1:min(nf, maxconhist))) or np.isneginf(conhist(:, 1:min(nf, maxconhist))))
+            # assert np.size(chist) == maxchist
+            # assert not any(chist(1:min(nf, maxchist)) < 0 or np.isnan(chist(1:min(nf, maxchist))) or np.isposinf(chist(1:min(nf, maxchist))))
+            # nhist = minval([nf, maxfhist, maxchist])
+            # assert not any(isbetter(fhist(1:nhist), chist(1:nhist), f, cstrv, ctol))
+        return x, f, constr, cstrv, nf, xhist, fhist, chist, conhist, info
+
+
+    # Set some more initial values.
+    # We must initialize shortd, ratio, and jdrop_tr because these get defined on
+    # branches that are not guaranteed to be executed, but their values are used later.
+    # Our initialization of CPEN differs from Powell's in two ways. First, we use the
+    # ratio defined in (13) of Powell's COBYLA paper to initialize CPEN. Second, we
+    # impose CPEN >= CPENMIN > 0. Powell's code simply initializes CPEN to 0.
+    rho = rhobeg
+    delta = rhobeg
+    cpen = np.maximum(cpenmin, np.minimum(1.0E3, fcratio(conmat, fval)))  # Powell's code: CPEN = ZERO
+    shortd = False
+    ratio = -1
+    jdrop_tr = 0
+
+    # If DELTA <= GAMMA3*RHO after an update, we set DELTA to RHO. GAMMA3 must be less
+    # than GAMMA2. The reason is as follows. Imagine a very successful step with
+    # DNORM = the un-updated DELTA = RHO. The TRRAD will update DELTA to GAMMA2*RHO.
+    # If GAMMA3 >= GAMMA2, then DELTA will be reset to RHO, which is not reasonable as
+    # D is very successful. See paragraph two of Sec 5.2.5 in T. M. Ragonneau's thesis:
+    # "Model-Based Derivative-Free Optimization Methods and Software." According to
+    # test on 20230613, for COBYLA, this Powellful updating scheme of DELTA works
+    # slightly better than setting directly DELTA = max(NEW_DELTA, RHO).
+    gamma3 = np.maximum(1, np.minimum(0.75 * gamma2, 1.5))
+
+    # MAXTR is the maximal number of trust region iterations. Each trust-region
+    # iteration takes 1 or 2 function evaluations unless the trust-region step is short
+    # or the trust-region subproblem solver fails but the geometry step is not invoked.
+    # Thus the following MAXTR is unlikely to be reached.
+    maxtr = 10 * maxfun
+    info = MAXTR_REACHED
+
+    # Begin the iterative procedure
+    # After solving a trust-region subproblem, we use three boolean variables to
+    # control the workflow.
+    # SHORTD - Is the trust-region trial step too short to invoke # a function
+    #          evaluation?
+    # IMPROVE_GEO - Will we improve the model after the trust-region iteration? If yes,
+    #               a geometry step will be taken, corresponding to the "Branch (Delta)"
+    #               in the COBYLA paper.
+    # REDUCE_RHO - Will we reduce rho after the trust-region iteration?
+    # COBYLA never sets IMPROVE_GEO and REDUCE_RHO to True simultaneously.
+    for tr in range(maxtr):
+        # Increase the penalty parameter CPEN, if needed, so that
+        # PREREM = PREREF + CPEN * PREREC > 0.
+        # This is the first (out of two) update of CPEN, where CPEN increases or
+        # remains the same.
+        # N.B.: CPEN and the merit function PHI = FVAL + CPEN*CVAL are used in three
+        # places only.
+        # 1. In FINDPOLE/UPDATEPOLE, deciding the optimal vertex of the current simplex.
+        # 2. After the trust-region trial step, calculating the reduction ratio.
+        # 3. In GEOSTEP, deciding the direction of the geometry step.
+        # They do not appear explicitly in the trust-region subproblem, though the
+        # trust-region center (i.e. the current optimal vertex) is defined by them.
+        cpen = getcpen(amat, bvec, conmat, cpen, cval, delta, fval, rho, sim, simi)
+
+        # Switch the best vertex of the current simplex to SIM[:, NUM_VARS].
+        conmat, cval, fval, sim, simi, subinfo = updatepole(cpen, conmat, cval, fval,
+                                                            sim, simi)
+        # Check whether to exit due to damaging rounding in UPDATEPOLE.
+        if subinfo == DAMAGING_ROUNDING:
+            info = subinfo
+            break  # Better action to take? Geometry step, or simply continue?
+
+        # Does the interpolation set have adequate geometry? It affects improve_geo and
+        # reduce_rho.
+        adequate_geo = all(primasum(primapow2(sim[:, :num_vars]), axis=0) <= 4 * primapow2(delta))
+
+        # Calculate the linear approximations to the objective and constraint functions.
+        # N.B.: TRSTLP accesses A mostly by columns, so it is more reasonable to save A
+        # instead of A^T.
+        # Zaikun 2023108: According to a test on 2023108, calculating G and
+        # A(:, M_LCON+1:M) by solving the linear systems SIM^T*G = FVAL(1:N)-FVAL(N+1)
+        # and SIM^T*A = CONMAT(:, 1:N)-CONMAT(:, N+1) does not seem to improve or worsen
+        # the performance of COBYLA in terms of the number of function evaluations. The
+        # system was solved by SOLVE in LINALG_MOD based on a QR factorization of SIM
+        # (not necessarily a good algorithm). No preconditioning or scaling was used.
+        g = matprod((fval[:num_vars] - fval[num_vars]), simi)
+        A[:, :m_lcon] = amat.T if amat is not None else amat
+        A[:, m_lcon:] = matprod((conmat[m_lcon:, :num_vars] -
+                          np.tile(conmat[m_lcon:, num_vars], (num_vars, 1)).T), simi).T
+
+        # Calculate the trust-region trial step d. Note that d does NOT depend on cpen.
+        d = trstlp(A, -conmat[:, num_vars], delta, g)
+        dnorm = min(delta, norm(d))
+
+        # Is the trust-region trial step short? N.B.: we compare DNORM with RHO, not
+        # DELTA. Powell's code especially defines SHORTD by SHORTD = (DNORM < 0.5 *
+        # RHO). In our tests 1/10 seems to work better than 1/2 or 1/4, especially for
+        # linearly constrained problems. Note that LINCOA has a slightly more
+        # sophisticated way of defining SHORTD, taking into account whether D causes a
+        # change to the active set. Should we try the same here?
+        shortd = (dnorm <= 0.1 * rho)
+
+        # Predict the change to F (PREREF) and to the constraint violation (PREREC) due
+        # to D. We have the following in precise arithmetic. They may fail to hold due
+        # to rounding errors.
+        # 1. B[:NUM_CONSTRAINTS] = -CONMAT[:, NUM_VARS] and hence
+        # np.max(np.append(B[:NUM_CONSTRAINTS] - D@A[:, :NUM_CONSTRAINTS], 0)) is the
+        # L-infinity violation of the linearized constraints corresponding to D. When
+        # D=0, the violation is np.max(np.append(B[:NUM_CONSTRAINTS], 0)) =
+        # CVAL[NUM_VARS]. PREREC is the reduction of this violation achieved by D,
+        # which is nonnegative in theory; PREREC = 0 iff B[:NUM_CONSTRAINTS] <= 0, i.e.
+        # the trust-region center satisfies the linearized constraints.
+        # 2. PREREF may be negative or 0, but it is positive when PREREC = 0 and shortd
+        # is False
+        # 3. Due to 2, in theory, max(PREREC, PREREF) > 0 if shortd is False.
+        preref = -inprod(d, g)  # Can be negative
+        prerec = cval[num_vars] - np.max(np.append(0, conmat[:, num_vars] + matprod(d, A)))
+
+        # Evaluate PREREM, which is the predicted reduction in the merit function.
+        # In theory, PREREM >= 0 and it is 0 iff CPEN = 0 = PREREF. This may not be true
+        # numerically.
+        prerem = preref + cpen * prerec
+        trfail = not (prerem > 1.0E-6 * min(cpen, 1) * rho)
+
+        if shortd or trfail:
+            # Reduce DELTA if D is short or if D fails to render PREREM > 0. The latter
+            # can only happen due to rounding errors. This seems quite important for
+            # performance
+            delta *= 0.1
+            if delta <= gamma3 * rho:
+                delta = rho  # set delta to rho when it is close to or below
+        else:
+            # Calculate the next value of the objective and constraint functions.
+            # If X is close to one of the points in the interpolation set, then we do
+            # not evaluate the objective and constraints at X, assuming them to have
+            # the values at the closest point.
+            # N.B.: If this happens, do NOT include X into the filter, as F and CONSTR
+            # are inaccurate.
+            x = sim[:, num_vars] + d
+            distsq[num_vars] = primasum(primapow2(x - sim[:, num_vars]))
+            distsq[:num_vars] = primasum(primapow2(x.reshape(num_vars, 1) -
+                (sim[:, num_vars].reshape(num_vars, 1) + sim[:, :num_vars])), axis=0)
+            j = np.argmin(distsq)
+            if distsq[j] <= primapow2(1e-4 * rhoend):
+                f = fval[j]
+                constr = conmat[:, j]
+                cstrv = cval[j]
+            else:
+                # Evaluate the objective and constraints at X, taking care of possible
+                # inf/nan values.
+                f, constr = evaluate(calcfc, x, m_nlcon, amat, bvec)
+                cstrv = np.max(np.append(0, constr))
+                nf += 1
+                # Save X, F, CONSTR, CSTRV into the history.
+                savehist(maxhist, x, xhist, f, fhist, cstrv, chist, constr, conhist)
+                # Save X, F, CONSTR, CSTRV into the filter.
+                nfilt, cfilt, ffilt, xfilt, confilt = savefilt(cstrv, ctol, cweight, f,
+                                                               x, nfilt, cfilt, ffilt,
+                                                               xfilt, constr, confilt)
+
+            # Print a message about the function/constraint evaluation according to
+            # iprint
+            fmsg(solver, 'Trust region', iprint, nf, delta, f, x, cstrv, constr)
+
+            # Evaluate ACTREM, which is the actual reduction in the merit function
+            actrem = (fval[num_vars] + cpen * cval[num_vars]) - (f + cpen * cstrv)
+
+            # Calculate the reduction  ratio by redrat, which hands inf/nan carefully
+            ratio = redrat(actrem, prerem, eta1)
+
+            # Update DELTA. After this, DELTA < DNORM may hold.
+            # N.B.:
+            # 1. Powell's code uses RHO as the trust-region radius and updates it as
+            #    follows.
+            #    Reduce RHO to GAMMA1*RHO if ADEQUATE_GEO is TRUE and either SHORTD is
+            #    TRUE or RATIO < ETA1, and then revise RHO to RHOEND if its new value is
+            #    not more than GAMMA3*RHOEND; RHO remains unchanged in all other cases;
+            #    in particular, RHO is never increased.
+            # 2. Our implementation uses DELTA as the trust-region radius, while using
+            #    RHO as a lower bound for DELTA. DELTA is updated in a way that is
+            #    typical for trust-region methods, and it is revised to RHO if its new
+            #    value is not more than GAMMA3*RHO. RHO reflects the current resolution
+            #    of the algorithm; its update is essentially the same as the update of
+            #    RHO in Powell's code (see the definition of REDUCE_RHO below). Our
+            #    implementation aligns with UOBYQA/NEWUOA/BOBYQA/LINCOA and improves the
+            #    performance of COBYLA.
+            # 3. The same as Powell's code, we do not reduce RHO unless ADEQUATE_GEO is
+            #    TRUE. This is also how Powell updated RHO in
+            #    UOBYQA/NEWUOA/BOBYQA/LINCOA. What about we also use ADEQUATE_GEO ==
+            #    TRUE as a prerequisite for reducing DELTA? The argument would be that
+            #    the bad (small) value of RATIO may be because of a bad geometry (and
+            #    hence a bad model) rather than an improperly large DELTA, and it might
+            #    be good to try improving the geometry first without reducing DELTA.
+            #    However, according to a test on 20230206, it does not improve the
+            #    performance if we skip the update of DELTA when ADEQUATE_GEO is FALSE
+            #    and RATIO < 0.1. Therefore, we choose to update DELTA without checking
+            #    ADEQUATE_GEO.
+
+            delta = trrad(delta, dnorm, eta1, eta2, gamma1, gamma2, ratio)
+            if delta <= gamma3*rho:
+                delta = rho  # Set delta to rho when it is close to or below.
+
+            # Is the newly generated X better than the current best point?
+            ximproved = actrem > 0  # If ACTREM is NaN, then XIMPROVED should and will be False
+
+            # Set JDROP_TR to the index of the vertex to be replaced with X. JDROP_TR = 0 means there
+            # is no good point to replace, and X will not be included into the simplex; in this case,
+            # the geometry of the simplex likely needs improvement, which will be handled below.
+            jdrop_tr = setdrop_tr(ximproved, d, delta, rho, sim, simi)
+
+            # Update SIM, SIMI, FVAL, CONMAT, and CVAL so that SIM[:, JDROP_TR] is replaced with D.
+            # UPDATEXFC does nothing if JDROP_TR is None, as the algorithm decides to discard X.
+            sim, simi, fval, conmat, cval, subinfo = updatexfc(jdrop_tr, constr, cpen, cstrv, d, f, conmat, cval, fval, sim, simi)
+            # Check whether to break due to damaging rounding in UPDATEXFC
+            if subinfo == DAMAGING_ROUNDING:
+                info = subinfo
+                break  # Better action to take? Geometry step, or a RESCUE as in BOBYQA?
+
+            # Check whether to break due to maxfun, ftarget, etc.
+            subinfo = checkbreak_con(maxfun, nf, cstrv, ctol, f, ftarget, x)
+            if subinfo != INFO_DEFAULT:
+                info = subinfo
+                break
+        # End of if SHORTD or TRFAIL. The normal trust-region calculation ends.
+
+        # Before the next trust-region iteration, we possibly improve the geometry of the simplex or
+        # reduce RHO according to IMPROVE_GEO and REDUCE_RHO. Now we decide these indicators.
+        # N.B.: We must ensure that the algorithm does not set IMPROVE_GEO = True at infinitely many
+        # consecutive iterations without moving SIM[:, NUM_VARS] or reducing RHO. Otherwise, the algorithm
+        # will get stuck in repetitive invocations of GEOSTEP. This is ensured by the following facts:
+        # 1. If an iteration sets IMPROVE_GEO to True, it must also reduce DELTA or set DELTA to RHO.
+        # 2. If SIM[:, NUM_VARS] and RHO remain unchanged, then ADEQUATE_GEO will become True after at
+        # most NUM_VARS invocations of GEOSTEP.
+
+        # BAD_TRSTEP: Is the last trust-region step bad?
+        bad_trstep = shortd or trfail or ratio <= 0 or jdrop_tr is None
+        # IMPROVE_GEO: Should we take a geometry step to improve the geometry of the interpolation set?
+        improve_geo = bad_trstep and not adequate_geo
+        # REDUCE_RHO: Should we enhance the resolution by reducing rho?
+        reduce_rho = bad_trstep and adequate_geo and max(delta, dnorm) <= rho
+
+        # COBYLA never sets IMPROVE_GEO and REDUCE_RHO to True simultaneously.
+        # assert not (IMPROVE_GEO and REDUCE_RHO), 'IMPROVE_GEO or REDUCE_RHO are not both TRUE, COBYLA'
+
+        # If SHORTD or TRFAIL is True, then either IMPROVE_GEO or REDUCE_RHO is True unless ADEQUATE_GEO
+        # is True and max(DELTA, DNORM) > RHO.
+        # assert not (shortd or trfail) or (improve_geo or reduce_rho or (adequate_geo and max(delta, dnorm) > rho)), \
+        #     'If SHORTD or TRFAIL is TRUE, then either IMPROVE_GEO or REDUCE_RHO is TRUE unless ADEQUATE_GEO is TRUE and MAX(DELTA, DNORM) > RHO'
+
+        # Comments on BAD_TRSTEP:
+        # 1. Powell's definition of BAD_TRSTEP is as follows. The one used above seems to work better,
+        # especially for linearly constrained problems due to the factor TENTH (= ETA1).
+        # !bad_trstep = (shortd .or. actrem <= 0 .or. actrem < TENTH * prerem .or. jdrop_tr == 0)
+        # Besides, Powell did not check PREREM > 0 in BAD_TRSTEP, which is reasonable to do but has
+        # little impact upon the performance.
+        # 2. NEWUOA/BOBYQA/LINCOA would define BAD_TRSTEP, IMPROVE_GEO, and REDUCE_RHO as follows. Two
+        # different thresholds are used in BAD_TRSTEP. It outperforms Powell's version.
+        # !bad_trstep = (shortd .or. trfail .or. ratio <= eta1 .or. jdrop_tr == 0)
+        # !improve_geo = bad_trstep .and. .not. adequate_geo
+        # !bad_trstep = (shortd .or. trfail .or. ratio <= 0 .or. jdrop_tr == 0)
+        # !reduce_rho = bad_trstep .and. adequate_geo .and. max(delta, dnorm) <= rho
+        # 3. Theoretically, JDROP_TR > 0 when ACTREM > 0 (guaranteed by RATIO > 0). However, in Powell's
+        # implementation, JDROP_TR may be 0 even RATIO > 0 due to NaN. The modernized code has rectified
+        # this in the function SETDROP_TR. After this rectification, we can indeed simplify the
+        # definition of BAD_TRSTEP by removing the condition JDROP_TR == 0. We retain it for robustness.
+
+        # Comments on REDUCE_RHO:
+        # When SHORTD is TRUE, UOBYQA/NEWUOA/BOBYQA/LINCOA all set REDUCE_RHO to TRUE if the recent
+        # models are sufficiently accurate according to certain criteria. See the paragraph around (37)
+        # in the UOBYQA paper and the discussions about Box 14 in the NEWUOA paper. This strategy is
+        # crucial for the performance of the solvers. However, as of 20221111, we have not managed to
+        # make it work in COBYLA. As in NEWUOA, we recorded the errors of the recent models, and set
+        # REDUCE_RHO to true if they are small (e.g., ALL(ABS(MODERR_REC) <= 0.1 * MAXVAL(ABS(A))*RHO) or
+        # ALL(ABS(MODERR_REC) <= RHO**2)) when SHORTD is TRUE. It made little impact on the performance.
+
+
+        # Since COBYLA never sets IMPROVE_GEO and REDUCE_RHO to TRUE simultaneously, the following
+        # two blocks are exchangeable: IF (IMPROVE_GEO) ... END IF and IF (REDUCE_RHO) ... END IF.
+
+        # Improve the geometry of the simplex by removing a point and adding a new one.
+        # If the current interpolation set has acceptable geometry, then we skip the geometry step.
+        # The code has a small difference from Powell's original code here: If the current geometry
+        # is acceptable, then we will continue with a new trust-region iteration; however, at the
+        # beginning of the iteration, CPEN may be updated, which may alter the pole point SIM(:, N+1)
+        # by UPDATEPOLE; the quality of the interpolation point depends on SIM(:, N + 1), meaning
+        # that the same interpolation set may have good or bad geometry with respect to different
+        # "poles"; if the geometry turns out bad with the new pole, the original COBYLA code will
+        # take a geometry step, but our code here will NOT do it but continue to take a trust-region
+        # step. The argument is this: even if the geometry step is not skipped in the first place, the
+        # geometry may turn out bad again after the pole is altered due to an update to CPEN; should
+        # we take another geometry step in that case? If no, why should we do it here? Indeed, this
+        # distinction makes no practical difference for CUTEst problems with at most 100 variables
+        # and 5000 constraints, while the algorithm framework is simplified.
+        if improve_geo and not all(primasum(primapow2(sim[:, :num_vars]), axis=0) <= 4 * primapow2(delta)):
+            # Before the geometry step, updatepole has been called either implicitly by UPDATEXFC or
+            # explicitly after CPEN is updated, so that SIM[:, :NUM_VARS] is the optimal vertex.
+
+            # Decide a vertex to drop from the simplex. It will be replaced with SIM[:, NUM_VARS] + D to
+            # improve the geometry of the simplex.
+            # N.B.:
+            # 1. COBYLA never sets JDROP_GEO = num_vars.
+            # 2. The following JDROP_GEO comes from UOBYQA/NEWUOA/BOBYQA/LINCOA.
+            # 3. In Powell's original algorithm, the geometry of the simplex is considered acceptable
+            # iff the distance between any vertex and the pole is at most 2.1*DELTA, and the distance
+            # between any vertex and the opposite face of the simplex is at least 0.25*DELTA, as
+            # specified in (14) of the COBYLA paper. Correspondingly, JDROP_GEO is set to the index of
+            # the vertex with the largest distance to the pole provided that the distance is larger than
+            # 2.1*DELTA, or the vertex with the smallest distance to the opposite face of the simplex,
+            # in which case the distance must be less than 0.25*DELTA, as the current simplex does not
+            # have acceptable geometry (see (15)--(16) of the COBYLA paper). Once JDROP_GEO is set, the
+            # algorithm replaces SIM(:, JDROP_GEO) with D specified in (17) of the COBYLA paper, which
+            # is orthogonal to the face opposite to SIM(:, JDROP_GEO) and has a length of 0.5*DELTA,
+            # intending to improve the geometry of the simplex as per (14).
+            # 4. Powell's geometry-improving procedure outlined above has an intrinsic flaw: it may lead
+            # to infinite cycling, as was observed in a test on 20240320. In this test, the geometry-
+            # improving point introduced in the previous iteration was replaced with the trust-region
+            # trial point in the current iteration, which was then replaced with the same geometry-
+            # improving point in the next iteration, and so on. In this process, the simplex alternated
+            # between two configurations, neither of which had acceptable geometry. Thus RHO was never
+            # reduced, leading to infinite cycling. (N.B.: Our implementation uses DELTA as the trust
+            # region radius, with RHO being its lower bound. When the infinite cycling occurred in this
+            # test, DELTA = RHO and it could not be reduced due to the requirement that DELTA >= RHO.)
+            jdrop_geo = np.argmax(primasum(primapow2(sim[:, :num_vars]), axis=0), axis=0)
+
+            # Calculate the geometry step D.
+            delbar = delta/2
+            d = geostep(jdrop_geo, amat, bvec, conmat, cpen, cval, delbar, fval, simi)
+
+            # Calculate the next value of the objective and constraint functions.
+            # If X is close to one of the points in the interpolation set, then we do not evaluate the
+            # objective and constraints at X, assuming them to have the values at the closest point.
+            # N.B.:
+            # 1. If this happens, do NOT include X into the filter, as F and CONSTR are inaccurate.
+            # 2. In precise arithmetic, the geometry improving step ensures that the distance between X
+            # and any interpolation point is at least DELBAR, yet X may be close to them due to
+            # rounding. In an experiment with single precision on 20240317, X = SIM(:, N+1) occurred.
+            x = sim[:, num_vars] + d
+            distsq[num_vars] = primasum(primapow2(x - sim[:, num_vars]))
+            distsq[:num_vars] = primasum(primapow2(x.reshape(num_vars, 1) -
+                (sim[:, num_vars].reshape(num_vars, 1) + sim[:, :num_vars])), axis=0)
+            j = np.argmin(distsq)
+            if distsq[j] <= primapow2(1e-4 * rhoend):
+                f = fval[j]
+                constr = conmat[:, j]
+                cstrv = cval[j]
+            else:
+                # Evaluate the objective and constraints at X, taking care of possible
+                # inf/nan values.
+                f, constr = evaluate(calcfc, x, m_nlcon, amat, bvec)
+                cstrv = np.max(np.append(0, constr))
+                nf += 1
+                # Save X, F, CONSTR, CSTRV into the history.
+                savehist(maxhist, x, xhist, f, fhist, cstrv, chist, constr, conhist)
+                # Save X, F, CONSTR, CSTRV into the filter.
+                nfilt, cfilt, ffilt, xfilt, confilt = savefilt(cstrv, ctol, cweight, f,
+                                                               x, nfilt, cfilt, ffilt,
+                                                               xfilt, constr, confilt)
+
+            # Print a message about the function/constraint evaluation according to iprint
+            fmsg(solver, 'Geometry', iprint, nf, delta, f, x, cstrv, constr)
+            # Update SIM, SIMI, FVAL, CONMAT, and CVAL so that SIM(:, JDROP_GEO) is replaced with D.
+            sim, simi, fval, conmat, cval, subinfo = updatexfc(jdrop_geo, constr, cpen, cstrv, d, f, conmat, cval, fval, sim, simi)
+            # Check whether to break due to damaging rounding in UPDATEXFC
+            if subinfo == DAMAGING_ROUNDING:
+                info = subinfo
+                break  # Better action to take? Geometry step, or simply continue?
+
+            # Check whether to break due to maxfun, ftarget, etc.
+            subinfo = checkbreak_con(maxfun, nf, cstrv, ctol, f, ftarget, x)
+            if subinfo != INFO_DEFAULT:
+                info = subinfo
+                break
+        # end of if improve_geo. The procedure of improving the geometry ends.
+
+        # The calculations with the current RHO are complete. Enhance the resolution of the algorithm
+        # by reducing RHO; update DELTA and CPEN at the same time.
+        if reduce_rho:
+            if rho <= rhoend:
+                info = SMALL_TR_RADIUS
+                break
+            delta = max(0.5 * rho, redrho(rho, rhoend))
+            rho = redrho(rho, rhoend)
+            # THe second (out of two) updates of CPEN, where CPEN decreases or remains the same.
+            # Powell's code: cpen = min(cpen, fcratio(fval, conmat)), which may set CPEN to 0.
+            cpen = np.maximum(cpenmin, np.minimum(cpen, fcratio(conmat, fval)))
+            # Print a message about the reduction of rho according to iprint
+            rhomsg(solver, iprint, nf, fval[num_vars], rho, sim[:, num_vars], cval[num_vars], conmat[:, num_vars], cpen)
+            conmat, cval, fval, sim, simi, subinfo = updatepole(cpen, conmat, cval, fval, sim, simi)
+            # Check whether to break due to damaging rounding detected in updatepole
+            if subinfo == DAMAGING_ROUNDING:
+                info = subinfo
+                break  # Better action to take? Geometry step, or simply continue?
+        # End of if reduce_rho. The procedure of reducing RHO ends.
+        # Report the current best value, and check if user asks for early termination.
+        if callback:
+            terminate = callback(sim[:, num_vars], fval[num_vars], nf, tr, cval[num_vars], conmat[:, num_vars])
+            if terminate:
+                info = CALLBACK_TERMINATE
+                break
+    # End of for loop. The iterative procedure ends
+
+    # Return from the calculation, after trying the last trust-region step if it has not been tried yet.
+    # Ensure that D has not been updated after SHORTD == TRUE occurred, or the code below is incorrect.
+    x = sim[:, num_vars] + d
+    if (info == SMALL_TR_RADIUS and
+            shortd and
+            norm(x - sim[:, num_vars]) > 1.0E-3 * rhoend and
+            nf < maxfun):
+        # Zaikun 20230615: UPDATEXFC or UPDATEPOLE is not called since the last trust-region step. Hence
+        # SIM[:, NUM_VARS] remains unchanged. Otherwise SIM[:, NUM_VARS] + D would not make sense.
+        f, constr = evaluate(calcfc, x, m_nlcon, amat, bvec)
+        cstrv = np.max(np.append(0, constr))
+        nf += 1
+        savehist(maxhist, x, xhist, f, fhist, cstrv, chist, constr, conhist)
+        nfilt, cfilt, ffilt, xfilt, confilt = savefilt(cstrv, ctol, cweight, f, x, nfilt, cfilt, ffilt, xfilt, constr, confilt)
+        # Zaikun 20230512: DELTA has been updated. RHO is only indicative here. TO BE IMPROVED.
+        fmsg(solver, 'Trust region', iprint, nf, rho, f, x, cstrv, constr)
+
+    # Return the best calculated values of the variables
+    # N.B.: SELECTX and FINDPOLE choose X by different standards, one cannot replace the other.
+    kopt = selectx(ffilt[:nfilt], cfilt[:nfilt], max(cpen, cweight), ctol)
+    x = xfilt[:, kopt]
+    f = ffilt[kopt]
+    constr = confilt[:, kopt]
+    cstrv = cfilt[kopt]
+
+    # Print a return message according to IPRINT.
+    retmsg(solver, info, iprint, nf, f, x, cstrv, constr)
+    return x, f, constr, cstrv, nf, xhist, fhist, chist, conhist, info
+
+
+
+def getcpen(amat, bvec, conmat, cpen, cval, delta, fval, rho, sim, simi):
+    '''
+    This function gets the penalty parameter CPEN so that PREREM = PREREF + CPEN * PREREC > 0.
+    See the discussions around equation (9) of the COBYLA paper.
+    '''
+
+    # Even after nearly all of the pycutest problems were showing nearly bit for bit
+    # identical results between Python and the Fortran bindings, HS102 was still off by
+    # more than machine epsilon. It turned out to be due to the fact that getcpen was
+    # modifying fval, among other. It just goes to show that even when you're nearly
+    # perfect, you can still have non trivial bugs.
+    conmat = conmat.copy()
+    cval = cval.copy()
+    fval = fval.copy()
+    sim = sim.copy()
+    simi = simi.copy()
+
+    # Intermediate variables
+    A = np.zeros((np.size(sim, 0), np.size(conmat, 0)))
+    itol = 1
+
+    # Sizes
+    m_lcon = np.size(bvec) if bvec is not None else 0
+    num_constraints = np.size(conmat, 0)
+    num_vars = np.size(sim, 0)
+
+    # Preconditions
+    if DEBUGGING:
+        assert num_constraints >= 0
+        assert num_vars >= 1
+        assert cpen > 0
+        assert np.size(conmat, 0) == num_constraints and np.size(conmat, 1) == num_vars + 1
+        assert not (np.isnan(conmat) | np.isneginf(conmat)).any()
+        assert np.size(cval) == num_vars + 1 and \
+            not any(cval < 0 | np.isnan(cval) | np.isposinf(cval))
+        assert np.size(fval) == num_vars + 1 and not any(np.isnan(fval) | np.isposinf(fval))
+        assert np.size(sim, 0) == num_vars and np.size(sim, 1) == num_vars + 1
+        assert np.isfinite(sim).all()
+        assert all(np.max(abs(sim[:, :num_vars]), axis=0) > 0)
+        assert np.size(simi, 0) == num_vars and np.size(simi, 1) == num_vars
+        assert np.isfinite(simi).all()
+        assert isinv(sim[:, :num_vars], simi, itol)
+        assert delta >= rho and rho > 0
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # Initialize INFO which is needed in the postconditions
+    info = INFO_DEFAULT
+
+    # Increase CPEN if necessary to ensure PREREM > 0. Branch back for the next loop
+    # if this change alters the optimal vertex of the current simplex.
+    # Note the following:
+    # 1. In each loop, CPEN is changed only if PREREC > 0 > PREREF, in which case
+    #    PREREM is guaranteed positive after the update. Note that PREREC >= 0 and
+    #    max(PREREC, PREREF) > 0 in theory. If this holds numerically as well then CPEN
+    #    is not changed only if PREREC = 0 or PREREF >= 0, in which case PREREM is
+    #    currently positive, explaining why CPEN needs no update.
+    # 2. Even without an upper bound for the loop counter, the loop can occur at most
+    #    NUM_VARS+1 times. This is because the update of CPEN does not decrease CPEN,
+    #    and hence it can make vertex J (J <= NUM_VARS) become the new optimal vertex
+    #    only if CVAL[J] is less than CVAL[NUM_VARS], which can happen at most NUM_VARS
+    #    times. See the paragraph below (9) in the COBYLA paper. After the "correct"
+    #    optimal vertex is found, one more loop is needed to calculate CPEN, and hence
+    #    the loop can occur at most NUM_VARS+1 times.
+    for iter in range(num_vars + 1):
+        # Switch the best vertex of the current simplex to SIM[:, NUM_VARS]
+        conmat, cval, fval, sim, simi, info = updatepole(cpen, conmat, cval, fval, sim,
+                                                         simi)
+        # Check whether to exit due to damaging rounding in UPDATEPOLE
+        if info == DAMAGING_ROUNDING:
+            break
+
+        # Calculate the linear approximations to the objective and constraint functions.
+        g = matprod(fval[:num_vars] - fval[num_vars], simi)
+        A[:, :m_lcon] = amat.T if amat is not None else amat
+        A[:, m_lcon:] = matprod((conmat[m_lcon:, :num_vars] -
+                          np.tile(conmat[m_lcon:, num_vars], (num_vars, 1)).T), simi).T
+
+        # Calculate the trust-region trial step D. Note that D does NOT depend on CPEN.
+        d = trstlp(A, -conmat[:, num_vars], delta, g)
+
+        # Predict the change to F (PREREF) and to the constraint violation (PREREC) due
+        # to D.
+        preref = -inprod(d, g)  # Can be negative
+        prerec = cval[num_vars] - np.max(np.append(0, conmat[:, num_vars] + matprod(d, A)))
+
+        # PREREC <= 0 or PREREF >=0 or either is NaN
+        if not (prerec > 0 and preref < 0):
+            break
+
+        # Powell's code defines BARMU = -PREREF / PREREC, and CPEN is increased to
+        # 2*BARMU if and only if it is currently less than 1.5*BARMU, a very
+        # "Powellful" scheme. In our implementation, however, we set CPEN directly to
+        # the maximum between its current value and 2*BARMU while handling possible
+        # overflow. The simplifies the scheme without worsening the performance of
+        # COBYLA.
+        cpen = max(cpen, min(-2 * preref / prerec, REALMAX))
+
+        if findpole(cpen, cval, fval) == num_vars:
+            break
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert cpen >= cpen and cpen > 0
+        assert preref + cpen * prerec > 0 or info == DAMAGING_ROUNDING or \
+            not (prerec >= 0 and np.maximum(prerec, preref) > 0) or not np.isfinite(preref)
+
+    return cpen
+
+
+def fcratio(conmat, fval):
+    '''
+    This function calculates the ratio between the "typical change" of F and that of CONSTR.
+    See equations (12)-(13) in Section 3 of the COBYLA paper for the definition of the ratio.
+    '''
+
+    # Preconditions
+    if DEBUGGING:
+        assert np.size(fval) >= 1
+        assert np.size(conmat, 1) == np.size(fval)
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    cmin = np.min(-conmat, axis=1)
+    cmax = np.max(-conmat, axis=1)
+    fmin = min(fval)
+    fmax = max(fval)
+    if any(cmin < 0.5 * cmax) and fmin < fmax:
+        denom = np.min(np.maximum(cmax, 0) - cmin, where=cmin < 0.5 * cmax, initial=np.inf)
+        # Powell mentioned the following alternative in section 4 of his COBYLA paper. According to a test
+        # on 20230610, it does not make much difference to the performance.
+        # denom = np.max(max(*cmax, 0) - cmin, mask=(cmin < 0.5 * cmax))
+        r = (fmax - fmin) / denom
+    else:
+        r = 0
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert r >= 0
+
+    return r
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/geometry.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/geometry.py
new file mode 100644
index 0000000000000000000000000000000000000000..c03e5626696f5a40939792b6448972d304b31d71
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/geometry.py
@@ -0,0 +1,226 @@
+'''
+This module contains subroutines concerning the geometry-improving of the interpolation set.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+from ..common.consts import DEBUGGING
+from ..common.linalg import isinv, matprod, inprod, norm, primasum, primapow2
+import numpy as np
+
+
+def setdrop_tr(ximproved, d, delta, rho, sim, simi):
+    '''
+    This function finds (the index) of a current interpolation point to be replaced with
+    the trust-region trial point. See (19)-(22) of the COBYLA paper.
+    N.B.:
+    1. If XIMPROVED == True, then JDROP > 0 so that D is included into XPT. Otherwise,
+       it is a bug.
+    2. COBYLA never sets JDROP = NUM_VARS
+    TODO: Check whether it improves the performance if JDROP = NUM_VARS is allowed when
+    XIMPROVED is True. Note that UPDATEXFC should be revised accordingly.
+    '''
+
+    # Local variables
+    itol = 0.1
+
+    # Sizes
+    num_vars = np.size(sim, 0)
+
+    # Preconditions
+    if DEBUGGING:
+        assert num_vars >= 1
+        assert np.size(d) == num_vars and all(np.isfinite(d))
+        assert delta >= rho and rho > 0
+        assert np.size(sim, 0) == num_vars and np.size(sim, 1) == num_vars + 1
+        assert np.isfinite(sim).all()
+        assert all(np.max(abs(sim[:, :num_vars]), axis=0) > 0)
+        assert np.size(simi, 0) == num_vars and np.size(simi, 1) == num_vars
+        assert np.isfinite(simi).all()
+        assert isinv(sim[:, :num_vars], simi, itol)
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # -------------------------------------------------------------------------------------------------- #
+    #  The following code is Powell's scheme for defining JDROP.
+    # -------------------------------------------------------------------------------------------------- #
+    # ! JDROP = 0 by default. It cannot be removed, as JDROP may not be set below in some cases (e.g.,
+    # ! when XIMPROVED == FALSE, MAXVAL(ABS(SIMID)) <= 1, and MAXVAL(VETA) <= EDGMAX).
+    # jdrop = 0
+    #
+    # ! SIMID(J) is the value of the J-th Lagrange function at D. It is the counterpart of VLAG in UOBYQA
+    # ! and DEN in NEWUOA/BOBYQA/LINCOA, but it excludes the value of the (N+1)-th Lagrange function.
+    # simid = matprod(simi, d)
+    # if (any(abs(simid) > 1) .or. (ximproved .and. any(.not. is_nan(simid)))) then
+    #     jdrop = int(maxloc(abs(simid), mask=(.not. is_nan(simid)), dim=1), kind(jdrop))
+    #     !!MATLAB: [~, jdrop] = max(simid, [], 'omitnan');
+    # end if
+    #
+    # ! VETA(J) is the distance from the J-th vertex of the simplex to the best vertex, taking the trial
+    # ! point SIM(:, N+1) + D into account.
+    # if (ximproved) then
+    #     veta = sqrt(sum((sim(:, 1:n) - spread(d, dim=2, ncopies=n))**2, dim=1))
+    #     !!MATLAB: veta = sqrt(sum((sim(:, 1:n) - d).^2));  % d should be a column! Implicit expansion
+    # else
+    #     veta = sqrt(sum(sim(:, 1:n)**2, dim=1))
+    # end if
+    #
+    # ! VSIG(J) (J=1, .., N) is the Euclidean distance from vertex J to the opposite face of the simplex.
+    # vsig = ONE / sqrt(sum(simi**2, dim=2))
+    # sigbar = abs(simid) * vsig
+    #
+    # ! The following JDROP will overwrite the previous one if its premise holds.
+    # mask = (veta > factor_delta * delta .and. (sigbar >= factor_alpha * delta .or. sigbar >= vsig))
+    # if (any(mask)) then
+    #     jdrop = int(maxloc(veta, mask=mask, dim=1), kind(jdrop))
+    #     !!MATLAB: etamax = max(veta(mask)); jdrop = find(mask & ~(veta < etamax), 1, 'first');
+    # end if
+    #
+    # ! Powell's code does not include the following instructions. With Powell's code, if SIMID consists
+    # ! of only NaN, then JDROP can be 0 even when XIMPROVED == TRUE (i.e., D reduces the merit function).
+    # ! With the following code, JDROP cannot be 0 when XIMPROVED == TRUE, unless VETA is all NaN, which
+    # ! should not happen if X0 does not contain NaN, the trust-region/geometry steps never contain NaN,
+    # ! and we exit once encountering an iterate containing Inf (due to overflow).
+    # if (ximproved .and. jdrop <= 0) then  ! Write JDROP <= 0 instead of JDROP == 0 for robustness.
+    #     jdrop = int(maxloc(veta, mask=(.not. is_nan(veta)), dim=1), kind(jdrop))
+    #     !!MATLAB: [~, jdrop] = max(veta, [], 'omitnan');
+    # end if
+    # -------------------------------------------------------------------------------------------------- #
+    #  Powell's scheme ends here.
+    # -------------------------------------------------------------------------------------------------- #
+
+    # The following definition of JDROP is inspired by SETDROP_TR in UOBYQA/NEWUOA/BOBYQA/LINCOA.
+    # It is simpler and works better than Powell's scheme. Note that we allow JDROP to be NUM_VARS+1 if
+    # XIMPROVED is True, whereas Powell's code does not.
+    # See also (4.1) of Scheinberg-Toint-2010: Self-Correcting Geometry in Model-Based Algorithms for
+    # Derivative-Free Unconstrained Optimization, which refers to the strategy here as the "combined
+    # distance/poisedness criteria".
+
+    # DISTSQ[j] is the square of the distance from the jth vertex of the simplex to get "best" point so
+    # far, taking the trial point SIM[:, NUM_VARS] + D into account.
+    distsq = np.zeros(np.size(sim, 1))
+    if ximproved:
+        distsq[:num_vars] = primasum(primapow2(sim[:, :num_vars] - np.tile(d, (num_vars, 1)).T), axis=0)
+        distsq[num_vars] = primasum(d*d)
+    else:
+        distsq[:num_vars] = primasum(primapow2(sim[:, :num_vars]), axis=0)
+        distsq[num_vars] = 0
+
+    weight = np.maximum(1, distsq / primapow2(np.maximum(rho, delta/10)))  # Similar to Powell's NEWUOA code.
+
+    # Other possible definitions of weight. They work almost the same as the one above.
+    # weight = distsq  # Similar to Powell's LINCOA code, but WRONG. See comments in LINCOA/geometry.f90.
+    # weight = max(1, max(25 * distsq / delta**2))  # Similar to Powell's BOBYQA code, works well.
+    # weight = max(1, max(10 * distsq / delta**2))
+    # weight = max(1, max(1e2 * distsq / delta**2))
+    # weight = max(1, max(distsq / rho**2))  ! Similar to Powell's UOBYQA
+
+    # If 0 <= j < NUM_VARS, SIMID[j] is the value of the jth Lagrange function at D; the value of the
+    # (NUM_VARS+1)th Lagrange function is 1 - sum(SIMID). [SIMID, 1 - sum(SIMID)] is the counterpart of
+    # VLAG in UOBYQA and DEN in NEWUOA/BOBYQA/LINCOA.
+    simid = matprod(simi, d)
+    score = weight * abs(np.array([*simid, 1 - primasum(simid)]))
+
+    # If XIMPROVED = False (D does not render a better X), set SCORE[NUM_VARS] = -1 to avoid JDROP = NUM_VARS.
+    if not ximproved:
+        score[num_vars] = -1
+
+    # score[j] is NaN implies SIMID[j] is NaN, but we want abs(SIMID) to be big. So we
+    # exclude such j.
+    score[np.isnan(score)] = -1
+
+    jdrop = None
+    # The following if statement works a bit better than
+    # `if any(score > 1) or (any(score > 0) and ximproved)` from Powell's UOBYQA and
+    # NEWUOA code.
+    if any(score > 0):  # Powell's BOBYQA and LINCOA code.
+        jdrop = np.argmax(score)
+
+    if (ximproved and jdrop is None):
+        jdrop = np.argmax(distsq)
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert jdrop is None or (0 <= jdrop < num_vars + 1)
+        assert jdrop <= num_vars or ximproved
+        assert jdrop >= 0 or not ximproved
+        # JDROP >= 1 when XIMPROVED = TRUE unless NaN occurs in DISTSQ, which should not happen if the
+        # starting point does not contain NaN and the trust-region/geometry steps never contain NaN.
+
+    return jdrop
+
+
+
+
+def geostep(jdrop, amat, bvec, conmat, cpen, cval, delbar, fval, simi):
+    '''
+    This function calculates a geometry step so that the geometry of the interpolation set is improved
+    when SIM[: JDROP_GEO] is replaced with SIM[:, NUM_VARS] + D. See (15)--(17) of the COBYLA paper.
+    '''
+
+    # Sizes
+    m_lcon = np.size(bvec, 0) if bvec is not None else 0
+    num_constraints = np.size(conmat, 0)
+    num_vars = np.size(simi, 0)
+
+    # Preconditions
+    if DEBUGGING:
+        assert num_constraints >= m_lcon >= 0
+        assert num_vars >= 1
+        assert delbar > 0
+        assert cpen > 0
+        assert np.size(simi, 0) == num_vars and np.size(simi, 1) == num_vars
+        assert np.isfinite(simi).all()
+        assert np.size(fval) == num_vars + 1 and not any(np.isnan(fval) | np.isposinf(fval))
+        assert np.size(conmat, 0) == num_constraints and np.size(conmat, 1) == num_vars + 1
+        assert not np.any(np.isnan(conmat) | np.isposinf(conmat))
+        assert np.size(cval) == num_vars + 1 and not any(cval < 0 | np.isnan(cval) | np.isposinf(cval))
+        assert 0 <= jdrop < num_vars
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # SIMI[JDROP, :] is a vector perpendicular to the face of the simplex to the opposite of vertex
+    # JDROP. Set D to the vector in this direction and with length DELBAR.
+    d = simi[jdrop, :]
+    d = delbar * (d / norm(d))
+
+    # The code below chooses the direction of D according to an approximation of the merit function.
+    # See (17) of the COBYLA paper and  line 225 of Powell's cobylb.f.
+
+    # Calculate the coefficients of the linear approximations to the objective and constraint functions.
+    # N.B.: CONMAT and SIMI have been updated after the last trust-region step, but G and A have not.
+    # So we cannot pass G and A from outside.
+    g = matprod(fval[:num_vars] - fval[num_vars], simi)
+    A = np.zeros((num_vars, num_constraints))
+    A[:, :m_lcon] = amat.T if amat is not None else amat
+    A[:, m_lcon:] = matprod((conmat[m_lcon:, :num_vars] -
+                          np.tile(conmat[m_lcon:, num_vars], (num_vars, 1)).T), simi).T
+    # CVPD and CVND are the predicted constraint violation of D and -D by the linear models.
+    cvpd = np.max(np.append(0, conmat[:, num_vars] + matprod(d, A)))
+    cvnd = np.max(np.append(0, conmat[:, num_vars] - matprod(d, A)))
+    if -inprod(d, g) + cpen * cvnd < inprod(d, g) + cpen * cvpd:
+        d *= -1
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert np.size(d) == num_vars and all(np.isfinite(d))
+        # In theory, ||S|| == DELBAR, which may be false due to rounding, but not too far.
+        # It is crucial to ensure that the geometry step is nonzero, which holds in theory.
+        assert 0.9 * delbar < np.linalg.norm(d) <= 1.1 * delbar
+    return d
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/initialize.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/initialize.py
new file mode 100644
index 0000000000000000000000000000000000000000..c8c3da8e2c7b0ec09bb30b7bf67ec55238022a94
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/initialize.py
@@ -0,0 +1,215 @@
+'''
+This module contains subroutines for initialization.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+from ..common.checkbreak import checkbreak_con
+from ..common.consts import DEBUGGING, REALMAX
+from ..common.infos import INFO_DEFAULT
+from ..common.evaluate import evaluate
+from ..common.history import savehist
+from ..common.linalg import inv
+from ..common.message import fmsg
+from ..common.selectx import savefilt
+
+import numpy as np
+
+def initxfc(calcfc, iprint, maxfun, constr0, amat, bvec, ctol, f0, ftarget, rhobeg, x0,
+            xhist, fhist, chist, conhist, maxhist):
+    '''
+    This subroutine does the initialization concerning X, function values, and
+    constraints.
+    '''
+
+    # Local variables
+    solver = 'COBYLA'
+    srname = "INITIALIZE"
+
+    # Sizes
+    num_constraints = np.size(constr0)
+    m_lcon = np.size(bvec) if bvec is not None else 0
+    m_nlcon = num_constraints - m_lcon
+    num_vars = np.size(x0)
+
+    # Preconditions
+    if DEBUGGING:
+        assert num_constraints >= 0, f'M >= 0 {srname}'
+        assert num_vars >= 1, f'N >= 1 {srname}'
+        assert abs(iprint) <= 3, f'IPRINT is 0, 1, -1, 2, -2, 3, or -3 {srname}'
+        # assert conmat.shape == (num_constraints , num_vars + 1), f'CONMAT.shape = [M, N+1] {srname}'
+        # assert cval.size == num_vars + 1, f'CVAL.size == N+1 {srname}'
+        # assert maxchist * (maxchist - maxhist) == 0, f'CHIST.shape == 0 or MAXHIST {srname}'
+        # assert conhist.shape[0] == num_constraints and maxconhist * (maxconhist - maxhist) == 0, 'CONHIST.shape[0] == num_constraints, SIZE(CONHIST, 2) == 0 or MAXHIST {srname)}'
+        # assert maxfhist * (maxfhist - maxhist) == 0, f'FHIST.shape == 0 or MAXHIST {srname}'
+        # assert xhist.shape[0] == num_vars and maxxhist * (maxxhist - maxhist) == 0, 'XHIST.shape[0] == N, SIZE(XHIST, 2) == 0 or MAXHIST {srname)}'
+        assert all(np.isfinite(x0)), f'X0 is finite {srname}'
+        assert rhobeg > 0, f'RHOBEG > 0 {srname}'
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # Initialize info to the default value. At return, a value different from this
+    # value will indicate an abnormal return
+    info = INFO_DEFAULT
+
+    # Initialize the simplex. It will be revised during the initialization.
+    sim = np.eye(num_vars, num_vars+1) * rhobeg
+    sim[:, num_vars] = x0
+
+    # Initialize the matrix simi. In most cases simi is overwritten, but not always.
+    simi = np.eye(num_vars) / rhobeg
+
+    # evaluated[j] = True iff the function/constraint of SIM[:, j] has been evaluated.
+    evaluated = np.zeros(num_vars+1, dtype=bool)
+
+    # Initialize fval
+    fval = np.zeros(num_vars+1) + REALMAX
+    cval = np.zeros(num_vars+1) + REALMAX
+    conmat = np.zeros((num_constraints, num_vars+1)) + REALMAX
+
+
+    for k in range(num_vars + 1):
+        x = sim[:, num_vars].copy()
+        # We will evaluate F corresponding to SIM(:, J).
+        if k == 0:
+            j = num_vars
+            f = f0
+            constr = constr0
+        else:
+            j = k - 1
+            x[j] += rhobeg
+            f, constr = evaluate(calcfc, x, m_nlcon, amat, bvec)
+        cstrv = np.max(np.append(0, constr))
+
+        # Print a message about the function/constraint evaluation according to IPRINT.
+        fmsg(solver, 'Initialization', iprint, k, rhobeg, f, x, cstrv, constr)
+
+        # Save X, F, CONSTR, CSTRV into the history.
+        savehist(maxhist, x, xhist, f, fhist, cstrv, chist, constr, conhist)
+
+        # Save F, CONSTR, and CSTRV to FVAL, CONMAT, and CVAL respectively.
+        evaluated[j] = True
+        fval[j] = f
+        conmat[:, j] = constr
+        cval[j] = cstrv
+
+        # Check whether to exit.
+        subinfo = checkbreak_con(maxfun, k, cstrv, ctol, f, ftarget, x)
+        if subinfo != INFO_DEFAULT:
+            info = subinfo
+            break
+
+        # Exchange the new vertex of the initial simplex with the optimal vertex if necessary.
+        # This is the ONLY part that is essentially non-parallel.
+        if j < num_vars and fval[j] < fval[num_vars]:
+            fval[j], fval[num_vars] = fval[num_vars], fval[j]
+            cval[j], cval[num_vars] = cval[num_vars], cval[j]
+            conmat[:, [j, num_vars]] = conmat[:, [num_vars, j]]
+            sim[:, num_vars] = x
+            sim[j, :j+1] = -rhobeg  # SIM[:, :j+1] is lower triangular
+
+    nf = np.count_nonzero(evaluated)
+
+    if evaluated.all():
+        # Initialize SIMI to the inverse of SIM[:, :num_vars]
+        simi = inv(sim[:, :num_vars])
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert nf <= maxfun, f'NF <= MAXFUN {srname}'
+        assert evaluated.size == num_vars + 1, f'EVALUATED.size == Num_vars + 1 {srname}'
+        # assert chist.size == maxchist, f'CHIST.size == MAXCHIST {srname}'
+        # assert conhist.shape== (num_constraints, maxconhist), f'CONHIST.shape == [M, MAXCONHIST] {srname}'
+        assert conmat.shape == (num_constraints, num_vars + 1), f'CONMAT.shape = [M, N+1] {srname}'
+        assert not (np.isnan(conmat).any() or np.isneginf(conmat).any()), f'CONMAT does not contain NaN/-Inf {srname}'
+        assert cval.size == num_vars + 1 and not (any(cval < 0) or any(np.isnan(cval)) or any(np.isposinf(cval))), f'CVAL.shape == Num_vars+1 and CVAL does not contain negative values or NaN/+Inf {srname}'
+        # assert fhist.shape == maxfhist, f'FHIST.shape == MAXFHIST {srname}'
+        # assert maxfhist * (maxfhist - maxhist) == 0, f'FHIST.shape == 0 or MAXHIST {srname}'
+        assert fval.size == num_vars + 1 and not (any(np.isnan(fval)) or any(np.isposinf(fval))), f'FVAL.shape == Num_vars+1 and FVAL is not NaN/+Inf {srname}'
+        # assert xhist.shape == (num_vars, maxxhist), f'XHIST.shape == [N, MAXXHIST] {srname}'
+        assert sim.shape == (num_vars, num_vars + 1), f'SIM.shape == [N, N+1] {srname}'
+        assert np.isfinite(sim).all(), f'SIM is finite {srname}'
+        assert all(np.max(abs(sim[:, :num_vars]), axis=0) > 0), f'SIM(:, 1:N) has no zero column {srname}'
+        assert simi.shape == (num_vars, num_vars), f'SIMI.shape == [N, N] {srname}'
+        assert np.isfinite(simi).all(), f'SIMI is finite {srname}'
+        assert np.allclose(sim[:, :num_vars] @ simi, np.eye(num_vars), rtol=0.1, atol=0.1) or not all(evaluated), f'SIMI = SIM(:, 1:N)^{-1} {srname}'
+
+    return evaluated, conmat, cval, sim, simi, fval, nf, info
+
+
+def initfilt(conmat, ctol, cweight, cval, fval, sim, evaluated, cfilt, confilt, ffilt, xfilt):
+    '''
+    This function initializes the filter (XFILT, etc) that will be used when selecting
+    x at the end of the solver.
+    N.B.:
+    1. Why not initialize the filters using XHIST, etc? Because the history is empty if
+    the user chooses not to output it.
+    2. We decouple INITXFC and INITFILT so that it is easier to parallelize the former
+    if needed.
+    '''
+
+    # Sizes
+    num_constraints = conmat.shape[0]
+    num_vars = sim.shape[0]
+    maxfilt = len(ffilt)
+
+    # Preconditions
+    if DEBUGGING:
+        assert num_constraints >= 0
+        assert num_vars >= 1
+        assert maxfilt >= 1
+        assert np.size(confilt, 0) == num_constraints and np.size(confilt, 1) == maxfilt
+        assert np.size(cfilt) == maxfilt
+        assert np.size(xfilt, 0) == num_vars and np.size(xfilt, 1) == maxfilt
+        assert np.size(ffilt) == maxfilt
+        assert np.size(conmat, 0) == num_constraints and np.size(conmat, 1) == num_vars + 1
+        assert not (np.isnan(conmat) | np.isneginf(conmat)).any()
+        assert np.size(cval) == num_vars + 1 and not any(cval < 0 | np.isnan(cval) | np.isposinf(cval))
+        assert np.size(fval) == num_vars + 1 and not any(np.isnan(fval) | np.isposinf(fval))
+        assert np.size(sim, 0) == num_vars and np.size(sim, 1) == num_vars + 1
+        assert np.isfinite(sim).all()
+        assert all(np.max(abs(sim[:, :num_vars]), axis=0) > 0)
+        assert np.size(evaluated) == num_vars + 1
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+
+    nfilt = 0
+    for i in range(num_vars+1):
+        if evaluated[i]:
+            if i < num_vars:
+                x = sim[:, i] + sim[:, num_vars]
+            else:
+                x = sim[:, i]  # i == num_vars, i.e. the last column
+            nfilt, cfilt, ffilt, xfilt, confilt = savefilt(cval[i], ctol, cweight, fval[i], x, nfilt, cfilt, ffilt, xfilt, conmat[:, i], confilt)
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert nfilt <= maxfilt
+        assert np.size(confilt, 0) == num_constraints and np.size(confilt, 1) == maxfilt
+        assert not (np.isnan(confilt[:, :nfilt]) | np.isneginf(confilt[:, :nfilt])).any()
+        assert np.size(cfilt) == maxfilt
+        assert not any(cfilt[:nfilt] < 0 | np.isnan(cfilt[:nfilt]) | np.isposinf(cfilt[:nfilt]))
+        assert np.size(xfilt, 0) == num_vars and np.size(xfilt, 1) == maxfilt
+        assert not (np.isnan(xfilt[:, :nfilt])).any()
+        # The last calculated X can be Inf (finite + finite can be Inf numerically).
+        assert np.size(ffilt) == maxfilt
+        assert not any(np.isnan(ffilt[:nfilt]) | np.isposinf(ffilt[:nfilt]))
+
+    return nfilt
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/trustregion.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/trustregion.py
new file mode 100644
index 0000000000000000000000000000000000000000..3e97d7c0b5066a94e96168bd2f42e72197f4b632
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/trustregion.py
@@ -0,0 +1,492 @@
+'''
+This module provides subroutines concerning the trust-region calculations of COBYLA.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+import numpy as np
+import numpy.typing as npt
+from ..common.consts import DEBUGGING, REALMIN, REALMAX, EPS
+from ..common.powalg import qradd_Rdiag, qrexc_Rdiag
+from ..common.linalg import isminor, matprod, inprod, lsqr, primasum
+
+
+def trstlp(A, b, delta, g):
+    '''
+    This function calculated an n-component vector d by the following two stages. In the first
+    stage, d is set to the shortest vector that minimizes the greatest violation of the constraints
+        A.T @ D <= B,  K = 1, 2, 3, ..., M,
+    subject to the Euclidean length of d being at most delta. If its length is strictly less than
+    delta, then the second stage uses the resultant freedom in d to minimize the objective function
+        G.T @ D
+    subject to no increase in any greatest constraint violation.
+
+    It is possible but rare that a degeneracy may prevent d from attaining the target length delta.
+
+    cviol is the largest constraint violation of the current d: max(max(A.T@D - b), 0)
+    icon is the index of a most violated constraint if cviol is positive.
+
+    nact is the number of constraints in the active set and iact[0], ..., iact[nact-1] are their indices,
+    while the remainder of the iact contains a permutation of the remaining constraint indicies.
+    N.B.: nact <= min(num_constraints, num_vars). Obviously nact <= num_constraints. In addition, the constraints
+    in iact[0, ..., nact-1] have linearly independent gradients (see the comments above the instruction
+    that delete a constraint from the active set to make room for the new active constraint with index iact[icon]);
+    it can also be seen from the update of nact: starting from 0, nact is incremented only if nact < n.
+
+    Further, Z is an orthogonal matrix whose first nact columns can be regarded as the result of
+    Gram-Schmidt applied to the active constraint gradients. For j = 0, 1, ..., nact-1, the number
+    zdota[j] is the scalar product of the jth column of Z with the gradient of the jth active
+    constraint. d is the current vector of variables and here the residuals of the active constraints
+    should be zero. Further, the active constraints have nonnegative Lagrange multipliers that are
+    held at the beginning of vmultc. The remainder of this vector holds the residuals of the inactive
+    constraints at d, the ordering of the components of vmultc being in agreement with the permutation
+    of the indices of the constraints that is in iact. All these residuals are nonnegative, which is
+    achieved by the shift cviol that makes the least residual zero.
+
+    N.B.:
+    0. In Powell's implementation, the constraints are A.T @ D >= B. In other words, the A and B in
+    our implementation are the negative of those in Powell's implementation.
+    1. The algorithm was NOT documented in the COBYLA paper. A note should be written to introduce it!
+    2. As a major part of the algorithm (see trstlp_sub), the code maintains and updates the QR
+    factorization of A[iact[:nact]], i.e. the gradients of all the active (linear) constraints. The
+    matrix Z is indeed Q, and the vector zdota is the diagonal of R. The factorization is updated by
+    Givens rotations when an index is added in or removed from iact.
+    3. There are probably better algorithms available for the trust-region linear programming problem.
+    '''
+
+    # Sizes
+    num_constraints = A.shape[1]
+    num_vars = A.shape[0]
+
+    # Preconditions
+    if DEBUGGING:
+        assert num_vars >= 1
+        assert num_constraints >= 0
+        assert np.size(g) == num_vars
+        assert np.size(b) == num_constraints
+        assert delta > 0
+
+
+    vmultc = np.zeros(num_constraints + 1)
+    iact = np.zeros(num_constraints + 1, dtype=int)
+    nact = 0
+    d = np.zeros(num_vars)
+    z = np.zeros((num_vars, num_vars))
+
+    # ==================
+    # Calculation starts
+    # ==================
+
+    # Form A_aug and B_aug. This allows the gradient of the objective function to be regarded as the
+    # gradient of a constraint in the second stage.
+    A_aug = np.hstack([A, g.reshape((num_vars, 1))])
+    b_aug = np.hstack([b, 0])
+
+
+    # Scale the problem if A contains large values. Otherwise floating point exceptions may occur.
+    # Note that the trust-region step is scale invariant.
+    for i in range(num_constraints+1):  # Note that A_aug.shape[1] == num_constraints+1
+        if (maxval:=max(abs(A_aug[:, i]))) > 1e12:
+            modscal = max(2*REALMIN, 1/maxval)
+            A_aug[:, i] *= modscal
+            b_aug[i] *= modscal
+
+    # Stage 1: minimize the 1+infinity constraint violation of the linearized constraints.
+    iact[:num_constraints], nact, d, vmultc[:num_constraints], z = trstlp_sub(iact[:num_constraints], nact, 1, A_aug[:, :num_constraints], b_aug[:num_constraints], delta, d, vmultc[:num_constraints], z)
+
+    # Stage 2: minimize the linearized objective without increasing the 1_infinity constraint violation.
+    iact, nact, d, vmultc, z = trstlp_sub(iact, nact, 2, A_aug, b_aug, delta, d, vmultc, z)
+
+    # ================
+    # Calculation ends
+    # ================
+
+    # Postconditions
+    if DEBUGGING:
+        assert all(np.isfinite(d))
+        # Due to rounding, it may happen that ||D|| > DELTA, but ||D|| > 2*DELTA is highly improbable.
+        assert np.linalg.norm(d) <= 2 * delta
+
+    return d
+
+def trstlp_sub(iact: npt.NDArray, nact: int, stage, A, b, delta, d, vmultc, z):
+    '''
+    This subroutine does the real calculations for trstlp, both stage 1 and stage 2.
+    Major differences between stage 1 and stage 2:
+    1. Initialization. Stage 2 inherits the values of some variables from stage 1, so they are
+    initialized in stage 1 but not in stage 2.
+    2. cviol. cviol is updated after at iteration in stage 1, while it remains a constant in stage2.
+    3. sdirn. See the definition of sdirn in the code for details.
+    4. optnew. The two stages have different objectives, so optnew is updated differently.
+    5. step. step <= cviol in stage 1.
+    '''
+    zdasav = np.zeros(z.shape[1])
+    vmultd = np.zeros(np.size(vmultc))
+    zdota = np.zeros(np.size(z, 1))
+
+    # Sizes
+    mcon = np.size(A, 1)
+    num_vars = np.size(A, 0)
+
+    # Preconditions
+    if DEBUGGING:
+        assert num_vars >= 1
+        assert stage == 1 or stage == 2
+        assert (mcon >= 0 and stage == 1) or (mcon >= 1 and stage == 2)
+        assert np.size(b) == mcon
+        assert np.size(iact) == mcon
+        assert np.size(vmultc) == mcon
+        assert np.size(d) == num_vars
+        assert np.size(z, 0) == num_vars and np.size(z, 1) == num_vars
+        assert delta > 0
+        if stage == 2:
+            assert all(np.isfinite(d)) and np.linalg.norm(d) <= 2 * delta
+            assert nact >= 0 and nact <= np.minimum(mcon, num_vars)
+            assert all(vmultc[:mcon]) >= 0
+            # N.B.: Stage 1 defines only VMULTC(1:M); VMULTC(M+1) is undefined!
+
+
+    # Initialize according to stage
+    if stage == 1:
+        iact = np.linspace(0, mcon-1, mcon, dtype=int)
+        nact = 0
+        d = np.zeros(num_vars)
+        cviol = np.max(np.append(0, -b))
+        vmultc = cviol + b
+        z = np.eye(num_vars)
+        if mcon == 0 or cviol <= 0:
+            # Check whether a quick return is possible. Make sure the in-outputs have been initialized.
+            return iact, nact, d, vmultc, z
+
+        if all(np.isnan(b)):
+            return iact, nact, d, vmultc, z
+        else:
+            icon = np.nanargmax(-b)
+        num_constraints = mcon
+        sdirn = np.zeros(len(d))
+    else:
+        if inprod(d, d) >= delta*delta:
+            # Check whether a quick return is possible.
+            return iact, nact, d, vmultc, z
+
+        iact[mcon-1] = mcon-1
+        vmultc[mcon-1] = 0
+        num_constraints = mcon - 1
+        icon = mcon - 1
+
+        # In Powell's code, stage 2 uses the zdota and cviol calculated by stage1. Here we recalculate
+        # them so that they need not be passed from stage 1 to 2, and hence the coupling is reduced.
+        cviol = np.max(np.append(0, matprod(d, A[:, :num_constraints]) - b[:num_constraints]))
+    zdota[:nact] = [inprod(z[:, k], A[:, iact[k]]) for k in range(nact)]
+
+    # More initialization
+    optold = REALMAX
+    nactold = nact
+    nfail = 0
+
+    # Zaikun 20211011: vmultd is computed from scratch at each iteration, but vmultc is inherited
+
+    # Powell's code can encounter infinite cycling, which did happen when testing the following CUTEst
+    # problems: DANWOODLS, GAUSS1LS, GAUSS2LS, GAUSS3LS, KOEBHELB, TAX13322, TAXR13322. Indeed, in all
+    # these cases, Inf/NaN appear in d due to extremely large values in A (up to 10^219). To resolve
+    # this, we set the maximal number of iterations to maxiter, and terminate if Inf/NaN occurs in d.
+    maxiter = np.minimum(10000, 100*max(num_constraints, num_vars))
+    for iter in range(maxiter):
+        if DEBUGGING:
+            assert all(vmultc >= 0)
+        if stage == 1:
+            optnew = cviol
+        else:
+            optnew = inprod(d, A[:, mcon-1])
+
+        # End the current stage of the calculation if 3 consecutive iterations have either failed to
+        # reduce the best calculated value of the objective function or to increase the number of active
+        # constraints since the best value was calculated. This strategy prevents cycling, but there is
+        # a remote possibility that it will cause premature termination.
+        if optnew < optold or nact > nactold:
+            nactold = nact
+            nfail = 0
+        else:
+            nfail += 1
+        optold = np.minimum(optold, optnew)
+        if nfail == 3:
+            break
+
+        # If icon exceeds nact, then we add the constraint with index iact[icon] to the active set.
+        if icon >= nact:  # In Python this needs to be >= since Python is 0-indexed (in Fortran we have 1 > 0, in Python we need 0 >= 0)
+            zdasav[:nact] = zdota[:nact]
+            nactsav = nact
+            z, zdota, nact = qradd_Rdiag(A[:, iact[icon]], z, zdota, nact)  # May update nact to nact+1
+            # Indeed it suffices to pass zdota[:min(num_vars, nact+1)] to qradd as follows:
+            # qradd(A[:, iact[icon]], z, zdota[:min(num_vars, nact+1)], nact)
+
+            if nact == nactsav + 1:
+                # N.B.: It is possible to index arrays using [nact, icon] when nact == icon.
+                # Zaikun 20211012: Why should vmultc[nact] = 0?
+                if nact != (icon + 1):  # Need to add 1 to Python for 0 indexing
+                    vmultc[[icon, nact-1]] = vmultc[nact-1], 0
+                    iact[[icon, nact-1]] = iact[[nact-1, icon]]
+                else:
+                    vmultc[nact-1] = 0
+            else:
+                # Zaikun 20211011:
+                # 1. VMULTD is calculated from scratch for the first time (out of 2) in one iteration.
+                # 2. Note that IACT has not been updated to replace IACT[NACT] with IACT[ICON]. Thus
+                # A[:, IACT[:NACT]] is the UNUPDATED version before QRADD (note Z[:, :NACT] remains the
+                # same before and after QRADD). Therefore if we supply ZDOTA to LSQR (as Rdiag) as
+                # Powell did, we should use the UNUPDATED version, namely ZDASAV.
+                # vmultd[:nact] = lsqr(A[:, iact[:nact]], A[:, iact[icon]], z[:, :nact], zdasav[:nact])
+                vmultd[:nact] = lsqr(A[:, iact[:nact]], A[:, iact[icon]], z[:, :nact], zdasav[:nact])
+                if not any(np.logical_and(vmultd[:nact] > 0, iact[:nact] <= num_constraints)):
+                    # N.B.: This can be triggered by NACT == 0 (among other possibilities)! This is
+                    # important, because NACT will be used as an index in the sequel.
+                    break
+                # vmultd[NACT+1:mcon] is not used, but we have to initialize it in Fortran, or compilers
+                # complain about the where construct below (another solution: restrict where to 1:NACT).
+                vmultd[nact:mcon] = -1  # len(vmultd) == mcon
+
+                # Revise the Lagrange multipliers. The revision is not applicable to vmultc[nact:num_constraints].
+                fracmult = [vmultc[i]/vmultd[i] if vmultd[i] > 0 and iact[i] <= num_constraints else REALMAX for i in range(nact)]
+                # Only the places with vmultd > 0 and iact <= m is relevant below, if any.
+                frac = min(fracmult[:nact])  # fracmult[nact:mcon] may contain garbage
+                vmultc[:nact] = np.maximum(np.zeros(len(vmultc[:nact])), vmultc[:nact] - frac*vmultd[:nact])
+
+                # Reorder the active constraints so that the one to be replaced is at the end of the list.
+                # Exit if the new value of zdota[nact] is not acceptable. Powell's condition for the
+                # following If: not abs(zdota[nact]) > 0. Note that it is different from
+                # 'abs(zdota[nact]) <=0)' as zdota[nact] can be NaN.
+                # N.B.: We cannot arrive here with nact == 0, which should have triggered a break above
+                if np.isnan(zdota[nact - 1]) or abs(zdota[nact - 1]) <= EPS**2:
+                    break
+                vmultc[[icon, nact - 1]] = 0, frac  # vmultc[[icon, nact]] is valid as icon > nact
+                iact[[icon, nact - 1]] = iact[[nact - 1, icon]]
+            # end if nact == nactsav + 1
+
+            # In stage 2, ensure that the objective continues to be treated as the last active constraint.
+            # Zaikun 20211011, 20211111: Is it guaranteed for stage 2 that iact[nact-1] = mcon when
+            # iact[nact] != mcon??? If not, then how does the following procedure ensure that mcon is
+            # the last of iact[:nact]?
+            if stage == 2 and iact[nact - 1] != (mcon - 1):
+                if nact <= 1:
+                    # We must exit, as nact-2 is used as an index below. Powell's code does not have this.
+                    break
+                z, zdota[:nact] = qrexc_Rdiag(A[:, iact[:nact]], z, zdota[:nact], nact - 2)  # We pass nact-2 in Python instead of nact-1
+                # Indeed, it suffices to pass Z[:, :nact] to qrexc as follows:
+                # z[:, :nact], zdota[:nact] = qrexc(A[:, iact[:nact]], z[:, :nact], zdota[:nact], nact - 1)
+                iact[[nact-2, nact-1]] = iact[[nact-1, nact-2]]
+                vmultc[[nact-2, nact-1]] = vmultc[[nact-1, nact-2]]
+            # Zaikun 20211117: It turns out that the last few lines do not guarantee iact[nact] == num_vars in
+            # stage 2; the following test cannot be passed. IS THIS A BUG?!
+            # assert iact[nact] == mcon or stage == 1, 'iact[nact] must == mcon in stage 2'
+
+            # Powell's code does not have the following. It avoids subsequent floating points exceptions.
+            if np.isnan(zdota[nact-1]) or abs(zdota[nact-1]) <= EPS**2:
+                break
+
+            # Set sdirn to the direction of the next change to the current vector of variables
+            # Usually during stage 1 the vector sdirn gives a search direction that reduces all the
+            # active constraint violations by one simultaneously.
+            if stage == 1:
+                sdirn -= ((inprod(sdirn, A[:, iact[nact-1]]) + 1)/zdota[nact-1])*z[:, nact-1]
+            else:
+                sdirn = -1/zdota[nact-1]*z[:, nact-1]
+        else:  # icon < nact
+            # Delete the constraint with the index iact[icon] from the active set, which is done by
+            # reordering iact[icon:nact] into [iact[icon+1:nact], iact[icon]] and then reduce nact to
+            # nact - 1. In theory, icon > 0.
+            # assert icon > 0, "icon > 0 is required"  #  For Python I think this is irrelevant
+            z, zdota[:nact] = qrexc_Rdiag(A[:, iact[:nact]], z, zdota[:nact], icon)  # qrexc does nothing if icon == nact
+            # Indeed, it suffices to pass Z[:, :nact] to qrexc as follows:
+            # z[:, :nact], zdota[:nact] = qrexc(A[:, iact[:nact]], z[:, :nact], zdota[:nact], icon)
+            iact[icon:nact] = [*iact[icon+1:nact], iact[icon]]
+            vmultc[icon:nact] = [*vmultc[icon+1:nact], vmultc[icon]]
+            nact -= 1
+
+            # Powell's code does not have the following. It avoids subsequent exceptions.
+            # Zaikun 20221212: In theory, nact > 0 in stage 2, as the objective function should always
+            # be considered as an "active constraint" --- more precisely, iact[nact] = mcon. However,
+            # looking at the code, I cannot see why in stage 2 nact must be positive after the reduction
+            # above. It did happen in stage 1 that nact became 0 after the reduction --- this is
+            # extremely rare, and it was never observed until 20221212, after almost one year of
+            # random tests. Maybe nact is theoretically positive even in stage 1?
+            if stage == 2 and nact < 0:
+                break  # If this case ever occurs, we have to break, as nact is used as an index below.
+            if nact > 0:
+                if np.isnan(zdota[nact-1]) or abs(zdota[nact-1]) <= EPS**2:
+                    break
+
+            # Set sdirn to the direction of the next change to the current vector of variables.
+            if stage == 1:
+                sdirn -= inprod(sdirn, z[:, nact]) * z[:, nact]
+                # sdirn is orthogonal to z[:, nact+1]
+            else:
+                sdirn = -1/zdota[nact-1] * z[:, nact-1]
+        # end if icon > nact
+
+        # Calculate the step to the trust region boundary or take the step that reduces cviol to 0.
+        # ----------------------------------------------------------------------------------------- #
+        # The following calculation of step is adopted from NEWUOA/BOBYQA/LINCOA. It seems to improve
+        # the performance of COBYLA. We also found that removing the precaution about underflows is
+        # beneficial to the overall performance of COBYLA --- the underflows are harmless anyway.
+        dd = delta*delta - inprod(d, d)
+        ss = inprod(sdirn, sdirn)
+        sd = inprod(sdirn, d)
+        if dd <= 0 or ss <= EPS * delta*delta or np.isnan(sd):
+            break
+        # sqrtd: square root of a discriminant. The max avoids sqrtd < abs(sd) due to underflow
+        sqrtd = max(np.sqrt(ss*dd + sd*sd), abs(sd), np.sqrt(ss * dd))
+        if sd > 0:
+            step = dd / (sqrtd + sd)
+        else:
+            step = (sqrtd - sd) / ss
+        # step < 0 should not happen. Step can be 0 or NaN when, e.g., sd or ss becomes inf
+        if step <= 0 or not np.isfinite(step):
+            break
+
+        # Powell's approach and comments are as follows.
+        # -------------------------------------------------- #
+        # The two statements below that include the factor eps prevent
+        # some harmless underflows that occurred in a test calculation
+        # (Zaikun: here, eps is the machine epsilon; Powell's original
+        # code used 1.0e-6, and Powell's code was written in single
+        # precision). Further, we skip the step if it could be 0 within
+        # a reasonable tolerance for computer rounding errors.
+
+        #  !dd = delta*delta - sum(d**2, mask=(abs(d) >= EPS * delta))
+        #  !ss = inprod(sdirn, sdirn)
+        #  !if (dd  <= 0) then
+        #  !    exit
+        #  !end if
+        #  !sd = inprod(sdirn, d)
+        #  !if (abs(sd) >= EPS * sqrt(ss * dd)) then
+        #  !    step = dd / (sqrt(ss * dd + sd*sd) + sd)
+        #  !else
+        #  !    step = dd / (sqrt(ss * dd) + sd)
+        #  !end if
+        # -------------------------------------------------- #
+
+        if stage == 1:
+            if isminor(cviol, step):
+                break
+            step = min(step, cviol)
+
+        # Set dnew to the new variables if step is the steplength, and reduce cviol to the corresponding
+        # maximum residual if stage 1 is being done
+        dnew = d + step * sdirn
+        if stage == 1:
+            cviol = np.max(np.append(0, matprod(dnew, A[:, iact[:nact]]) - b[iact[:nact]]))
+            # N.B.: cviol will be used when calculating vmultd[nact+1:mcon].
+
+        # Zaikun 20211011:
+        # 1. vmultd is computed from scratch for the second (out of 2) time in one iteration.
+        # 2. vmultd[:nact] and vmultd[nact:mcon] are calculated separately with no coupling.
+        # 3. vmultd will be calculated from scratch again in the next iteration.
+        # Set vmultd to the vmultc vector that would occur if d became dnew. A device is included to
+        # force vmultd[k] = 0 if deviations from this value can be attributed to computer rounding
+        # errors. First calculate the new Lagrange multipliers.
+        vmultd[:nact] = -lsqr(A[:, iact[:nact]], dnew, z[:, :nact], zdota[:nact])
+        if stage == 2:
+            vmultd[nact-1] = max(0, vmultd[nact-1])  # This seems never activated.
+        # Complete vmultd by finding the new constraint residuals. (Powell wrote "Complete vmultc ...")
+        cvshift = cviol - (matprod(dnew, A[:, iact]) - b[iact])  # Only cvshift[nact+1:mcon] is needed
+        cvsabs = matprod(abs(dnew), abs(A[:, iact])) + abs(b[iact]) + cviol
+        cvshift[isminor(cvshift, cvsabs)] = 0
+        vmultd[nact:mcon] = cvshift[nact:mcon]
+
+        # Calculate the fraction of the step from d to dnew that will be taken
+        fracmult = [vmultc[i]/(vmultc[i] - vmultd[i]) if vmultd[i] < 0 else REALMAX for i in range(len(vmultd))]
+        # Only the places with vmultd < 0 are relevant below, if any.
+        icon = np.argmin(np.append(1, fracmult)) - 1
+        frac = min(np.append(1, fracmult))
+
+        # Update d, vmultc, and cviol
+        dold = d
+        d = (1 - frac)*d + frac * dnew
+        vmultc = np.maximum(0, (1 - frac)*vmultc + frac*vmultd)
+        # Break in the case of inf/nan in d or vmultc.
+        if not (np.isfinite(primasum(abs(d))) and np.isfinite(primasum(abs(vmultc)))):
+            d = dold  # Should we restore also iact, nact, vmultc, and z?
+            break
+
+        if stage == 1:
+            # cviol = (1 - frac) * cvold + frac * cviol  # Powell's version
+            # In theory, cviol = np.max(np.append(d@A - b, 0)), yet the
+            # cviol updated as above can be quite different from this value if A has huge entries (e.g., > 1e20)
+            cviol = np.max(np.append(0, matprod(d, A) - b))
+
+        if icon < 0 or icon >= mcon:
+            # In Powell's code, the condition is icon == 0. Indeed, icon < 0 cannot hold unless
+            # fracmult contains only nan, which should not happen; icon >= mcon should never occur.
+            break
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert np.size(iact) == mcon
+        assert np.size(vmultc) == mcon
+        assert all(vmultc >= 0)
+        assert np.size(d) == num_vars
+        assert all(np.isfinite(d))
+        assert np.linalg.norm(d) <= 2 * delta
+        assert np.size(z, 0) == num_vars and np.size(z, 1) == num_vars
+        assert nact >= 0 and nact <= np.minimum(mcon, num_vars)
+
+    return iact, nact, d, vmultc, z
+
+
+def trrad(delta_in, dnorm, eta1, eta2, gamma1, gamma2, ratio):
+    '''
+    This function updates the trust region radius according to RATIO and DNORM.
+    '''
+
+    # Preconditions
+    if DEBUGGING:
+        assert delta_in >= dnorm > 0
+        assert 0 <= eta1 <= eta2 < 1
+        assert 0 < gamma1 < 1 < gamma2
+        # By the definition of RATIO in ratio.f90, RATIO cannot be NaN unless the
+        # actual reduction is NaN, which should NOT happen due to the moderated extreme
+        # barrier.
+        assert not np.isnan(ratio)
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    if ratio <= eta1:
+        delta = gamma1 * dnorm  # Powell's UOBYQA/NEWUOA
+        # delta = gamma1 * delta_in  # Powell's COBYLA/LINCOA
+        # delta = min(gamma1 * delta_in, dnorm)  # Powell's BOBYQA
+    elif ratio <= eta2:
+        delta = max(gamma1 * delta_in, dnorm)  # Powell's UOBYQA/NEWUOA/BOBYQA/LINCOA
+    else:
+        delta = max(gamma1 * delta_in, gamma2 * dnorm)  # Powell's NEWUOA/BOBYQA
+        # delta = max(delta_in, gamma2 * dnorm)  # Modified version. Works well for UOBYQA
+        # For noise-free CUTEst problems of <= 100 variables, Powell's version works slightly better
+        # than the modified one.
+        # delta = max(delta_in, 1.25*dnorm, dnorm + rho)  # Powell's UOBYQA
+        # delta = min(max(gamma1 * delta_in, gamma2 * dnorm), gamma3 * delta_in)  # Powell's LINCOA, gamma3 = np.sqrt(2)
+
+    # For noisy problems, the following may work better.
+    # if ratio <= eta1:
+    #     delta = gamma1 * dnorm
+    # elseif ratio <= eta2:  # Ensure DELTA >= DELTA_IN
+    #     delta = delta_in
+    # else:  # Ensure DELTA > DELTA_IN with a constant factor
+    #     delta = max(delta_in * (1 + gamma2) / 2, gamma2 * dnorm)
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert delta > 0
+    return delta
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/update.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/update.py
new file mode 100644
index 0000000000000000000000000000000000000000..66a3fa3623f9373b27346ebe052ddbf6f3ba68a4
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/cobyla/update.py
@@ -0,0 +1,289 @@
+'''
+This module contains subroutines concerning the update of the interpolation set.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+from ..common.consts import DEBUGGING
+from ..common.infos import DAMAGING_ROUNDING, INFO_DEFAULT
+from ..common.linalg import isinv, matprod, outprod, inprod, inv, primasum
+import numpy as np
+
+
+def updatexfc(jdrop, constr, cpen, cstrv, d, f, conmat, cval, fval, sim, simi):
+    '''
+    This function revises the simplex by updating the elements of SIM, SIMI, FVAL, CONMAT, and CVAL
+    '''
+
+    # Local variables
+    itol = 1
+
+    # Sizes
+    num_constraints = np.size(constr)
+    num_vars = np.size(sim, 0)
+
+    # Preconditions
+    if DEBUGGING:
+        assert num_constraints >= 0
+        assert num_vars >= 1
+        assert jdrop >= 0 and jdrop <= num_vars + 1
+        assert not any(np.isnan(constr) | np.isneginf(constr))
+        assert not (np.isnan(cstrv) | np.isposinf(cstrv))
+        assert np.size(d) == num_vars and all(np.isfinite(d))
+        assert not (np.isnan(f) | np.isposinf(f))
+        assert np.size(conmat, 0) == num_constraints and np.size(conmat, 1) == num_vars + 1
+        assert not (np.isnan(conmat) | np.isneginf(conmat)).any()
+        assert np.size(cval) == num_vars + 1 and not any(cval < 0 | np.isnan(cval) | np.isposinf(cval))
+        assert np.size(fval) == num_vars + 1 and not any(np.isnan(fval) | np.isposinf(fval))
+        assert np.size(sim, 0) == num_vars and np.size(sim, 1) == num_vars + 1
+        assert np.isfinite(sim).all()
+        assert all(primasum(abs(sim[:, :num_vars]), axis=0) > 0)
+        assert np.size(simi, 0) == num_vars and np.size(simi, 1) == num_vars
+        assert np.isfinite(simi).all()
+        assert isinv(sim[:, :num_vars], simi, itol)
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+
+    # Do nothing when JDROP is None. This can only happen after a trust-region step.
+    if jdrop is None:  # JDROP is None is impossible if the input is correct.
+        return conmat, cval, fval, sim, simi, INFO_DEFAULT
+
+    sim_old = sim
+    simi_old = simi
+    if jdrop < num_vars:
+        sim[:, jdrop] = d
+        simi_jdrop = simi[jdrop, :] / inprod(simi[jdrop, :], d)
+        simi -= outprod(matprod(simi, d), simi_jdrop)
+        simi[jdrop, :] = simi_jdrop
+    else:  # jdrop == num_vars
+        sim[:, num_vars] += d
+        sim[:, :num_vars] -= np.tile(d, (num_vars, 1)).T
+        simid = matprod(simi, d)
+        sum_simi = primasum(simi, axis=0)
+        simi += outprod(simid, sum_simi / (1 - sum(simid)))
+
+    # Check whether SIMI is a poor approximation to the inverse of SIM[:, :NUM_VARS]
+    # Calculate SIMI from scratch if the current one is damaged by rounding errors.
+    itol = 1
+    erri = np.max(abs(matprod(simi, sim[:, :num_vars]) - np.eye(num_vars)))  # np.max returns NaN if any input is NaN
+    if erri > 0.1 * itol or np.isnan(erri):
+        simi_test = inv(sim[:, :num_vars])
+        erri_test = np.max(abs(matprod(simi_test, sim[:, :num_vars]) - np.eye(num_vars)))
+        if erri_test < erri or (np.isnan(erri) and not np.isnan(erri_test)):
+            simi = simi_test
+            erri = erri_test
+
+    # If SIMI is satisfactory, then update FVAL, CONMAT, CVAL, and the pole position. Otherwise restore
+    # SIM and SIMI, and return with INFO = DAMAGING_ROUNDING.
+    if erri <= itol:
+        fval[jdrop] = f
+        conmat[:, jdrop] = constr
+        cval[jdrop] = cstrv
+        # Switch the best vertex to the pole position SIM[:, NUM_VARS] if it is not there already
+        conmat, cval, fval, sim, simi, info = updatepole(cpen, conmat, cval, fval, sim, simi)
+    else:
+        info = DAMAGING_ROUNDING
+        sim = sim_old
+        simi = simi_old
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert np.size(conmat, 0) == num_constraints and np.size(conmat, 1) == num_vars + 1
+        assert not (np.isnan(conmat) | np.isneginf(conmat)).any()
+        assert np.size(cval) == num_vars + 1 and not any(cval < 0 | np.isnan(cval) | np.isposinf(cval))
+        assert np.size(fval) == num_vars + 1 and not any(np.isnan(fval) | np.isposinf(fval))
+        assert np.size(sim, 0) == num_vars and np.size(sim, 1) == num_vars + 1
+        assert np.isfinite(sim).all()
+        assert all(primasum(abs(sim[:, :num_vars]), axis=0) > 0)
+        assert np.size(simi, 0) == num_vars and np.size(simi, 1) == num_vars
+        assert np.isfinite(simi).all()
+        assert isinv(sim[:, :num_vars], simi, itol) or info == DAMAGING_ROUNDING
+
+    return sim, simi, fval, conmat, cval, info
+
+def findpole(cpen, cval, fval):
+    '''
+    This subroutine identifies the best vertex of the current simplex with respect to the merit
+    function PHI = F + CPEN * CSTRV.
+    '''
+
+    # Size
+    num_vars = np.size(fval) - 1
+
+    # Preconditions
+    if DEBUGGING:
+        assert cpen > 0
+        assert np.size(cval) == num_vars + 1 and not any(cval < 0 | np.isnan(cval) | np.isposinf(cval))
+        assert np.size(fval) == num_vars + 1 and not any(np.isnan(fval) | np.isposinf(fval))
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # Identify the optimal vertex of the current simplex
+    jopt = np.size(fval) - 1
+    phi = fval + cpen * cval
+    phimin = min(phi)
+    # Essentially jopt = np.argmin(phi). However, we keep jopt = num_vars unless there
+    # is a strictly better choice. When there are multiple choices, we choose the jopt
+    # with the smallest value of cval.
+    if phimin < phi[jopt] or any((cval < cval[jopt]) & (phi <= phi[jopt])):
+        # While we could use argmin(phi), there may be two places where phi achieves
+        # phimin, and in that case we should choose the one with the smallest cval.
+        jopt = np.ma.array(cval, mask=(phi > phimin)).argmin()
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert jopt >= 0 and jopt < num_vars + 1
+        assert jopt == num_vars or phi[jopt] < phi[num_vars] or (phi[jopt] <= phi[num_vars] and cval[jopt] < cval[num_vars])
+    return jopt
+
+
+def updatepole(cpen, conmat, cval, fval, sim, simi):
+    #--------------------------------------------------------------------------------------------------!
+    # This subroutine identifies the best vertex of the current simplex with respect to the merit
+    # function PHI = F + CPEN * CSTRV, and then switch this vertex to SIM[:, NUM_VARS], which Powell called
+    # the "pole position" in his comments. CONMAT, CVAL, FVAL, and SIMI are updated accordingly.
+    #
+    # N.B. 1: In precise arithmetic, the following two procedures produce the same results:
+    # 1) apply UPDATEPOLE to SIM twice, first with CPEN = CPEN1 and then with CPEN = CPEN2;
+    # 2) apply UPDATEPOLE to SIM with CPEN = CPEN2.
+    # In finite-precision arithmetic, however, they may produce different results unless CPEN1 = CPEN2.
+    #
+    # N.B. 2: When JOPT == N+1, the best vertex is already at the pole position, so there is nothing to
+    # switch. However, as in Powell's code, the code below will check whether SIMI is good enough to
+    # work as the inverse of SIM(:, 1:N) or not. If not, Powell's code would invoke an error return of
+    # COBYLB; our implementation, however, will try calculating SIMI from scratch; if the recalculated
+    # SIMI is still of poor quality, then UPDATEPOLE will return with INFO = DAMAGING_ROUNDING,
+    # informing COBYLB that SIMI is poor due to damaging rounding errors.
+    #
+    # N.B. 3: UPDATEPOLE should be called when and only when FINDPOLE can potentially returns a value
+    # other than N+1. The value of FINDPOLE is determined by CPEN, CVAL, and FVAL, the latter two being
+    # decided by SIM. Thus UPDATEPOLE should be called after CPEN or SIM changes. COBYLA updates CPEN at
+    # only two places: the beginning of each trust-region iteration, and when REDRHO is called;
+    # SIM is updated only by UPDATEXFC, which itself calls UPDATEPOLE internally. Therefore, we only
+    # need to call UPDATEPOLE after updating CPEN at the beginning of each trust-region iteration and
+    # after each invocation of REDRHO.
+
+    # Local variables
+    itol = 1
+
+    # Sizes
+    num_constraints = conmat.shape[0]
+    num_vars = sim.shape[0]
+
+    # Preconditions
+    if DEBUGGING:
+        assert num_constraints >= 0
+        assert num_vars >= 1
+        assert cpen > 0
+        assert np.size(conmat, 0) == num_constraints and np.size(conmat, 1) == num_vars + 1
+        assert not (np.isnan(conmat) | np.isneginf(conmat)).any()
+        assert np.size(cval) == num_vars + 1 and not any(cval < 0 | np.isnan(cval) | np.isposinf(cval))
+        assert np.size(fval) == num_vars + 1 and not any(np.isnan(fval) | np.isposinf(fval))
+        assert np.size(sim, 0) == num_vars and np.size(sim, 1) == num_vars + 1
+        assert np.isfinite(sim).all()
+        assert all(primasum(abs(sim[:, :num_vars]), axis=0) > 0)
+        assert np.size(simi, 0) == num_vars and np.size(simi, 1) == num_vars
+        assert np.isfinite(simi).all()
+        assert isinv(sim[:, :num_vars], simi, itol)
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # INFO must be set, as it is an output.
+    info = INFO_DEFAULT
+
+    # Identify the optimal vertex of the current simplex.
+    jopt = findpole(cpen, cval, fval)
+
+    # Switch the best vertex to the pole position SIM[:, NUM_VARS] if it is not there already and update
+    # SIMI. Before the update, save a copy of SIM and SIMI. If the update is unsuccessful due to
+    # damaging rounding errors, we restore them and return with INFO = DAMAGING_ROUNDING.
+    sim_old = sim.copy()
+    simi_old = simi.copy()
+    if 0 <= jopt < num_vars:
+        # Unless there is a bug in FINDPOLE it is guaranteed that JOPT >= 0
+        # When JOPT == NUM_VARS, there is nothing to switch; in addition SIMI[JOPT, :] will be illegal.
+        # fval[[jopt, -1]] = fval[[-1, jopt]]
+        # conmat[:, [jopt, -1]] = conmat[:, [-1, jopt]] # Exchange CONMAT[:, JOPT] AND CONMAT[:, -1]
+        # cval[[jopt, -1]] = cval[[-1, jopt]]
+        sim[:, num_vars] += sim[:, jopt]
+        sim_jopt = sim[:, jopt].copy()
+        sim[:, jopt] = 0  # np.zeros(num_constraints)?
+        sim[:, :num_vars] -= np.tile(sim_jopt, (num_vars, 1)).T
+        # The above update is equivalent to multiplying SIM[:, :NUM_VARS] from the right side by a matrix whose
+        # JOPT-th row is [-1, -1, ..., -1], while all the other rows are the same as those of the
+        # identity matrix. It is easy to check that the inverse of this matrix is itself. Therefore,
+        # SIMI should be updated by a multiplication with this matrix (i.e. its inverse) from the left
+        # side, as is done in the following line. The JOPT-th row of the updated SIMI is minus the sum
+        # of all rows of the original SIMI, whereas all the other rows remain unchanged.
+        # NDB 20250114: In testing the cutest problem 'SYNTHES2' between the Python implementation and
+        # the Fortran bindings, I saw a difference between the following for loop and the
+        # np.sum command. The differences were small, on the order of 1e-16, i.e. epsilon.
+        # According to numpy documentation, np.sum sometimes uses partial pairwise summation,
+        # depending on the memory layout of the array and the axis specified.
+        # for i in range(simi.shape[1]):
+        #     simi[jopt, i] = -sum(simi[:, i])
+        simi[jopt, :] = -primasum(simi, axis=0)
+
+    # Check whether SIMI is a poor approximation to the inverse of SIM[:, :NUM_VARS]
+    # Calculate SIMI from scratch if the current one is damaged by rounding errors.
+    erri = np.max(abs(matprod(simi, sim[:, :num_vars]) - np.eye(num_vars)))  # np.max returns NaN if any input is NaN
+    itol = 1
+    if erri > 0.1 * itol or np.isnan(erri):
+        simi_test = inv(sim[:, :num_vars])
+        erri_test = np.max(abs(matprod(simi_test, sim[:, :num_vars]) - np.eye(num_vars)))
+        if erri_test < erri or (np.isnan(erri) and not np.isnan(erri_test)):
+            simi = simi_test
+            erri = erri_test
+
+
+    # If SIMI is satisfactory, then update FVAL, CONMAT, and CVAL. Otherwise restore SIM and SIMI, and
+    # return with INFO = DAMAGING_ROUNDING.
+    if erri <= itol:
+        if 0 <= jopt < num_vars:
+            fval[[jopt, num_vars]] = fval[[num_vars, jopt]]
+            conmat[:, [jopt, num_vars]] = conmat[:, [num_vars, jopt]]
+            cval[[jopt, num_vars]] = cval[[num_vars, jopt]]
+    else:  # erri > itol or erri is NaN
+        info = DAMAGING_ROUNDING
+        sim = sim_old
+        simi = simi_old
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert findpole(cpen, cval, fval) == num_vars or info == DAMAGING_ROUNDING
+        assert np.size(conmat, 0) == num_constraints and np.size(conmat, 1) == num_vars + 1
+        assert not (np.isnan(conmat) | np.isneginf(conmat)).any()
+        assert np.size(cval) == num_vars + 1 and not any(cval < 0 | np.isnan(cval) | np.isposinf(cval))
+        assert np.size(fval) == num_vars + 1 and not any(np.isnan(fval) | np.isposinf(fval))
+        assert np.size(sim, 0) == num_vars and np.size(sim, 1) == num_vars + 1
+        assert np.isfinite(sim).all()
+        assert all(primasum(abs(sim[:, :num_vars]), axis=0) > 0)
+        assert np.size(simi, 0) == num_vars and np.size(simi, 1) == num_vars
+        assert np.isfinite(simi).all()
+        # Do not check SIMI = SIM[:, :num_vars]^{-1}, as it may not be true due to damaging rounding.
+        assert isinv(sim[:, :num_vars], simi, itol) or info == DAMAGING_ROUNDING
+
+    return conmat, cval, fval, sim, simi, info
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_bounds.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_bounds.py
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index 0000000000000000000000000000000000000000..89afe9529f21235fc659d661df5f6037688bfdcf
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_bounds.py
@@ -0,0 +1,34 @@
+import numpy as np
+from scipy.optimize import Bounds
+
+def process_bounds(bounds, lenx0):
+    '''
+    `bounds` can either be an object with the properties lb and ub, or a list of tuples
+    indicating a lower bound and an upper bound for each variable. If the list contains
+    fewer entries than the length of x0, the remaining entries will generated as -/+ infinity.
+    Some examples of valid lists of tuple, assuming len(x0) == 3:
+    [(0, 1), (2, 3), (4, 5)] -> returns [0, 2, 4], [1, 3, 5]
+    [(0, 1), (None, 3)]      -> returns [0, -inf, -inf], [1, 3, inf]
+    [(0, 1), (-np.inf, 3)]   -> returns [0, -inf, -inf], [1, 3, inf]
+    '''
+
+    if bounds is None:
+        lb = np.array([-np.inf]*lenx0, dtype=np.float64)
+        ub = np.array([np.inf]*lenx0, dtype=np.float64)
+        return lb, ub
+    
+    if isinstance(bounds, Bounds):
+        lb = np.array(bounds.lb, dtype=np.float64)
+        ub = np.array(bounds.ub, dtype=np.float64)
+        lb = np.concatenate((lb, -np.inf*np.ones(lenx0 - len(lb))))
+        ub = np.concatenate((ub, np.inf*np.ones(lenx0 - len(ub))))
+        return lb, ub
+    
+    # If neither of the above conditions are true, we assume that bounds is a list of tuples
+    lb = np.array([bound[0] if bound[0] is not None else -np.inf for bound in bounds], dtype=np.float64)
+    ub = np.array([bound[1] if bound[1] is not None else np.inf for bound in bounds], dtype=np.float64)
+    # If there were fewer bounds than variables, pad the rest with -/+ infinity
+    lb = np.concatenate((lb, -np.inf*np.ones(lenx0 - len(lb))))
+    ub = np.concatenate((ub, np.inf*np.ones(lenx0 - len(ub))))
+    
+    return lb, ub
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_linear_constraints.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_linear_constraints.py
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index 0000000000000000000000000000000000000000..be508dced7edd7cda998d840bf195411a140b2ad
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_linear_constraints.py
@@ -0,0 +1,46 @@
+import numpy as np
+from scipy.optimize import LinearConstraint
+
+
+def combine_multiple_linear_constraints(constraints):
+    full_A = constraints[0].A
+    full_lb = constraints[0].lb
+    full_ub = constraints[0].ub
+    for constraint in constraints[1:]:
+        full_A = np.concatenate((full_A, constraint.A), axis=0)
+        full_lb = np.concatenate((full_lb, constraint.lb), axis=0)
+        full_ub = np.concatenate((full_ub, constraint.ub), axis=0)
+    return LinearConstraint(full_A, full_lb, full_ub)
+
+
+def separate_LC_into_eq_and_ineq(linear_constraint):
+    # The Python interface receives linear constraints lb <= A*x <= ub, but the
+    # Fortran backend of PRIMA expects that the linear constraints are specified
+    # as A_eq*x = b_eq, A_ineq*x <= b_ineq.
+    # As such, we must:
+    # 1. for constraints with lb == ub, rewrite them as A_eq*x = lb;
+    # 2. for constraints with lb < ub, rewrite them as A_ineq*x <= b_ineq.
+
+    # We suppose lb == ub if ub <= lb + 2*epsilon, assuming that the preprocessing
+    # ensures lb <= ub.
+    epsilon = np.finfo(np.float64).eps
+
+    eq_indices = (linear_constraint.ub <= (linear_constraint.lb + 2*epsilon))
+    A_eq = linear_constraint.A[eq_indices]
+    b_eq = (linear_constraint.lb[eq_indices] + linear_constraint.ub[eq_indices])/2.0
+
+    ineq_lb_indices = (linear_constraint.lb > -np.inf)
+    A_ineq_lb = -linear_constraint.A[~eq_indices & ineq_lb_indices]
+    b_ineq_lb = -linear_constraint.lb[~eq_indices & ineq_lb_indices]
+    ineq_ub_indices = (linear_constraint.ub < np.inf)
+    A_ineq_ub = linear_constraint.A[~eq_indices & ineq_ub_indices]
+    b_ineq_ub = linear_constraint.ub[~eq_indices & ineq_ub_indices]
+    A_ineq = np.concatenate((A_ineq_lb, A_ineq_ub))
+    b_ineq = np.concatenate((b_ineq_lb, b_ineq_ub))
+
+    # Ensure dtype is float64, or set to None if empty
+    A_eq = np.array(A_eq, dtype=np.float64) if len(A_eq) > 0 else None
+    b_eq = np.array(b_eq, dtype=np.float64) if len(b_eq) > 0 else None
+    A_ineq = np.array(A_ineq, dtype=np.float64) if len(A_ineq) > 0 else None
+    b_ineq = np.array(b_ineq, dtype=np.float64) if len(b_ineq) > 0 else None
+    return A_eq, b_eq, A_ineq, b_ineq
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_nonlinear_constraints.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_nonlinear_constraints.py
new file mode 100644
index 0000000000000000000000000000000000000000..bfee3b7f2cf2e591b5d956cf3a1ae75cc79f1a19
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_nonlinear_constraints.py
@@ -0,0 +1,54 @@
+import numpy as np
+        
+def transform_constraint_function(nlc):
+    '''
+    The Python interfaces receives the constraints as lb <= constraint(x) <= ub, 
+    but the Fortran backend expects the nonlinear constraints to be constraint(x) <= 0.
+    Thus a conversion is needed.
+    
+    In addition to the conversion, we add a check to ensure that the provided lower/upper bounds
+    have a shape consistent with the output of the constraint function.
+    '''
+
+    def newconstraint(x):
+        values = np.atleast_1d(np.array(nlc.fun(x), dtype=np.float64))
+        
+        # Upgrade the lower/upper bounds to vectors if necessary
+        lb = nlc.lb
+        try:
+            _ = len(lb)
+        except TypeError:
+            lb = np.array([nlc.lb]*len(values), dtype=np.float64)
+
+        ub = nlc.ub
+        try:
+            _ = len(ub)
+        except TypeError:
+            ub = np.array([nlc.ub]*len(values), dtype=np.float64)
+        
+        
+        # Check the shapes and raise an exception if they do not match
+        if len(values) != len(lb):
+            raise ValueError("The number of elements in the constraint function's output does not match the number of elements in the lower bound.")
+        if len(values) != len(ub):
+            raise ValueError("The number of elements in the constraint function's output does not match the number of elements in the upper bound.")
+        
+        # Combine the upper and lower bounds to transform the function into the form
+        # expected by the Fortran backend.
+        return np.concatenate(([lb_ii - vi for lb_ii, vi in zip(lb, values) if lb_ii > -np.inf],
+                               [vi - ub_ii for ub_ii, vi in zip(ub, values) if ub_ii < np.inf],
+                            ))
+    return newconstraint
+
+
+def process_nl_constraints(nlcs):
+    functions = []
+    for nlc in nlcs:
+        fun_i = transform_constraint_function(nlc)
+        functions.append(fun_i)
+    def constraint_function(x):
+        values = np.empty(0, dtype=np.float64)
+        for fun in functions:
+            values = np.concatenate((values, fun(x)))
+        return values
+    return constraint_function
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_project.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_project.py
new file mode 100644
index 0000000000000000000000000000000000000000..233a4e32e905d9a4d3b91f3918de766f51a085fc
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/_project.py
@@ -0,0 +1,173 @@
+'''
+This module provides the _project function that attempts to project the initial guess
+onto the feasible set.
+
+Adapted from the corresponding function in the PDFO package (https://www.pdfo.net) by
+Tom M. Ragonneau (https://ragonneau.github.io) and Zaikun Zhang (https://www.zhangzk.net).
+'''
+
+import numpy as np
+from ._linear_constraints import LinearConstraint
+from scipy.optimize import OptimizeResult
+
+# All the accepted scalar types; np.generic correspond to all NumPy types.
+scalar_types = (int, float, np.generic)
+eps = np.finfo(np.float64).eps
+
+def _project(x0, lb, ub, constraints):
+    """Projection of the initial guess onto the feasible set.
+
+    Parameters
+    ----------
+    x0: ndarray, shape (n,)
+        The same as in prepdfo.
+    lb: ndarray, shape (n,)
+        The same as in prepdfo.
+    ub: ndarray, shape (n,)
+        The same as in prepdfo.
+    constraints: dict
+        The general constraints of the problem, defined as a dictionary with
+        fields:
+            linear: LinearConstraint
+                The linear constraints of the problem.
+            nonlinear: dict
+                The nonlinear constraints of the problem. When ``_project`` is called, the nonlinear constraints are
+                None.
+
+    Returns
+    -------
+    result: OptimizeResult
+        The result of the projection.
+
+    Authors
+    -------
+    Tom M. RAGONNEAU (ragonneau.github.io)
+    and Zaikun ZHANG (www.zhangzk.net)
+
+    Dedicated to the late Professor M. J. D. Powell FRS (1936--2015).
+    """
+    invoker = 'prima'
+
+    # Validate x0.
+    if isinstance(x0, scalar_types):
+        x0_c = [x0]
+    elif hasattr(x0, '__len__'):
+        x0_c = x0
+    else:
+        raise ValueError('{}: UNEXPECTED ERROR: x0 should be a vector.'.format(invoker))
+    try:
+        x0_c = np.asarray(x0_c, dtype=np.float64)
+    except ValueError:
+        raise ValueError('{}: UNEXPECTED ERROR: x0 should contain only scalars.'.format(invoker))
+    if len(x0_c.shape) != 1:
+        raise ValueError('{}: UNEXPECTED ERROR: x0 should be a vector.'.format(invoker))
+    lenx0 = x0_c.size
+
+    # Validate lb.
+    if isinstance(lb, scalar_types):
+        lb_c = [lb]
+    elif hasattr(lb, '__len__'):
+        lb_c = lb
+    else:
+        raise ValueError('{}: UNEXPECTED ERROR: lb should be a vector.'.format(invoker))
+    try:
+        lb_c = np.asarray(lb_c, dtype=np.float64)
+    except ValueError:
+        raise ValueError('{}: UNEXPECTED ERROR: lb should contain only scalars.'.format(invoker))
+    if len(lb_c.shape) != 1 or lb_c.size != lenx0:
+        raise ValueError('{}: UNEXPECTED ERROR: the size of lb is inconsistent with x0.'.format(invoker))
+
+    # Validate ub.
+    if isinstance(ub, scalar_types):
+        ub_c = [ub]
+    elif hasattr(ub, '__len__'):
+        ub_c = ub
+    else:
+        raise ValueError('{}: UNEXPECTED ERROR: ub should be a vector.'.format(invoker))
+    try:
+        ub_c = np.asarray(ub_c, dtype=np.float64)
+    except ValueError:
+        raise ValueError('{}: UNEXPECTED ERROR: ub should contain only scalars.'.format(invoker))
+    if len(ub_c.shape) != 1 or ub_c.size != lenx0:
+        raise ValueError('{}: UNEXPECTED ERROR: the size of ub is inconsistent with x0.'.format(invoker))
+
+    # Validate constraints.
+    if not isinstance(constraints, dict) or not ({'linear', 'nonlinear'} <= set(constraints.keys())) or \
+            not (isinstance(constraints['linear'], LinearConstraint) or constraints['linear'] is None):
+        # the nonlinear constraints will not be taken into account in this function and are, therefore, not validated
+        raise ValueError('{}: UNEXPECTED ERROR: The constraints are ill-defined.'.format(invoker))
+
+    max_con = 1e20  # Decide whether an inequality constraint can be ignored
+
+    # Project onto the feasible set.
+    if constraints['linear'] is None:
+        # Direct projection onto the bound constraints
+        x_proj = np.nanmin((np.nanmax((x0_c, lb_c), axis=0), ub_c), axis=0)
+        return OptimizeResult(x=x_proj)
+    elif all(np.less_equal(np.abs(constraints['linear'].ub - constraints['linear'].lb), eps)) and \
+            np.max(lb_c) <= -max_con and np.min(ub_c) >= max_con:
+        # The linear constraints are all equality constraints. The projection can therefore be done by solving the
+        # least-squares problem: min ||A*x - (b - A*x_0)||.
+        a = constraints['linear'].A
+        b = (constraints['linear'].lb + constraints['linear'].ub) / 2
+        xi, _, _, _ = np.linalg.lstsq(a, b - np.dot(a, x0_c), rcond=None)
+
+        # The problem is not bounded. However, if the least-square solver returned values bigger in absolute value
+        # than max_con, they will be reduced to this bound.
+        x_proj = np.nanmin((np.nanmax((x0_c + xi, lb_c), axis=0), ub_c), axis=0)
+
+        return OptimizeResult(x=x_proj)
+
+    if constraints['linear'] is not None:
+        try:
+            # Project the initial guess onto the linear constraints via SciPy.
+            from scipy.optimize import minimize
+            from scipy.optimize import Bounds as ScipyBounds
+            from scipy.optimize import LinearConstraint as ScipyLinearConstraint
+
+            linear = constraints['linear']
+
+            # To be more efficient, SciPy asks to separate the equality and the inequality constraints into two
+            # different LinearConstraint structures
+            pc_args_ineq, pc_args_eq = dict(), dict()
+            pc_args_ineq['A'], pc_args_eq['A'] = np.asarray([[]]), np.asarray([[]])
+            pc_args_ineq['A'] = pc_args_ineq['A'].reshape(0, linear.A.shape[1])
+            pc_args_eq['A'] = pc_args_eq['A'].reshape(0, linear.A.shape[1])
+            pc_args_ineq['lb'], pc_args_eq['lb'] = np.asarray([]), np.asarray([])
+            pc_args_ineq['ub'], pc_args_eq['ub'] = np.asarray([]), np.asarray([])
+
+            for i in range(linear.lb.size):
+                if linear.lb[i] != linear.ub[i]:
+                    pc_args_ineq['A'] = np.concatenate((pc_args_ineq['A'], linear.A[i:i+1, :]), axis=0)
+                    pc_args_ineq['lb'] = np.r_[pc_args_ineq['lb'], linear.lb[i]]
+                    pc_args_ineq['ub'] = np.r_[pc_args_ineq['ub'], linear.ub[i]]
+                else:
+                    pc_args_eq['A'] = np.concatenate((pc_args_eq['A'], linear.A[i:i+1, :]), axis=0)
+                    pc_args_eq['lb'] = np.r_[pc_args_eq['lb'], linear.lb[i]]
+                    pc_args_eq['ub'] = np.r_[pc_args_eq['ub'], linear.ub[i]]
+
+            if pc_args_ineq['A'].size > 0 and pc_args_ineq['lb'].size > 0 and pc_args_eq['lb'].size > 0:
+                project_constraints = [ScipyLinearConstraint(**pc_args_ineq), ScipyLinearConstraint(**pc_args_eq)]
+            elif pc_args_ineq['A'].size > 0 and pc_args_ineq['lb'].size > 0:
+                project_constraints = ScipyLinearConstraint(**pc_args_ineq)
+            elif pc_args_eq['A'].size > 0:
+                project_constraints = ScipyLinearConstraint(**pc_args_eq)
+            else:
+                project_constraints = ()
+
+            # Perform the actual projection.
+            ax_ineq = np.dot(pc_args_ineq['A'], x0_c)
+            ax_eq = np.dot(pc_args_eq['A'], x0_c)
+            if np.greater(ax_ineq, pc_args_ineq['ub']).any() or np.greater(pc_args_ineq['lb'], ax_ineq).any() or \
+                    np.not_equal(ax_eq, pc_args_eq['lb']).any() or \
+                    np.greater(x0_c, ub_c).any() or np.greater(lb_c, x0_c).any():
+                return minimize(lambda x: np.dot(x - x0_c, x - x0_c) / 2, x0_c, jac=lambda x: (x - x0_c),
+                                bounds=ScipyBounds(lb_c, ub_c), constraints=project_constraints)
+            else:
+                # Do not perform any projection if the initial guess is feasible.
+                return OptimizeResult(x=x0_c)
+
+        except ImportError:
+            return OptimizeResult(x=x0_c)
+
+    return OptimizeResult(x=x0_c)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/checkbreak.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/checkbreak.py
new file mode 100644
index 0000000000000000000000000000000000000000..95efd6c14b3dc6e572b3d83a7f47b419ac050c93
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/checkbreak.py
@@ -0,0 +1,93 @@
+'''
+This module checks whether to break out of the solver loop.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+from .infos import INFO_DEFAULT, NAN_INF_X, NAN_INF_F, FTARGET_ACHIEVED, MAXFUN_REACHED
+
+import numpy as np
+
+def checkbreak_unc(maxfun, nf, f, ftarget, x):
+    '''
+    This module checks whether to break out of the solver loop in the unconstrained case.
+    '''
+
+    # Outputs
+    info = INFO_DEFAULT
+
+    # Local variables
+    srname = "CHECKbreak_UNC"
+
+    # Preconditions
+    assert INFO_DEFAULT not in [NAN_INF_X, NAN_INF_F, FTARGET_ACHIEVED, MAXFUN_REACHED], f'NAN_INF_X, NAN_INF_F, FTARGET_ACHIEVED, and MAXFUN_REACHED differ from INFO_DFT {srname}'
+    # X does not contain NaN if the initial X does not contain NaN and the subroutines generating
+    # trust-region/geometry steps work properly so that they never produce a step containing NaN/Inf.
+    assert not any(np.isnan(x)), f'X does not contain NaN {srname}'
+    # With the moderated extreme barrier, F cannot be NaN/+Inf.
+    assert not (any(np.isnan(f)) or any(np.isposinf(f))), f'F is not NaN/+Inf {srname}'
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # Although X should not contain NaN unless there is a bug, we include the following for security.
+    # X can be Inf, as finite + finite can be Inf numerically.
+    if any(np.isnan(x)) or any(np.isinf(x)):
+        info = NAN_INF_X
+
+    # Although NAN_INF_F should not happen unless there is a bug, we include the following for security.
+    if any(np.isnan(f)) or any(np.isposinf(f)):
+        info = NAN_INF_F
+
+    if f <= ftarget:
+        info = FTARGET_ACHIEVED
+
+    if nf >= maxfun:
+        info = MAXFUN_REACHED
+
+    return info
+
+def checkbreak_con(maxfun, nf, cstrv, ctol, f, ftarget, x):
+    '''
+    This module checks whether to break out of the solver loop in the constrained case.
+    '''
+
+    # Outputs
+    info = INFO_DEFAULT
+
+    # Local variables
+    srname = "CHECKbreak_CON"
+
+    # Preconditions
+    assert INFO_DEFAULT not in [NAN_INF_X, NAN_INF_F, FTARGET_ACHIEVED, MAXFUN_REACHED], f'NAN_INF_X, NAN_INF_F, FTARGET_ACHIEVED, and MAXFUN_REACHED differ from INFO_DFT {srname}'
+    # X does not contain NaN if the initial X does not contain NaN and the subroutines generating
+    # trust-region/geometry steps work properly so that they never produce a step containing NaN/Inf.
+    assert not any(np.isnan(x)), f'X does not contain NaN {srname}'
+    # With the moderated extreme barrier, F or CSTRV cannot be NaN/+Inf.
+    assert not (np.isnan(f) or np.isposinf(f) or np.isnan(cstrv) or np.isposinf(cstrv)), f'F or CSTRV is not NaN/+Inf {srname}'
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # Although X should not contain NaN unless there is a bug, we include the following for security.
+    # X can be Inf, as finite + finite can be Inf numerically.
+    if any(np.isnan(x)) or any(np.isinf(x)):
+        info = NAN_INF_X
+
+    # Although NAN_INF_F should not happen unless there is a bug, we include the following for security.
+    if np.isnan(f) or np.isposinf(f) or np.isnan(cstrv) or np.isposinf(cstrv):
+        info = NAN_INF_F
+
+    if cstrv <= ctol and f <= ftarget:
+        info = FTARGET_ACHIEVED
+
+    if nf >= maxfun:
+        info = MAXFUN_REACHED
+
+    return info
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/consts.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/consts.py
new file mode 100644
index 0000000000000000000000000000000000000000..1916bae39cf08a495af8008cd623eb45680914e8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/consts.py
@@ -0,0 +1,47 @@
+'''
+This is a module defining some constants.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+import numpy as np
+import os
+
+DEBUGGING = bool(os.getenv('PRIMA_DEBUGGING'))
+
+REALMIN = np.finfo(float).tiny
+REALMAX = np.finfo(float).max
+FUNCMAX = 10.0**30
+CONSTRMAX = FUNCMAX
+EPS = np.finfo(float).eps
+
+# Any bound with an absolute value at least BOUNDMAX is considered as no bound.
+BOUNDMAX = REALMAX/4
+
+# Some default values
+RHOBEG_DEFAULT = 1
+RHOEND_DEFAULT = 1e-6
+FTARGET_DEFAULT = -REALMAX
+CTOL_DEFAULT = np.sqrt(EPS)
+CWEIGHT_DEFAULT = 1e8
+ETA1_DEFAULT = 0.1
+ETA2_DEFAULT = 0.7
+GAMMA1_DEFAULT = 0.5
+GAMMA2_DEFAULT = 2
+IPRINT_DEFAULT = 0
+MAXFUN_DIM_DEFAULT = 500
+
+PRIMA_MAX_HIST_MEM_MB = 300  # 1MB > 10^5*REAL64. 100 can be too small.
+
+# Maximal amount of memory (Byte) allowed for XHIST, FHIST, CONHIST, CHIST, and the filters.
+MHM = PRIMA_MAX_HIST_MEM_MB * 10**6
+# Make sure that MAXHISTMEM does not exceed HUGE(0) to avoid overflow and memory errors.
+MAXHISTMEM = min(MHM, np.iinfo(np.int32).max)
+
+# Maximal length of the filter used in constrained solvers.
+MIN_MAXFILT = 200  # Should be positive; < 200 is not recommended.
+MAXFILT_DEFAULT = 10 * MIN_MAXFILT
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/evaluate.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/evaluate.py
new file mode 100644
index 0000000000000000000000000000000000000000..075e1d42fa30fcd0eaeb7b40a491f41623e27293
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/evaluate.py
@@ -0,0 +1,99 @@
+'''
+This is a module evaluating the objective/constraint function with Nan/Inf handling.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+import numpy as np
+from .consts import FUNCMAX, CONSTRMAX, REALMAX, DEBUGGING
+from .linalg import matprod, primasum
+
+# This is a module evaluating the objective/constraint function with Nan/Inf handling.
+
+
+def moderatex(x):
+    '''
+    This function moderates a decision variable. It replaces NaN by 0 and Inf/-Inf by
+    REALMAX/-REALMAX.
+    '''
+    x[np.isnan(x)] = 0
+    x = np.clip(x, -REALMAX, REALMAX)
+    return x
+
+def moderatef(f):
+    """
+    This function moderates the function value of a MINIMIZATION problem. It replaces
+    NaN and any value above FUNCMAX by FUNCMAX.
+    """
+    f = FUNCMAX if np.isnan(f) else f
+    f = np.clip(f, -REALMAX, FUNCMAX)
+    # We may moderate huge negative function values as follows, but we decide not to.
+    # f = np.clip(f, -FUNCMAX, FUNCMAX)
+    return f
+
+
+def moderatec(c):
+    """
+    This function moderates the constraint value, the constraint demanding this value
+    to be NONNEGATIVE. It replaces any value below -CONSTRMAX by -CONSTRMAX, and any
+    NaN or value above CONSTRMAX by CONSTRMAX.
+    """
+    np.nan_to_num(c, copy=False, nan=CONSTRMAX)
+    c = np.clip(c, -CONSTRMAX, CONSTRMAX)
+    return c
+
+
+def evaluate(calcfc, x, m_nlcon, amat, bvec):
+    """
+    This function evaluates CALCFC at X, returning the objective function value and the
+    constraint value. Nan/Inf are handled by a moderated extreme barrier.
+    """
+
+    # Sizes
+    m_lcon = len(bvec) if bvec is not None else 0
+
+    # Preconditions
+    if DEBUGGING:
+        # X should not contain NaN if the initial X does not contain NaN and the
+        # subroutines generating # trust-region/geometry steps work properly so that
+        # they never produce a step containing NaN/Inf.
+        assert not any(np.isnan(x))
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    constr = np.zeros(m_lcon + m_nlcon)
+    if amat is not None:
+        constr[:m_lcon] = matprod(x, amat.T) - bvec
+
+    if any(np.isnan(x)):
+        # Although this should not happen unless there is a bug, we include this case
+        # for robustness.
+        f = primasum(x)
+        constr = np.ones(m_nlcon) * f
+    else:
+        f, constr[m_lcon:] = calcfc(moderatex(x))
+
+        # Moderated extreme barrier: replace NaN/huge objective or constraint values
+        # with a large but finite value. This is naive, and better approaches surely
+        # exist.
+        f = moderatef(f)
+        constr[m_lcon:] = moderatec(constr[m_lcon:])
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        # With X not containing NaN, and with the moderated extreme barrier, F cannot
+        # be NaN/+Inf, and CONSTR cannot be NaN/-Inf.
+        assert not (np.isnan(f) or np.isposinf(f))
+        assert not any(np.isnan(constr) | np.isposinf(constr))
+
+    return f, constr
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/history.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/history.py
new file mode 100644
index 0000000000000000000000000000000000000000..212db7305d890d0133afb312ed6c73b79f8bb0fa
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/history.py
@@ -0,0 +1,38 @@
+'''
+This module provides subroutines that handle the X/F/C histories of the solver, taking into
+account that MAXHIST may be smaller than NF.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+def savehist(maxhist, x, xhist, f, fhist, cstrv, chist, constr, conhist):
+    '''
+    Save the data values to the history lists.
+
+    The implementation of this function is vastly different from the Fortran implementation.
+    This is mostly due to the ease of creating and appending to lists in Python
+
+    However just like the Fortran version we should be concerned about both performance
+    and memory constraints. It will probably be better to initialize an array of NaN for
+    each of the histories and keep track of how many indices we have stored. Not needed for
+    the moment.
+    '''
+    if len(xhist) < maxhist:
+        xhist.append(x)
+        fhist.append(f)
+        chist.append(cstrv)
+        conhist.append(constr)
+    else:
+        # This effectively accomplishes what rangehist does in the Fortran implementation
+        xhist.pop(0)
+        fhist.pop(0)
+        chist.pop(0)
+        conhist.pop(0)
+        xhist.append(x)
+        fhist.append(f)
+        chist.append(cstrv)
+        conhist.append(constr)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/infos.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/infos.py
new file mode 100644
index 0000000000000000000000000000000000000000..27d0f1e144bdfabf1633ccfccaab2ac5dd93781f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/infos.py
@@ -0,0 +1,30 @@
+'''
+This is a module defining exit flags.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+INFO_DEFAULT = 0
+SMALL_TR_RADIUS = 0
+FTARGET_ACHIEVED = 1
+TRSUBP_FAILED = 2
+MAXFUN_REACHED = 3
+MAXTR_REACHED = 20
+NAN_INF_X = -1
+NAN_INF_F = -2
+NAN_INF_MODEL = -3
+NO_SPACE_BETWEEN_BOUNDS = 6
+DAMAGING_ROUNDING = 7
+ZERO_LINEAR_CONSTRAINT = 8
+CALLBACK_TERMINATE = 30
+
+# Stop-codes.
+# The following codes are used by ERROR STOP as stop-codes, which should be default integers.
+INVALID_INPUT = 100
+ASSERTION_FAILS = 101
+VALIDATION_FAILS = 102
+MEMORY_ALLOCATION_FAILS = 103
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/linalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/linalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..a5ee756aaf867ca76afe9cbb5f768c2097ecbadc
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/linalg.py
@@ -0,0 +1,435 @@
+'''
+This module provides some basic linear algebra procedures.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+import numpy as np
+from .consts import DEBUGGING, EPS, REALMAX, REALMIN
+from .present import present
+
+
+# We use naive implementations of matrix multiplication and other routines for two
+# reasons:
+# 1. When Fortran is compiled in debug mode, and Python is using these routines, we
+#    can get bit for bit identical results as compared to Fortran. This is helpful
+#    for comparing the two implementations. It will be particularly helpful when porting
+#    the other implementations like LINCOA, etc.
+# 2. On some problems this algorithm is very sensitive to errors in finite precision
+#    arithmetic. Switching to naive implementation will slow down the algorithm, but
+#    may be more stable.
+USE_NAIVE_MATH = False
+
+
+def inprod(x, y):
+    if not USE_NAIVE_MATH:
+        return np.dot(x, y)
+    result = 0
+    for i in range(len(x)):
+        result += x[i] * y[i]
+    return result
+
+
+def matprod12(x, y):
+    result = np.zeros(y.shape[1])
+    for i in range(y.shape[1]):
+        result[i] = inprod(x, y[:, i])
+    return result
+
+
+def matprod21(x, y):
+    result = np.zeros(x.shape[0])
+    for i in range(x.shape[1]):
+        result += x[:, i] * y[i]
+    return result
+
+
+def matprod22(x, y):
+    result = np.zeros((x.shape[0], y.shape[1]))
+    for i in range(y.shape[1]):
+        for j in range(x.shape[1]):
+            result[:, j] += x[:, i] * y[i, j]
+    return result
+
+
+def matprod(x, y):
+    if not USE_NAIVE_MATH:
+        return x@y
+    if len(x.shape) == 1 and len(y.shape) == 1:
+        return inprod(x, y)
+    elif len(x.shape) == 1 and len(y.shape) == 2:
+        return matprod12(x, y)
+    elif len(x.shape) == 2 and len(y.shape) == 1:
+        return matprod21(x, y)
+    elif len(x.shape) == 2 and len(y.shape) == 2:
+        return matprod22(x, y)
+    else:
+        raise ValueError(f'Invalid shapes for x and y: {x.shape} and {y.shape}')
+
+
+def outprod(x, y):
+    if not USE_NAIVE_MATH:
+        return np.outer(x, y)
+    result = np.zeros((len(x), len(y)))
+    for i in range(len(x)):
+            result[:, i] = x * y[i]
+    return result
+
+
+def lsqr(A, b, Q, Rdiag):
+    if not USE_NAIVE_MATH:
+        return np.linalg.lstsq(A, b, rcond=None)[0]
+
+    m = A.shape[0]
+    n = A.shape[1]
+
+    rank = min(m, n)
+
+    x = np.zeros(n)
+    y = b.copy()
+
+    for i in range(rank - 1, -1, -1):
+        yq = inprod(y, Q[:, i])
+        yqa = inprod(np.abs(y), np.abs(Q[:, i]))
+        if isminor(yq, yqa):
+            x[i] = 0
+        else:
+            x[i] = yq / Rdiag[i]
+            y = y - x[i] * A[:, i]
+    return x
+
+
+def hypot(x1, x2):
+    if not USE_NAIVE_MATH:
+        return np.hypot(x1, x2)
+    if not np.isfinite(x1):
+        r = abs(x1)
+    elif not np.isfinite(x2):
+        r = abs(x2)
+    else:
+        y = abs(np.array([x1, x2]))
+        y = np.array([min(y), max(y)])
+        if y[0] > np.sqrt(REALMIN) and y[1] < np.sqrt(REALMAX/2.1):
+            r = np.sqrt(sum(y*y))
+        elif y[1] > 0:
+            r = y[1] * np.sqrt((y[0]/y[1])*(y[0]/y[1]) + 1)
+        else:
+            r = 0
+    return r
+
+
+def norm(x):
+    if not USE_NAIVE_MATH:
+        return np.linalg.norm(x)
+    # NOTE: Avoid np.pow! And exponentiation in general!
+    # It appears that in Fortran, x*x and x**2 are the same, but in Python they are not!
+    # Try it with x = 5 - 1e-15
+    result = np.sqrt(sum([xi*xi for xi in x]))
+    return result
+
+
+def istril(A, tol=0):
+    return primasum(abs(A) - np.tril(abs(A))) <= tol
+
+def istriu(A, tol=0):
+    return primasum(abs(A) - np.triu(abs(A))) <= tol
+
+
+def inv(A):
+    if not USE_NAIVE_MATH:
+        return np.linalg.inv(A)
+    A = A.copy()
+    n = A.shape[0]
+    if istril(A):
+        # This case is invoked in COBYLA.
+        R = A.T
+        B = np.zeros((n, n))
+        for i in range(n):
+            B[i, i] = 1 / R[i, i]
+            B[:i, i] = -matprod(B[:i, :i], R[:i, i]) / R[i, i]
+        return B.T
+    elif istriu(A):
+        B = np.zeros((n, n))
+        for i in range(n):
+            B[i, i] = 1 / A[i, i]
+            B[:i, i] = -matprod(B[:i, :i], A[:i, i]) / A[i, i]
+    else:
+        # This is NOT the best algorithm for the inverse, but since the QR subroutine is available ...
+        Q, R, P = qr(A)
+        R = R.T
+        B = np.zeros((n, n))
+        for i in range(n - 1, -1, -1):
+            B[:, i] = (Q[:, i] - matprod(B[:, i + 1:n], R[i + 1:n, i])) / R[i, i]
+        InvP = np.zeros(n, dtype=int)
+        InvP[P] = np.linspace(0, n-1, n)
+        B = B[:, InvP].T
+    return B
+
+
+def qr(A):
+    m = A.shape[0]
+    n = A.shape[1]
+
+    Q = np.eye(m)
+    T = A.T
+    P = np.linspace(0, n-1, n, dtype=int)
+
+    for j in range(n):
+        k = np.argmax(primasum(primapow2(T[j:n+1, j:m+1]), axis=1), axis=0)
+        if k > 0 and k <= n - j - 1:
+            k += j
+            P[j], P[k] = P[k], P[j]
+            T[[j, k], :] = T[[k, j], :]
+        for i in range(m-1, j, -1):
+            G = planerot(T[j, [j, i]]).T
+            T[j, [j, i]] = np.append(hypot(T[j, j], T[j, i]), 0)
+            T[j + 1:n + 1, [j, i]] = matprod(T[j + 1:n + 1, [j, i]], G)
+            Q[:, [j, i]] = matprod(Q[:, [j, i]], G)
+
+    R = T.T
+
+    return Q, R, P
+
+
+def primasum(x, axis=None):
+    '''
+    According to its documentation, np.sum will sometimes do partial pairwise summation.
+    For our purposes, when comparing, we want don't want to do anything fancy, and we
+    just want to add things up one at a time.
+    '''
+    if not USE_NAIVE_MATH:
+        return np.sum(x, axis=axis)
+    if axis is None:
+        if x.ndim == 2:
+            # Sum columns first, then sum the result
+            return sum(primasum(x, axis=0))
+        else:
+            return sum(x)
+    elif axis == 0:
+        result = np.zeros(x.shape[1])
+        for i in range(x.shape[1]):
+            result[i] = sum(x[:, i])
+        return result
+    elif axis == 1:
+        result = np.zeros(x.shape[0])
+        for i in range(x.shape[0]):
+            result[i] = sum(x[i, :])
+        return result
+
+
+def primapow2(x):
+    '''
+    Believe it or now, x**2 is not always the same as x*x in Python. In Fortran they
+    appear to be identical. Here's a quick one-line to find an example on your system
+    (well, two liner after importing numpy):
+    list(filter(lambda x: x[1], [(x:=np.random.random(), x**2 - x*x != 0) for _ in range(10000)]))
+    '''
+    return x*x
+
+
+def planerot(x):
+    '''
+    As in MATLAB, planerot(x) returns a 2x2 Givens matrix G for x in R2 so that Y=G@x has Y[1] = 0.
+    Roughly speaking, G = np.array([[x[0]/R, x[1]/R], [-x[1]/R, x[0]/R]]), where R = np.linalg.norm(x).
+    0. We need to take care of the possibilities of R=0, Inf, NaN, and over/underflow.
+    1. The G defined above is continuous with respect to X except at 0. Following this definition,
+    G = np.array([[np.sign(x[0]), 0], [0, np.sign(x[0])]]) if x[1] == 0,
+    G = np.array([[0, np.sign(x[1])], [np.sign(x[1]), 0]]) if x[0] == 0
+    Yet some implementations ignore the signs, leading to discontinuity and numerical instability.
+    2. Difference from MATLAB: if x contains NaN of consists of only Inf, MATLAB returns a NaN matrix,
+    but we return an identity matrix or a matrix of +/-np.sqrt(2). We intend to keep G always orthogonal.
+    '''
+
+    # Preconditions
+    if DEBUGGING:
+        assert len(x) == 2, "x must be a 2-vector"
+
+    # ==================
+    # Calculation starts
+    # ==================
+
+    # Define C = X(1) / R and S = X(2) / R with R = HYPOT(X(1), X(2)). Handle Inf/NaN, over/underflow.
+    if (any(np.isnan(x))):
+        # In this case, MATLAB sets G to NaN(2, 2). We refrain from doing so to keep G orthogonal.
+        c = 1
+        s = 0
+    elif (all(np.isinf(x))):
+        # In this case, MATLAB sets G to NaN(2, 2). We refrain from doing so to keep G orthogonal.
+        c = 1 / np.sqrt(2) * np.sign(x[0])
+        s = 1 / np.sqrt(2) * np.sign(x[1])
+    elif (abs(x[0]) <= 0 and abs(x[1]) <= 0): # X(1) == 0 == X(2).
+        c = 1
+        s = 0
+    elif (abs(x[1]) <= EPS * abs(x[0])):
+        # N.B.:
+        # 0. With <= instead of <, this case covers X(1) == 0 == X(2), which is treated above separately
+        # to avoid the confusing SIGN(., 0) (see 1).
+        # 1. SIGN(A, 0) = ABS(A) in Fortran but sign(0) = 0 in MATLAB, Python, Julia, and R#
+        # 2. Taking SIGN(X(1)) into account ensures the continuity of G with respect to X except at 0.
+        c = np.sign(x[0])
+        s = 0
+    elif (abs(x[0]) <= EPS * abs(x[1])):
+        # N.B.: SIGN(A, X) = ABS(A) * sign of X /= A * sign of X # Therefore, it is WRONG to define G
+        # as SIGN(RESHAPE([ZERO, -ONE, ONE, ZERO], [2, 2]), X(2)). This mistake was committed on
+        # 20211206 and took a whole day to debug! NEVER use SIGN on arrays unless you are really sure.
+        c = 0
+        s = np.sign(x[1])
+    else:
+        # Here is the normal case. It implements the Givens rotation in a stable & continuous way as in:
+        # Bindel, D., Demmel, J., Kahan, W., and Marques, O. (2002). On computing Givens rotations
+        # reliably and efficiently. ACM Transactions on Mathematical Software (TOMS), 28(2), 206-238.
+        # N.B.: 1. Modern compilers compute SQRT(REALMIN) and SQRT(REALMAX/2.1) at compilation time.
+        # 2. The direct calculation without involving T and U seems to work better; use it if possible.
+        if (all(np.logical_and(np.sqrt(REALMIN) < np.abs(x), np.abs(x) < np.sqrt(REALMAX / 2.1)))):
+            # Do NOT use HYPOTENUSE here; the best implementation for one may be suboptimal for the other
+            r = norm(x)
+            c = x[0] / r
+            s = x[1] / r
+        elif (abs(x[0]) > abs(x[1])):
+            t = x[1] / x[0]
+            u = max(1, abs(t), np.sqrt(1 + t*t))  # MAXVAL: precaution against rounding error.
+            u *= np.sign(x[0]) ##MATLAB: u = sign(x(1))*sqrt(1 + t**2)
+            c = 1 / u
+            s = t / u
+        else:
+            t = x[0] / x[1]
+            u = max([1, abs(t), np.sqrt(1 + t*t)])  # MAXVAL: precaution against rounding error.
+            u *= np.sign(x[1]) ##MATLAB: u = sign(x(2))*sqrt(1 + t**2)
+            c = t / u
+            s = 1 / u
+
+    G = np.array([[c, s], [-s, c]]) #  MATLAB: G = [c, s; -s, c]
+
+    #====================#
+    #  Calculation ends  #
+    #====================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert G.shape == (2,2)
+        assert np.all(np.isfinite(G))
+        assert abs(G[0, 0] - G[1, 1]) + abs(G[0, 1] + G[1, 0]) <= 0
+        tol = np.maximum(1.0E-10, np.minimum(1.0E-1, 1.0E6 * EPS))
+        assert isorth(G, tol)
+        if all(np.logical_and(np.isfinite(x), np.abs(x) < np.sqrt(REALMAX / 2.1))):
+            r = np.linalg.norm(x)
+            assert max(abs(G@x - [r, 0])) <= max(tol, tol * r), 'G @ X = [||X||, 0]'
+
+    return G
+
+
+def isminor(x, ref):
+    '''
+    This function tests whether x is minor compared to ref. It is used by Powell, e.g., in COBYLA.
+    In precise arithmetic, isminor(x, ref) is true if and only if x == 0; in floating point
+    arithmetic, isminor(x, ref) is true if x is 0 or its nonzero value can be attributed to
+    computer rounding errors according to ref.
+    Larger sensitivity means the function is more strict/precise, the value 0.1 being due to Powell.
+
+    For example:
+    isminor(1e-20, 1e300) -> True, because in floating point arithmetic 1e-20 cannot be added to
+    1e300 without being rounded to 1e300.
+    isminor(1e300, 1e-20) -> False, because in floating point arithmetic adding 1e300 to 1e-20
+    dominates the latter number.
+    isminor(3, 4) -> False, because 3 can be added to 4 without being rounded off
+    '''
+
+    sensitivity = 0.1
+    refa = abs(ref) + sensitivity * abs(x)
+    refb = abs(ref) + 2 * sensitivity * abs(x)
+    return np.logical_or(abs(ref) >= refa, refa >= refb)
+
+
+def isinv(A, B, tol=None):
+    '''
+    This procedure tests whether A = B^{-1} up to the tolerance TOL.
+    '''
+
+    # Sizes
+    n = np.size(A, 0)
+
+    # Preconditions
+    if DEBUGGING:
+        assert np.size(A, 0) == np.size(A, 1)
+        assert np.size(B, 0) == np.size(B, 1)
+        assert np.size(A, 0) == np.size(B, 0)
+        if present(tol):
+            assert tol >= 0
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    tol = tol if present(tol) else np.minimum(1e-3, 1e2 * EPS * np.maximum(np.size(A, 0), np.size(A, 1)))
+    tol = np.max([tol, tol * np.max(abs(A)), tol * np.max(abs(B))])
+    is_inv = ((abs(matprod(A, B)) - np.eye(n)) <= tol).all() or ((abs(matprod(B, A) - np.eye(n))) <= tol).all()
+
+    #===================#
+    #  Calculation ends #
+    #===================#
+    return is_inv
+
+
+def isorth(A, tol=None):
+    '''
+    This function tests whether the matrix A has orthonormal columns up to the tolerance TOL.
+    '''
+
+    # Preconditions
+    if DEBUGGING:
+        if present(tol):
+            assert tol >= 0
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    num_vars = np.size(A, 1)
+
+    if num_vars > np.size(A, 0):
+        is_orth = False
+    elif (np.isnan(primasum(abs(A)))):
+        is_orth = False
+    else:
+        if present(tol):
+            is_orth = (abs(matprod(A.T, A) - np.eye(num_vars)) <= np.maximum(tol, tol * np.max(abs(A)))).all()
+        else:
+            is_orth = (abs(matprod(A.T, A) - np.eye(num_vars)) <= 0).all()
+
+    #====================#
+    #  Calculation ends  #
+    #====================#
+    return is_orth
+
+
+def get_arrays_tol(*arrays):
+    """
+    Get a relative tolerance for a set of arrays. Borrowed from COBYQA
+
+    Parameters
+    ----------
+    *arrays: tuple
+        Set of `numpy.ndarray` to get the tolerance for.
+
+    Returns
+    -------
+    float
+        Relative tolerance for the set of arrays.
+
+    Raises
+    ------
+    ValueError
+        If no array is provided.
+    """
+    if len(arrays) == 0:
+        raise ValueError("At least one array must be provided.")
+    size = max(array.size for array in arrays)
+    weight = max(
+        np.max(np.abs(array[np.isfinite(array)]), initial=1.0)
+        for array in arrays
+    )
+    return 10.0 * EPS * max(size, 1.0) * weight
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/message.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/message.py
new file mode 100644
index 0000000000000000000000000000000000000000..899d5fa63daa2b55bc6a1050f27786b569c0e92c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/message.py
@@ -0,0 +1,290 @@
+'''
+This module provides some functions that print messages to terminal/files.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+
+N.B.:
+1. In case parallelism is desirable (especially during initialization), the functions may
+have to be modified or disabled due to the IO operations.
+2. IPRINT indicates the level of verbosity, which increases with the absolute value of IPRINT.
+IPRINT = +/-3 can be expensive due to high IO operations.
+'''
+
+from .consts import DEBUGGING
+from .infos import FTARGET_ACHIEVED, MAXFUN_REACHED, MAXTR_REACHED, \
+    SMALL_TR_RADIUS, TRSUBP_FAILED, NAN_INF_F, NAN_INF_X, NAN_INF_MODEL, DAMAGING_ROUNDING, \
+    NO_SPACE_BETWEEN_BOUNDS, ZERO_LINEAR_CONSTRAINT, CALLBACK_TERMINATE
+from .present import present
+import numpy as np
+
+spaces = '   '
+
+
+def get_info_string(solver, info):
+    if info == FTARGET_ACHIEVED:
+        reason = 'the target function value is achieved.'
+    elif info == MAXFUN_REACHED:
+        reason = 'the objective function has been evaluated MAXFUN times.'
+    elif info == MAXTR_REACHED:
+        reason = 'the maximal number of trust region iterations has been reached.'
+    elif info == SMALL_TR_RADIUS:
+        reason = 'the trust region radius reaches its lower bound.'
+    elif info == TRSUBP_FAILED:
+        reason = 'a trust region step has failed to reduce the quadratic model.'
+    elif info == NAN_INF_X:
+        reason = 'NaN or Inf occurs in x.'
+    elif info == NAN_INF_F:
+        reason = 'the objective function returns NaN/+Inf.'
+    elif info == NAN_INF_MODEL:
+        reason = 'NaN or Inf occurs in the models.'
+    elif info == DAMAGING_ROUNDING:
+        reason = 'rounding errors are becoming damaging.'
+    elif info == NO_SPACE_BETWEEN_BOUNDS:
+        reason = 'there is no space between the lower and upper bounds of variable.'
+    elif info == ZERO_LINEAR_CONSTRAINT:
+        reason = 'one of the linear constraints has a zero gradient'
+    elif info == CALLBACK_TERMINATE:
+        reason = 'the callback function requested termination'
+    else:
+        reason = 'UNKNOWN EXIT FLAG'
+    ret_message = f'Return from {solver} because {reason.strip()}'
+    return ret_message
+
+
+def retmsg(solver, info, iprint, nf, f, x, cstrv=None, constr=None):
+    '''
+    This function prints messages at return.
+    '''
+    # Local variables
+    valid_exit_codes = [FTARGET_ACHIEVED, MAXFUN_REACHED, MAXTR_REACHED,
+        SMALL_TR_RADIUS, TRSUBP_FAILED, NAN_INF_F, NAN_INF_X, NAN_INF_MODEL, DAMAGING_ROUNDING,
+        NO_SPACE_BETWEEN_BOUNDS, ZERO_LINEAR_CONSTRAINT, CALLBACK_TERMINATE]
+
+    # Preconditions
+    if DEBUGGING:
+        assert info in valid_exit_codes
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    if abs(iprint) < 1:  # No printing (iprint == 0)
+        return
+    elif iprint > 0:  # Print the message to the standard out.
+        fname = ''
+    else:  # Print the message to a file named FNAME.
+        fname = f'{solver}_output.txt'
+
+    # Decide whether the problem is truly constrained.
+    if present(constr):
+        is_constrained = (np.size(constr) > 0)
+    else:
+        is_constrained = present(cstrv)
+
+    # Decide the constraint violation.
+    if present(cstrv):
+        cstrv_loc = cstrv
+    elif present(constr):
+        cstrv_loc = np.max(np.append(0, -constr))  # N.B.: We assume that the constraint is CONSTR >= 0.
+    else:
+        cstrv_loc = 0
+
+    # Decide the return message.
+    ret_message = get_info_string(solver, info)
+
+    if np.size(x) <= 2:
+        x_message = f'\nThe corresponding X is: {x}'  # Printed in one line
+    else:
+        x_message = f'\nThe corresponding X is:\n{x}'
+
+    if is_constrained:
+        nf_message = (f'\nNumber of function values = {nf}{spaces}'
+            f'Least value of F = {f}{spaces}Constraint violation = {cstrv_loc}')
+    else:
+        nf_message = f'\nNumber of function values = {nf}{spaces}Least value of F = {f}'
+
+    if is_constrained and present(constr):
+        if np.size(constr) <= 2:
+            constr_message = f'\nThe constraint value is: {constr}'  # Printed in one line
+        else:
+            constr_message = f'\nThe constraint value is:\n{constr}'
+    else:
+        constr_message = ''
+
+    # Print the message.
+    if abs(iprint) >= 2:
+        message = f'\n{ret_message}{nf_message}{x_message}{constr_message}\n'
+    else:
+        message = f'{ret_message}{nf_message}{x_message}{constr_message}\n'
+    if len(fname) > 0:
+        with open(fname, 'a') as f: f.write(message)
+    else:
+        print(message)
+
+
+def rhomsg(solver, iprint, nf, delta, f, rho, x, cstrv=None, constr=None, cpen=None):
+    '''
+    This function prints messages when RHO is updated.
+    '''
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    if abs(iprint) < 2:  # No printing
+        return
+    elif iprint > 0:  # Print the message to the standard out.
+        fname = ''
+    else:  # Print the message to a file named FNAME.
+        fname = f'{solver.strip()}_output.txt'
+
+    # Decide whether the problem is truly constrained.
+    if present(constr):
+        is_constrained = (np.size(constr) > 0)
+    else:
+        is_constrained = present(cstrv)
+
+    # Decide the constraint violation.
+    if present(cstrv):
+        cstrv_loc = cstrv
+    elif present(constr):
+        cstrv_loc = np.max(np.append(0, -constr))  # N.B.: We assume that the constraint is CONSTR >= 0.
+    else:
+        cstrv_loc = 0
+
+    if present(cpen):
+        rho_message = (f'\nNew RHO = {rho}{spaces}Delta = {delta}{spaces}'
+            f'CPEN = {cpen}')
+    else:
+        rho_message = f'\nNew RHO = {rho}{spaces}Delta = {delta}'
+
+    if np.size(x) <= 2:
+        x_message = f'\nThe corresponding X is: {x}'  # Printed in one line
+    else:
+        x_message = f'\nThe corresponding X is:\n{x}'
+
+    if is_constrained:
+        nf_message = (f'\nNumber of function values = {nf}{spaces}'
+            f'Least value of F = {f}{spaces}Constraint violation = {cstrv_loc}')
+    else:
+        nf_message = f'\nNumber of function values = {nf}{spaces}Least value of F = {f}'
+
+    if is_constrained and present(constr):
+        if np.size(constr) <= 2:
+            constr_message = f'\nThe constraint value is: {constr}'  # Printed in one line
+        else:
+            constr_message = f'\nThe constraint value is:\n{constr}'
+    else:
+        constr_message = ''
+
+    # Print the message.
+    if abs(iprint) >= 3:
+        message = f'\n{rho_message}{nf_message}{x_message}{constr_message}'
+    else:
+        message = f'{rho_message}{nf_message}{x_message}{constr_message}'
+    if len(fname) > 0:
+        with open(fname, 'a') as f: f.write(message)
+    else:
+        print(message)
+
+    #====================#
+    #  Calculation ends  #
+    #====================#
+
+
+def cpenmsg(solver, iprint, cpen):
+    '''
+    This function prints a message when CPEN is updated.
+    '''
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    if abs(iprint) < 2:  # No printing
+        return
+    elif iprint > 0:  # Print the message to the standard out.
+        fname = ''
+    else:  # Print the message to a file named FNAME.
+        fname = f'{solver.strip()}_output.txt'
+
+    # Print the message.
+    if abs(iprint) >= 3:
+        message = f'\nSet CPEN to {cpen}'
+    else:
+        message = f'\n\nSet CPEN to {cpen}'
+    if len(fname) > 0:
+        with open(fname, 'a') as f: f.write(message)
+    else:
+        print(message)
+
+    #====================#
+    #  Calculation ends  #
+    #====================#
+
+
+def fmsg(solver, state, iprint, nf, delta, f, x, cstrv=None, constr=None):
+    '''
+    This subroutine prints messages for each evaluation of the objective function.
+    '''
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    if abs(iprint) < 2:  # No printing
+        return
+    elif iprint > 0:  # Print the message to the standard out.
+        fname = ''
+    else:  # Print the message to a file named FNAME.
+        fname = f'{solver.strip()}_output.txt'
+
+    # Decide whether the problem is truly constrained.
+    if present(constr):
+        is_constrained = (np.size(constr) > 0)
+    else:
+        is_constrained = present(cstrv)
+
+    # Decide the constraint violation.
+    if present(cstrv):
+        cstrv_loc = cstrv
+    elif present(constr):
+        cstrv_loc = np.max(np.append(0, -constr))  # N.B.: We assume that the constraint is CONSTR >= 0.
+    else:
+        cstrv_loc = 0
+
+    delta_message = f'\n{state} step with radius = {delta}'
+
+    if is_constrained:
+        nf_message = (f'\nNumber of function values = {nf}{spaces}'
+            f'Least value of F = {f}{spaces}Constraint violation = {cstrv_loc}')
+    else:
+        nf_message = f'\nNumber of function values = {nf}{spaces}Least value of F = {f}'
+
+    if np.size(x) <= 2:
+        x_message = f'\nThe corresponding X is: {x}'  # Printed in one line
+    else:
+        x_message = f'\nThe corresponding X is:\n{x}'
+
+    if is_constrained and present(constr):
+        if np.size(constr) <= 2:
+            constr_message = f'\nThe constraint value is: {constr}'  # Printed in one line
+        else:
+            constr_message = f'\nThe constraint value is:\n{constr}'
+    else:
+        constr_message = ''
+
+    # Print the message.
+    message = f'{delta_message}{nf_message}{x_message}{constr_message}'
+    if len(fname) > 0:
+        with open(fname, 'a') as f: f.write(message)
+    else:
+        print(message)
+
+    #====================#
+    #  Calculation ends  #
+    #====================#
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/powalg.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/powalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a8268b2631ba830f8bd36129dd10a3fb9133dc1
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/powalg.py
@@ -0,0 +1,131 @@
+'''
+This module provides some Powell-style linear algebra procedures.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+import numpy as np
+from .linalg import isminor, planerot, matprod, inprod, hypot
+from .consts import DEBUGGING, EPS
+
+
+def qradd_Rdiag(c, Q, Rdiag, n):
+    '''
+    This function updates the QR factorization of an MxN matrix A of full column rank, attempting to
+    add a new column C to this matrix as the LAST column while maintaining the full-rankness.
+    Case 1. If C is not in range(A) (theoretically, it implies N < M), then the new matrix is np.hstack([A, C])
+    Case 2. If C is in range(A), then the new matrix is np.hstack([A[:, :n-1], C])
+    N.B.:
+    0. Instead of R, this subroutine updates Rdiag, which is np.diag(R), with a size at most M and at
+    least min(m, n+1). The number is min(m, n+1) rather than min(m, n) as n may be augmented by 1 in
+    the function.
+    1. With the two cases specified as above, this function does not need A as an input.
+    2. The function changes only Q[:, nsave:m] (nsave is the original value of n) and
+    R[:, n-1] (n takes the updated value)
+    3. Indeed, when C is in range(A), Powell wrote in comments that "set iOUT to the index of the
+    constraint (here, column of A --- Zaikun) to be deleted, but branch if no suitable index can be
+    found". The idea is to replace a column of A by C so that the new matrix still has full rank
+    (such a column must exist unless C = 0). But his code essentially sets iout=n always. Maybe he
+    found this worked well enough in practice. Meanwhile, Powell's code includes a snippet that can
+    never be reached, which was probably intended to deal with the case that IOUT != n
+    '''
+    m = Q.shape[1]
+    nsave = n  # Needed for debugging (only)
+
+    # As in Powell's COBYLA, CQ is set to 0 at the positions with CQ being negligible as per ISMINOR.
+    # This may not be the best choice if the subroutine is used in other contexts, e.g. LINCOA.
+    cq = matprod(c, Q)
+    cqa = matprod(abs(c), abs(Q))
+    # The line below basically makes an element of cq 0 if adding it to the corresponding element of
+    # cqa does not change the latter.
+    cq = np.array([0 if isminor(cqi, cqai) else cqi for cqi, cqai in zip(cq, cqa)])
+
+    # Update Q so that the columns of Q[:, n+1:m] are orthogonal to C. This is done by applying a 2D
+    # Givens rotation to Q[:, [k, k+1]] from the right to zero C' @ Q[:, k+1] out for K=n+1, ... m-1.
+    # Nothing will be done if n >= m-1
+    for k in range(m-2, n-1, -1):
+        if abs(cq[k+1]) > 0:
+            # Powell wrote cq[k+1] != 0 instead of abs. The two differ if cq[k+1] is NaN.
+            # If we apply the rotation below when cq[k+1] = 0, then cq[k] will get updated to |cq[k]|.
+            G = planerot(cq[k:k+2])
+            Q[:, [k, k+1]] = matprod(Q[:, [k, k+1]], G.T)
+            cq[k] = hypot(*cq[k:k+2])
+
+    # Augment n by 1 if C is not in range(A)
+    if n < m:
+        # Powell's condition for the following if: cq[n+1] != 0
+        if abs(cq[n]) > EPS**2 and not isminor(cq[n], cqa[n]):
+            n += 1
+
+    # Update Rdiag so that Rdiag[n] = cq[n] = np.dot(c, q[:, n]). Note that N may be been augmented.
+    if n - 1 >= 0 and n - 1 < m:  # n >= m should not happen unless the input is wrong
+        Rdiag[n - 1] = cq[n - 1]
+
+    if DEBUGGING:
+        assert nsave <= n <= min(nsave + 1, m)
+        assert n <= len(Rdiag) <= m
+        assert Q.shape == (m, m)
+
+    return Q, Rdiag, n
+
+
+def qrexc_Rdiag(A, Q, Rdiag, i):  # Used in COBYLA
+    '''
+    This function updates the QR factorization for an MxN matrix A=Q@R so that the updated Q and
+    R form a QR factorization of [A_0, ..., A_{I-1}, A_{I+1}, ..., A_{N-1}, A_I] which is the matrix
+    obtained by rearranging columns [I, I+1, ... N-1] of A to [I+1, ..., N-1, I]. Here A is ASSUMED TO
+    BE OF FULL COLUMN RANK, Q is a matrix whose columns are orthogonal, and R, which is not present,
+    is an upper triangular matrix whose diagonal entries are nonzero. Q and R need not be square.
+    N.B.:
+    0. Instead of R, this function updates Rdiag, which is np.diag(R), the size being n.
+    1. With L = Q.shape[1] = R.shape[0], we have M >= L >= N. Most often L = M or N.
+    2. This function changes only Q[:, i:] and Rdiag[i:]
+    3. (NDB 20230919) In Python, i is either icon or nact - 2, whereas in FORTRAN it is either icon or nact - 1.
+    '''
+
+    # Sizes
+    m, n = A.shape
+
+    # Preconditions
+    assert n >= 1 and n <= m
+    assert i >= 0 and i < n
+    assert len(Rdiag) == n
+    assert Q.shape[0] == m and Q.shape[1] >= n and Q.shape[1] <= m
+    # tol = max(1.0E-8, min(1.0E-1, 1.0E8 * EPS * m + 1))
+    # assert isorth(Q, tol)  # Costly!
+
+
+    if i < 0 or i >= n:
+        return Q, Rdiag
+
+    # Let R be the upper triangular matrix in the QR factorization, namely R = Q.T@A.
+    # For each k, find the Givens rotation G with G@(R[k:k+2, :]) = [hypt, 0], and update Q[:, k:k+2]
+    # to Q[:, k:k+2]@(G.T). Then R = Q.T@A is an upper triangular matrix as long as A[:, [k, k+1]] is
+    # updated to A[:, [k+1, k]]. Indeed, this new upper triangular matrix can be obtained by first
+    # updating R[[k, k+1], :] to G@(R[[k, k+1], :]) and then exchanging its columns K and K+1; at the same
+    # time, entries k and k+1 of R's diagonal Rdiag become [hypt, -(Rdiag[k+1]/hypt)*RDiag[k]].
+    # After this is done for each k = 0, ..., n-2, we obtain the QR factorization of the matrix that
+    # rearranges columns [i, i+1, ... n-1] of A as [i+1, ..., n-1, i].
+    # Powell's code, however, is slightly different: before everything, he first exchanged columns k and
+    # k+1 of Q (as well as rows k and k+1 of R). This makes sure that the entries of the update Rdiag
+    # are all positive if it is the case for the original Rdiag.
+    for k in range(i, n-1):
+        G = planerot([Rdiag[k+1], inprod(Q[:, k], A[:, k+1])])
+        Q[:, [k, k+1]] = matprod(Q[:, [k+1, k]], (G.T))
+        # Powell's code updates Rdiag in the following way:
+        # hypt = np.sqrt(Rdiag[k+1]**2 + np.dot(Q[:, k], A[:, k+1])**2)
+        # Rdiag[[k, k+1]] = [hypt, (Rdiag[k+1]/hypt)*Rdiag[k]]
+        # Note that Rdiag[n-1] inherits all rounding in Rdiag[i:n-1] and Q[:, i:n-1] and hence contains
+        # significant errors. Thus we may modify Powell's code to set only Rdiag[k] = hypt here and then
+        # calculate Rdiag[n] by an inner product after the loop. Nevertheless, we simple calculate RDiag
+        # from scratch below.
+
+    # Calculate Rdiag(i:n) from scratch
+    Rdiag[i:n-1] = [inprod(Q[:, k], A[:, k+1]) for k in range(i, n-1)]
+    Rdiag[n-1] = inprod(Q[:, n-1], A[:, i])
+
+    return Q, Rdiag
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/preproc.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/preproc.py
new file mode 100644
index 0000000000000000000000000000000000000000..465b0b2de289b61be4c560dec89482887002aa24
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/preproc.py
@@ -0,0 +1,277 @@
+'''
+This is a module that preprocesses the inputs.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+from .consts import DEBUGGING, EPS, IPRINT_DEFAULT, FTARGET_DEFAULT, \
+    MIN_MAXFILT, MAXFILT_DEFAULT, MAXHISTMEM, ETA1_DEFAULT, ETA2_DEFAULT, \
+    GAMMA1_DEFAULT, GAMMA2_DEFAULT, RHOBEG_DEFAULT, RHOEND_DEFAULT, \
+    CTOL_DEFAULT, CWEIGHT_DEFAULT
+from .present import present
+from warnings import warn
+import numpy as np
+
+
+def preproc(solver, num_vars, iprint, maxfun, maxhist, ftarget, rhobeg, rhoend,
+            num_constraints=None, npt=None, maxfilt=None, ctol=None, cweight=None,
+            eta1=None, eta2=None, gamma1=None, gamma2=None, is_constrained=None, has_rhobeg=None,
+            honour_x0=None, xl=None, xu=None, x0=None):
+    '''
+    This subroutine preprocesses the inputs. It does nothing to the inputs that are valid.
+    '''
+    # Preconditions
+    if DEBUGGING:
+        assert num_vars >= 1
+        if present(num_constraints):
+            assert num_constraints >= 0
+            assert num_constraints == 0 or solver.lower() == 'cobyla'
+        if solver.lower() == 'cobyla' and present(num_constraints) and present(is_constrained):
+            assert num_constraints == 0 or is_constrained
+        if solver.lower() == 'bobyqa':
+            assert present(xl) and present(xu)
+            assert all(xu - xl >= 2 * EPS)
+        if present(honour_x0):
+            assert solver.lower() == 'bobyqa' and present(has_rhobeg) and present(xl) and present(xu) and present(x0)
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # Read num_constraints, if necessary
+    num_constraints = num_constraints if (present(num_constraints) and solver.lower() == 'cobyla') else 0
+
+    # Decide whether the problem is truly constrained
+    is_constrained = is_constrained if (present(is_constrained)) else num_constraints > 0
+
+    # Validate IPRINT
+    if np.abs(iprint) > 3:
+        iprint = IPRINT_DEFAULT
+        warn(f'{solver}: Invalid IPRINT; it should be 0, 1, -1, 2, -2, 3, or -3; it is set to {iprint}')
+
+    # Validate MAXFUN
+    if solver.lower() == 'uobyqa':
+        min_maxfun = (num_vars + 1) * (num_vars + 2) / 2 + 1
+        min_maxfun_str = '(N+1)(N+2)/2 + 1'
+    elif solver.lower() == 'cobyla':
+        min_maxfun = num_vars + 2
+        min_maxfun_str = 'num_vars + 2'
+    else:  # CASE ('NEWUOA', 'BOBYQA', 'LINCOA')
+        min_maxfun = num_vars + 3
+        min_maxfun_str = 'num_vars + 3'
+    if maxfun < min_maxfun:
+        maxfun = min_maxfun
+        warn(f'{solver}: Invalid MAXFUN; it should be at least {min_maxfun_str}; it is set to {maxfun}')
+
+    # Validate MAXHIST
+    if maxhist < 0:
+        maxhist = maxfun
+        warn(f'{solver}: Invalid MAXHIST; it should be a nonnegative integer; it is set to {maxhist}')
+    maxhist = min(maxhist, maxfun)  # MAXHIST > MAXFUN is never needed.
+
+    # Validate FTARGET
+    if np.isnan(ftarget):
+        ftarget = FTARGET_DEFAULT
+        warn(f'{solver}: Invalid FTARGET; it should be a real number; it is set to {ftarget}')
+
+    # Validate NPT
+    if (solver.lower() == 'newuoa' or solver.lower() == 'bobyqa' or solver.lower() == 'lincoa') and present(npt):
+        if (npt < num_vars + 2 or npt > min(maxfun - 1, ((num_vars + 2) * (num_vars + 1)) / 2)):
+            npt = int(min(maxfun - 1, 2 * num_vars + 1))
+            warn(f'{solver}: Invalid NPT; it should be an integer in the interval [N+2, (N+1)(N+2)/2] and less than MAXFUN; it is set to {npt}')
+
+    # Validate MAXFILT
+    if present(maxfilt) and (solver.lower() == 'lincoa' or solver.lower() == 'cobyla'):
+        maxfilt_in = maxfilt
+        if maxfilt < 1:
+            maxfilt = MAXFILT_DEFAULT  # The inputted MAXFILT is obviously wrong.
+        else:
+            maxfilt = max(MIN_MAXFILT, maxfilt)  # The inputted MAXFILT is too small.
+        # Further revise MAXFILT according to MAXHISTMEM.
+        if solver.lower() == 'lincoa':
+            unit_memo = (num_vars + 2) * np.dtype(float).itemsize
+        elif solver.lower() == 'cobyla':
+            unit_memo = (num_constraints + num_vars + 2) * np.dtype(float).itemsize
+        else:
+            unit_memo = 1
+        # We cannot simply set MAXFILT = MIN(MAXFILT, MAXHISTMEM/...), as they may not have
+        # the same kind, and compilers may complain. We may convert them, but overflow may occur.
+        if maxfilt > MAXHISTMEM / unit_memo:
+            maxfilt = int(MAXHISTMEM / unit_memo)  # Integer division.
+        maxfilt = min(maxfun, max(MIN_MAXFILT, maxfilt))
+        if is_constrained:
+            if maxfilt_in < 1:
+                warn(f'{solver}: Invalid MAXFILT; it should be a positive integer; it is set to  {maxfilt}')
+            elif maxfilt_in < min(maxfun, MIN_MAXFILT):
+                warn(f'{solver}: MAXFILT is too small; it is set to {maxfilt}')
+            elif maxfilt < min(maxfilt_in, maxfun):
+                warn(f'{solver}: MAXFILT is set to {maxfilt} due to memory limit')
+
+    # Validate ETA1 and ETA2
+    eta1_local = eta1 if present(eta1) else ETA1_DEFAULT
+    eta2_local = eta2 if present(eta2) else ETA2_DEFAULT
+
+    # When the difference between ETA1 and ETA2 is tiny, we force them to equal.
+    # See the explanation around RHOBEG and RHOEND for the reason.
+    if present(eta1) and present(eta2):
+        if np.abs(eta1 - eta2) < 1.0E2 * EPS * max(np.abs(eta1), 1):
+            eta2 = eta1
+
+    if present(eta1):
+        if np.isnan(eta1):
+            # In this case, we take the value hard coded in Powell's original code
+            # without any warning. It is useful when interfacing with MATLAB/Python.
+            eta1 = ETA1_DEFAULT
+        elif eta1 < 0 or eta1 >= 1:
+            # Take ETA2 into account if it has a valid value.
+            if present(eta2) and eta2_local > 0 and eta2_local <= 1:
+                eta1 = max(EPS, eta2 / 7.0)
+            else:
+                eta1 = ETA1_DEFAULT
+            warn(f'{solver}: Invalid ETA1; it should be in the interval [0, 1) and not more than ETA2; it is set to {eta1}')
+
+    if present(eta2):
+        if np.isnan(eta2):
+            # In this case, we take the value hard coded in Powell's original code
+            # without any warning. It is useful when interfacing with MATLAB/Python.
+            eta2 = ETA2_DEFAULT
+        elif present(eta1) and (eta2 < eta1_local or eta2 > 1):
+            eta2 = (eta1 + 2) / 3.0
+            warn(f'{solver}: Invalid ETA2; it should be in the interval [0, 1) and not less than ETA1; it is set to {eta2}')
+
+    # Validate GAMMA1 and GAMMA2
+    if present(gamma1):
+        if np.isnan(gamma1):
+            # In this case, we take the value hard coded in Powell's original code
+            # without any warning. It is useful when interfacing with MATLAB/Python.
+            gamma1 = GAMMA1_DEFAULT
+        elif gamma1 <= 0 or gamma1 >= 1:
+            gamma1 = GAMMA1_DEFAULT
+            warn(f'{solver}: Invalid GAMMA1; it should in the interval (0, 1); it is set to {gamma1}')
+
+    if present(gamma2):
+        if np.isnan(gamma2):
+            # In this case, we take the value hard coded in Powell's original code
+            # without any warning. It is useful when interfacing with MATLAB/Python.
+            gamma2 = GAMMA2_DEFAULT
+        elif gamma2 < 1 or np.isinf(gamma2):
+            gamma2 = GAMMA2_DEFAULT
+            warn(f'{solver}: Invalid GAMMA2; it should be a real number not less than 1; it is set to {gamma2}')
+
+    # Validate RHOBEG and RHOEND
+
+    if np.abs(rhobeg - rhoend) < 1.0e2 * EPS * np.maximum(np.abs(rhobeg), 1):
+        # When the data is passed from the interfaces (e.g., MEX) to the Fortran code, RHOBEG, and RHOEND
+        # may change a bit. It was observed in a MATLAB test that MEX passed 1 to Fortran as
+        # 0.99999999999999978. Therefore, if we set RHOEND = RHOBEG in the interfaces, then it may happen
+        # that RHOEND > RHOBEG, which is considered as an invalid input. To avoid this situation, we
+        # force RHOBEG and RHOEND to equal when the difference is tiny.
+        rhoend = rhobeg
+
+    # Revise the default values for RHOBEG/RHOEND according to the solver.
+    if solver.lower() == 'bobyqa':
+        rhobeg_default = np.maximum(EPS, np.min(RHOBEG_DEFAULT, np.min(xu - xl) / 4.0))
+        rhoend_default = np.maximum(EPS, np.min(0.1 * rhobeg_default, RHOEND_DEFAULT))
+    else:
+        rhobeg_default = RHOBEG_DEFAULT
+        rhoend_default = RHOEND_DEFAULT
+
+    if solver.lower() == 'bobyqa':
+        # Do NOT merge the IF below into the ELIF above! Otherwise, XU and XL may be accessed even if
+        # the solver is not BOBYQA, because the logical evaluation is not short-circuit.
+        if rhobeg > np.min(xu - xl) / 2:
+            # Do NOT make this revision if RHOBEG not positive or not finite, because otherwise RHOBEG
+            # will get a huge value when XU or XL contains huge values that indicate unbounded variables.
+            rhobeg = np.min(xu - xl) / 4.0  # Here, we do not take RHOBEG_DEFAULT.
+            warn(f'{solver}: Invalid RHOBEG; {solver} requires 0 < RHOBEG <= np.min(XU-XL)/2; it is set to np.min(XU-XL)/4')
+    if rhobeg <= 0 or np.isnan(rhobeg) or np.isinf(rhobeg):
+        # Take RHOEND into account if it has a valid value. We do not do this if the solver is BOBYQA,
+        # which requires that RHOBEG <= (XU-XL)/2.
+        if np.isfinite(rhoend) and rhoend > 0 and solver.lower() != 'bobyqa':
+            rhobeg = max(10 * rhoend, rhobeg_default)
+        else:
+            rhobeg = rhobeg_default
+        warn(f'{solver}: Invalid RHOBEG; it should be a positive number; it is set to {rhobeg}')
+
+    if rhoend <= 0 or rhobeg < rhoend or np.isnan(rhoend) or np.isinf(rhoend):
+        rhoend = max(EPS, min(0.1 * rhobeg, rhoend_default))
+        warn(f'{solver}: Invalid RHOEND; it should be a positive number and RHOEND <= RHOBEG; it is set to {rhoend}')
+
+    # For BOBYQA, revise X0 or RHOBEG so that the distance between X0 and the inactive bounds is at
+    # least RHOBEG. If HONOUR_X0 == TRUE, revise RHOBEG if needed; otherwise, revise HONOUR_X0 if needed.
+    if present(honour_x0):
+        if honour_x0:
+            rhobeg_old = rhobeg;
+            lbx = np.isfinite(xl) & (x0 - xl <= EPS * np.maximum(1, np.abs(xl))) # X0 essentially equals XL
+            ubx = np.isfinite(xu) & (x0 - xu >= -EPS * np.maximum(1, np.abs(xu))) # X0 essentially equals XU
+            x0[lbx] = xl[lbx]
+            x0[ubx] = xu[ubx]
+            rhobeg = max(EPS, np.min([rhobeg, x0[~lbx] - xl[~lbx], xu[~ubx] - x0[~ubx]]))
+            if rhobeg_old - rhobeg > EPS * max(1, rhobeg_old):
+                rhoend = max(EPS, min(0.1 * rhobeg, rhoend)) # We do not revise RHOEND unless RHOBEG is truly revised.
+                if has_rhobeg:
+                    warn(f'{solver}: RHOBEG is revised to {rhobeg} and RHOEND to at most 0.1*RHOBEG so that the distance between X0 and the inactive bounds is at least RHOBEG')
+            else:
+                rhoend = np.minimum(rhoend, rhobeg)  # This may update RHOEND slightly.
+        else:
+            x0_old = x0  # Recorded to see whether X0 is really revised.
+            # N.B.: The following revision is valid only if XL <= X0 <= XU and RHOBEG <= MINVAL(XU-XL)/2,
+            # which should hold at this point due to the revision of RHOBEG and moderation of X0.
+            # The cases below are mutually exclusive in precise arithmetic as MINVAL(XU-XL) >= 2*RHOBEG.
+            lbx = x0 <= xl + 0.5 * rhobeg
+            lbx_plus = (x0 > xl + 0.5 * rhobeg) & (x0 < xl + rhobeg)
+            ubx = x0 >= xu - 0.5 * rhobeg
+            ubx_minus = (x0 < xu - 0.5 * rhobeg) & (x0 > xu - rhobeg)
+            x0[lbx] = xl[lbx]
+            x0[lbx_plus] = xl[lbx_plus] + rhobeg
+            x0[ubx] = xu[ubx]
+            x0[ubx_minus] = xu[ubx_minus] - rhobeg
+
+            if (any(np.abs(x0_old - x0) > 0)):
+                warn(f'{solver}: X0 is revised so that the distance between X0 and the inactive bounds is at least RHOBEG set HONOUR_X0 to .TRUE. if you prefer to keep X0 unchanged')
+
+    # Validate CTOL (it can be 0)
+    if (present(ctol)):
+        if (np.isnan(ctol) or ctol < 0):
+            ctol = CTOL_DEFAULT
+            if (is_constrained):
+                warn(f'{solver}: Invalid CTOL; it should be a nonnegative number; it is set to {ctol}')
+
+    # Validate CWEIGHT (it can be +Inf)
+    if (present(cweight)):
+        if (np.isnan(cweight) or cweight < 0):
+            cweight = CWEIGHT_DEFAULT
+            if (is_constrained):
+                warn(f'{solver}: Invalid CWEIGHT; it should be a nonnegative number; it is set to {cweight}')
+
+    #====================#
+    #  Calculation ends  #
+    #====================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert abs(iprint) <= 3
+        assert maxhist >= 0 and maxhist <= maxfun
+        if present(npt):
+            assert maxfun >= npt + 1
+            assert npt >= 3
+        if present(maxfilt):
+            assert maxfilt >= np.minimum(MIN_MAXFILT, maxfun) and maxfilt <= maxfun
+        if present(eta1) and present(eta2):
+            assert eta1 >= 0 and eta1 <= eta2 and eta2 < 1
+        if present(gamma1) and present(gamma2):
+            assert gamma1 > 0 and gamma1 < 1 and gamma2 > 1
+        assert rhobeg >= rhoend and rhoend > 0
+        if solver.lower() == 'bobyqa':
+            assert all(rhobeg <= (xu - xl) / 2)
+            assert all(np.isfinite(x0))
+            assert all(x0 >= xl and (x0 <= xl or x0 >= xl + rhobeg))
+            assert all(x0 <= xu and (x0 >= xu or x0 <= xu - rhobeg))
+        if present(ctol):
+            assert ctol >= 0
+
+    return iprint, maxfun, maxhist, ftarget, rhobeg, rhoend, npt, maxfilt, ctol, cweight, eta1, eta2, gamma1, gamma2, x0
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/present.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/present.py
new file mode 100644
index 0000000000000000000000000000000000000000..15f8b47b6721994399ebafff419087afe582b2b8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/present.py
@@ -0,0 +1,5 @@
+def present(x):
+    '''
+    This is a Python equivalent of the Fortran 'present' function for optional arguments.
+    '''
+    return x is not None
\ No newline at end of file
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/ratio.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/ratio.py
new file mode 100644
index 0000000000000000000000000000000000000000..c1c3a28ef4a49eeb47438c4a6ad3fb10e83dbc92
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/ratio.py
@@ -0,0 +1,54 @@
+'''
+This module calculates the reduction ratio for trust-region methods.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+from .consts import DEBUGGING, REALMAX
+import numpy as np
+
+def redrat(ared, pred, rshrink):
+    '''
+    This function evaluates the reduction ratio of a trust-region step, handling inf/nan properly.
+    '''
+
+    # Preconditions
+    if DEBUGGING:
+        assert rshrink >= 0
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    if np.isnan(ared):
+        # This should not happen in unconstrained problems due to the moderated extreme barrier.
+        ratio = -REALMAX
+    elif np.isnan(pred) or pred <= 0:
+        # The trust-region subproblem solver fails in this rare case. Instead of terminating as Powell's
+        # original code does, we set ratio as follows so that the solver may continue to progress.
+        if ared > 0:
+            # The trial point will be accepted, but the trust-region radius will be shrunk if rshrink>0
+            ratio = rshrink/2
+        else:
+            # Set the ration to a large negative number to signify a bad trust-region step, so that the
+            # solver will check whether to take a geometry step or reduce rho.
+            ratio = -REALMAX
+    elif np.isposinf(pred) and np.isposinf(ared):
+        ratio = 1  # ared/pred = NaN if calculated directly
+    elif np.isposinf(pred) and np.isneginf(ared):
+        ratio = -REALMAX  # ared/pred = NaN if calculated directly
+    else:
+        ratio = ared/pred
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert not np.isnan(ratio)
+    return ratio
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/redrho.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/redrho.py
new file mode 100644
index 0000000000000000000000000000000000000000..4b4c09b8400e694ed6f7016273aecfd384bf38a0
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/redrho.py
@@ -0,0 +1,47 @@
+'''
+This module provides a function that calculates RHO when it needs to be reduced.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+from .consts import DEBUGGING
+import numpy as np
+
+def redrho(rho_in, rhoend):
+    '''
+    This function calculates RHO when it needs to be reduced.
+    The scheme is shared by UOBYQA, NEWUOA, BOBYQA, LINCOA. For COBYLA, Powell's code reduces RHO by
+    'RHO *= 0.5; if RHO <= 1.5 * RHOEND: RHO = RHOEND' as specified in (11) of the COBYLA
+    paper. However, this scheme seems to work better, especially after we introduce DELTA.
+    '''
+
+    # Preconditions
+    if DEBUGGING:
+        assert rho_in > rhoend > 0
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    rho_ratio = rho_in / rhoend
+
+    if rho_ratio > 250:
+        rho = 0.1 * rho_in
+    elif rho_ratio <= 16:
+        rho = rhoend
+    else:
+        rho = np.sqrt(rho_ratio) * rhoend  # rho = np.sqrt(rho * rhoend)
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert rho_in > rho >= rhoend
+
+    return rho
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/selectx.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/selectx.py
new file mode 100644
index 0000000000000000000000000000000000000000..63d76ad709dac1c0a4d246ba24566f6c8e655124
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/pyprima/common/selectx.py
@@ -0,0 +1,296 @@
+'''
+This module provides subroutines that ensure the returned X is optimal among all the calculated
+points in the sense that no other point achieves both lower function value and lower constraint
+violation at the same time. This module is needed only in the constrained case.
+
+Translated from Zaikun Zhang's modern-Fortran reference implementation in PRIMA.
+
+Dedicated to late Professor M. J. D. Powell FRS (1936--2015).
+
+Python translation by Nickolai Belakovski.
+'''
+
+import numpy as np
+import numpy.typing as npt
+from .consts import DEBUGGING, EPS, CONSTRMAX, REALMAX, FUNCMAX
+from .present import present
+
+def isbetter(f1: float, c1: float, f2: float, c2: float, ctol: float) -> bool:
+    '''
+    This function compares whether FC1 = (F1, C1) is (strictly) better than FC2 = (F2, C2), which
+    basically means that (F1 < F2 and C1 <= C2) or (F1 <= F2 and C1 < C2).
+    It takes care of the cases where some of these values are NaN or Inf, even though some cases
+    should never happen due to the moderated extreme barrier.
+    At return, BETTER = TRUE if and only if (F1, C1) is better than (F2, C2).
+    Here, C means constraint violation, which is a nonnegative number.
+    '''
+
+    # Preconditions
+    if DEBUGGING:
+        assert not any(np.isnan([f1, c1]) | np.isposinf([f2, c2]))
+        assert not any(np.isnan([f2, c2]) | np.isposinf([f2, c2]))
+        assert c1 >= 0 and c2 >= 0
+        assert ctol >= 0
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    is_better = False
+    # Even though NaN/+Inf should not occur in FC1 or FC2 due to the moderated extreme barrier, for
+    # security and robustness, the code below does not make this assumption.
+    is_better = is_better or (any(np.isnan([f1, c1]) | np.isposinf([f1, c1])) and not any(np.isnan([f2, c2]) | np.isposinf([f2, c2])))
+
+    is_better = is_better or (f1 < f2 and c1 <= c2)
+    is_better = is_better or (f1 <= f2 and c1 < c2)
+
+    # If C1 <= CTOL and C2 is significantly larger/worse than CTOL, i.e., C2 > MAX(CTOL,CREF),
+    # then FC1 is better than FC2 as long as F1 < REALMAX. Normally CREF >= CTOL so MAX(CTOL, CREF)
+    # is indeed CREF. However, this may not be true if CTOL > 1E-1*CONSTRMAX.
+    cref = 10 * max(EPS, min(ctol, 1.0E-2 * CONSTRMAX))  # The MIN avoids overflow.
+    is_better = is_better or (f1 < REALMAX and c1 <= ctol and (c2 > max(ctol, cref) or np.isnan(c2)))
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert not (is_better and f1 >= f2 and c1 >= c2)
+        assert is_better or not (f1 <= f2 and c1 < c2)
+        assert is_better or not (f1 < f2 and c1 <= c2)
+
+    return is_better
+
+
+def savefilt(cstrv, ctol, cweight, f, x, nfilt, cfilt, ffilt, xfilt, constr=None, confilt=None):
+    '''
+    This subroutine saves X, F, and CSTRV in XFILT, FFILT, and CFILT (and CONSTR in CONFILT
+    if they are present), unless a vector in XFILT[:, :NFILT] is better than X.
+    If X is better than some vectors in XFILT[:, :NFILT] then these vectors will be
+    removed. If X is not better than any of XFILT[:, :NFILT], but NFILT == MAXFILT,
+    then we remove a column from XFILT according to the merit function
+    PHI = FFILT + CWEIGHT * max(CFILT - CTOL, 0)
+    N.B.:
+    1. Only XFILT[:, :NFILT] and FFILT[:, :NFILT] etc contains valid information,
+    while XFILT[:, NFILT+1:MAXFILT] and FFILT[:, NFILT+1:MAXFILT] etc are not
+    initialized yet.
+    2. We decide whether and X is better than another by the ISBETTER function
+    '''
+
+    # Sizes
+    if present(constr):
+        num_constraints = len(constr)
+    else:
+        num_constraints = 0
+    num_vars = len(x)
+    maxfilt = len(ffilt)
+
+    # Preconditions
+    if DEBUGGING:
+        # Check the size of X.
+        assert num_vars >= 1
+        # Check CWEIGHT and CTOL
+        assert cweight >= 0
+        assert ctol >= 0
+        # Check NFILT
+        assert nfilt >= 0 and nfilt <= maxfilt
+        # Check the sizes of XFILT, FFILT, CFILT.
+        assert maxfilt >= 1
+        assert np.size(xfilt, 0) == num_vars and np.size(xfilt, 1) == maxfilt
+        assert np.size(cfilt) == maxfilt
+        # Check the values of XFILT, FFILT, CFILT.
+        assert not (np.isnan(xfilt[:, :nfilt])).any()
+        assert not any(np.isnan(ffilt[:nfilt]) | np.isposinf(ffilt[:nfilt]))
+        assert not any(cfilt[:nfilt] < 0 | np.isnan(cfilt[:nfilt]) | np.isposinf(cfilt[:nfilt]))
+        # Check the values of X, F, CSTRV.
+        # X does not contain NaN if X0 does not and the trust-region/geometry steps are proper.
+        assert not any(np.isnan(x))
+        # F cannot be NaN/+Inf due to the moderated extreme barrier.
+        assert not (np.isnan(f) | np.isposinf(f))
+        # CSTRV cannot be NaN/+Inf due to the moderated extreme barrier.
+        assert not (cstrv < 0 | np.isnan(cstrv) | np.isposinf(cstrv))
+        # Check CONSTR and CONFILT.
+        assert present(constr) == present(confilt)
+        if present(constr):
+            # CONSTR cannot contain NaN/-Inf due to the moderated extreme barrier.
+            assert not any(np.isnan(constr) | np.isneginf(constr))
+            assert np.size(confilt, 0) == num_constraints and np.size(confilt, 1) == maxfilt
+            assert not (np.isnan(confilt[:, :nfilt]) | np.isneginf(confilt[:, :nfilt])).any()
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # Return immediately if any column of XFILT is better than X.
+    if any((isbetter(ffilt_i, cfilt_i, f, cstrv, ctol) for ffilt_i, cfilt_i in zip(ffilt[:nfilt], cfilt[:nfilt]))) or \
+        any(np.logical_and(ffilt[:nfilt] <= f, cfilt[:nfilt] <= cstrv)):
+        return nfilt, cfilt, ffilt, xfilt, confilt
+
+    # Decide which columns of XFILT to keep.
+    keep = np.logical_not([isbetter(f, cstrv, ffilt_i, cfilt_i, ctol) for ffilt_i, cfilt_i in zip(ffilt[:nfilt], cfilt[:nfilt])])
+
+    # If NFILT == MAXFILT and X is not better than any column of XFILT, then we remove the worst column
+    # of XFILT according to the merit function PHI = FFILT + CWEIGHT * MAX(CFILT - CTOL, ZERO).
+    if sum(keep) == maxfilt:  # In this case, NFILT = SIZE(KEEP) = COUNT(KEEP) = MAXFILT > 0.
+        cfilt_shifted = np.maximum(cfilt - ctol, 0)
+        if cweight <= 0:
+            phi = ffilt
+        elif np.isposinf(cweight):
+            phi = cfilt_shifted
+            # We should not use CFILT here; if MAX(CFILT_SHIFTED) is attained at multiple indices, then
+            # we will check FFILT to exhaust the remaining degree of freedom.
+        else:
+            phi = np.maximum(ffilt, -REALMAX)
+            phi = np.nan_to_num(phi, nan=-REALMAX)  # Replace NaN with -REALMAX and +/- inf with large numbers
+            phi += cweight * cfilt_shifted
+        # We select X to maximize PHI. In case there are multiple maximizers, we take the one with the
+        # largest CSTRV_SHIFTED; if there are more than one choices, we take the one with the largest F;
+        # if there are several candidates, we take the one with the largest CSTRV; if the last comparison
+        # still leads to more than one possibilities, then they are equally bad and we choose the first.
+        # N.B.:
+        # 1. This process is the opposite of selecting KOPT in SELECTX.
+        # 2. In finite-precision arithmetic, PHI_1 == PHI_2 and CSTRV_SHIFTED_1 == CSTRV_SHIFTED_2 do
+        # not ensure that F_1 == F_2!
+        phimax = max(phi)
+        cref = max(cfilt_shifted[phi >= phimax])
+        fref = max(ffilt[cfilt_shifted >= cref])
+        kworst = np.ma.array(cfilt, mask=(ffilt > fref)).argmax()
+        if kworst < 0 or kworst >= len(keep):  #  For security. Should not happen.
+            kworst = 0
+        keep[kworst] = False
+
+    # Keep the good xfilt values and remove all the ones that are strictly worse than the new x.
+    nfilt = sum(keep)
+    index_to_keep = np.where(keep)[0]
+    xfilt[:, :nfilt] = xfilt[:, index_to_keep]
+    ffilt[:nfilt] = ffilt[index_to_keep]
+    cfilt[:nfilt] = cfilt[index_to_keep]
+    if confilt is not None and constr is not None:
+        confilt[:, :nfilt] = confilt[:, index_to_keep]
+
+    # Once we have removed all the vectors that are strictly worse than x,
+    # we add x to the filter.
+    xfilt[:, nfilt] = x
+    ffilt[nfilt] = f
+    cfilt[nfilt] = cstrv
+    if confilt is not None and constr is not None:
+        confilt[:, nfilt] = constr
+    nfilt += 1  # In Python we need to increment the index afterwards
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        # Check NFILT and the sizes of XFILT, FFILT, CFILT.
+        assert nfilt >= 1 and nfilt <= maxfilt
+        assert np.size(xfilt, 0) == num_vars and np.size(xfilt, 1) == maxfilt
+        assert np.size(ffilt) == maxfilt
+        assert np.size(cfilt) == maxfilt
+        # Check the values of XFILT, FFILT, CFILT.
+        assert not (np.isnan(xfilt[:, :nfilt])).any()
+        assert not any(np.isnan(ffilt[:nfilt]) | np.isposinf(ffilt[:nfilt]))
+        assert not any(cfilt[:nfilt] < 0 | np.isnan(cfilt[:nfilt]) | np.isposinf(cfilt[:nfilt]))
+        # Check that no point in the filter is better than X, and X is better than no point.
+        assert not any([isbetter(ffilt_i, cfilt_i, f, cstrv, ctol) for ffilt_i, cfilt_i in zip(ffilt[:nfilt], cfilt[:nfilt])])
+        assert not any([isbetter(f, cstrv, ffilt_i, cfilt_i, ctol) for ffilt_i, cfilt_i in zip(ffilt[:nfilt], cfilt[:nfilt])])
+        # Check CONFILT.
+        if present(confilt):
+            assert np.size(confilt, 0) == num_constraints and np.size(confilt, 1) == maxfilt
+            assert not (np.isnan(confilt[:, :nfilt]) | np.isneginf(confilt[:, :nfilt])).any()
+
+
+    return nfilt, cfilt, ffilt, xfilt, confilt
+
+
+def selectx(fhist: npt.NDArray, chist: npt.NDArray, cweight: float, ctol: float):
+    '''
+    This subroutine selects X according to FHIST and CHIST, which represents (a part of) history
+    of F and CSTRV. Normally, FHIST and CHIST are not the full history but only a filter, e.g. ffilt
+    and CFILT generated by SAVEFILT. However, we name them as FHIST and CHIST because the [F, CSTRV]
+    in a filter should not dominate each other, but this subroutine does NOT assume such a property.
+    N.B.: CTOL is the tolerance of the constraint violation (CSTRV). A point is considered feasible if
+    its constraint violation is at most CTOL. Not that CTOL is absolute, not relative.
+    '''
+
+    # Sizes
+    nhist = len(fhist)
+
+    # Preconditions
+    if DEBUGGING:
+        assert nhist >= 1
+        assert np.size(chist) == nhist
+        assert not any(np.isnan(fhist) | np.isposinf(fhist))
+        assert not any(chist < 0 | np.isnan(chist) | np.isposinf(chist))
+        assert cweight >= 0
+        assert ctol >= 0
+
+    #====================#
+    # Calculation starts #
+    #====================#
+
+    # We select X among the points with F < FREF and CSTRV < CREF.
+    # Do NOT use F <= FREF, because F == FREF (FUNCMAX or REALMAX) may mean F == INF in practice!
+    if any(np.logical_and(fhist < FUNCMAX, chist < CONSTRMAX)):
+        fref = FUNCMAX
+        cref = CONSTRMAX
+    elif any(np.logical_and(fhist < REALMAX, chist < CONSTRMAX)):
+        fref = REALMAX
+        cref = CONSTRMAX
+    elif any(np.logical_and(fhist < FUNCMAX, chist < REALMAX)):
+        fref = FUNCMAX
+        cref = REALMAX
+    else:
+        fref = REALMAX
+        cref = REALMAX
+
+    if not any(np.logical_and(fhist < fref, chist < cref)):
+        kopt = nhist - 1
+    else:
+        # Shift the constraint violations by ctol, so that cstrv <= ctol is regarded as no violation.
+        chist_shifted = np.maximum(chist - ctol, 0)
+        # cmin is the minimal shift constraint violation attained in the history.
+        cmin = np.min(chist_shifted[fhist < fref])
+        # We consider only the points whose shifted constraint violations are at most the cref below.
+        # N.B.: Without taking np.maximum(EPS, .), cref would be 0 if cmin = 0. In that case, asking for
+        # cstrv_shift < cref would be WRONG!
+        cref = np.maximum(EPS, 2*cmin)
+        # We use the following phi as our merit function to select X.
+        if cweight <= 0:
+            phi = fhist
+        elif np.isposinf(cweight):
+            phi = chist_shifted
+            # We should not use chist here; if np.minimum(chist_shifted) is attained at multiple indices, then
+            # we will check fhist to exhaust the remaining degree of freedom.
+        else:
+            phi = np.maximum(fhist, -REALMAX) + cweight * chist_shifted
+            # np.maximum(fhist, -REALMAX) makes sure that phi will not contain NaN (unless there is a bug).
+
+        # We select X to minimize phi subject to f < fref and cstrv_shift <= cref (see the comments
+        # above for the reason of taking "<" and "<=" in these two constraints). In case there are
+        # multiple minimizers, we take the one with the least cstrv_shift; if there is more than one
+        # choice, we take the one with the least f; if there are several candidates, we take the one
+        # with the least cstrv; if the last comparison still leads to more than one possibility, then
+        # they are equally good and we choose the first.
+        # N.B.:
+        # 1. This process is the opposite of selecting kworst in savefilt
+        # 2. In finite-precision arithmetic, phi_2 == phi_2 and cstrv_shift_1 == cstrv_shifted_2 do
+        # not ensure thatn f_1 == f_2!
+        phimin = np.min(phi[np.logical_and(fhist < fref, chist_shifted <= cref)])
+        cref = np.min(chist_shifted[np.logical_and(fhist < fref, phi <= phimin)])
+        fref = np.min(fhist[chist_shifted <= cref])
+        # Can't use argmin here because using it with a mask throws off the index
+        kopt = np.ma.array(chist, mask=(fhist > fref)).argmin()
+
+    #==================#
+    # Calculation ends #
+    #==================#
+
+    # Postconditions
+    if DEBUGGING:
+        assert kopt >= 0 and kopt < nhist
+        assert not any([isbetter(fhisti, chisti, fhist[kopt], chist[kopt], ctol) for fhisti, chisti in zip(fhist[:nhist], chist[:nhist])])
+
+    return kopt
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__gcutils.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__gcutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..0e397af4fb7e9bc69f31d1e39aa80716469d5470
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__gcutils.py
@@ -0,0 +1,110 @@
+""" Test for assert_deallocated context manager and gc utilities
+"""
+import gc
+from threading import Lock
+
+from scipy._lib._gcutils import (set_gc_state, gc_state, assert_deallocated,
+                                 ReferenceError, IS_PYPY)
+
+from numpy.testing import assert_equal
+
+import pytest
+
+
+@pytest.fixture
+def gc_lock():
+    return Lock()
+
+
+def test_set_gc_state(gc_lock):
+    with gc_lock:
+        gc_status = gc.isenabled()
+        try:
+            for state in (True, False):
+                gc.enable()
+                set_gc_state(state)
+                assert_equal(gc.isenabled(), state)
+                gc.disable()
+                set_gc_state(state)
+                assert_equal(gc.isenabled(), state)
+        finally:
+            if gc_status:
+                gc.enable()
+
+
+def test_gc_state(gc_lock):
+    # Test gc_state context manager
+    with gc_lock:
+        gc_status = gc.isenabled()
+        try:
+            for pre_state in (True, False):
+                set_gc_state(pre_state)
+                for with_state in (True, False):
+                    # Check the gc state is with_state in with block
+                    with gc_state(with_state):
+                        assert_equal(gc.isenabled(), with_state)
+                    # And returns to previous state outside block
+                    assert_equal(gc.isenabled(), pre_state)
+                    # Even if the gc state is set explicitly within the block
+                    with gc_state(with_state):
+                        assert_equal(gc.isenabled(), with_state)
+                        set_gc_state(not with_state)
+                    assert_equal(gc.isenabled(), pre_state)
+        finally:
+            if gc_status:
+                gc.enable()
+
+
+@pytest.mark.skipif(IS_PYPY, reason="Test not meaningful on PyPy")
+def test_assert_deallocated(gc_lock):
+    # Ordinary use
+    class C:
+        def __init__(self, arg0, arg1, name='myname'):
+            self.name = name
+    with gc_lock:
+        for gc_current in (True, False):
+            with gc_state(gc_current):
+                # We are deleting from with-block context, so that's OK
+                with assert_deallocated(C, 0, 2, 'another name') as c:
+                    assert_equal(c.name, 'another name')
+                    del c
+                # Or not using the thing in with-block context, also OK
+                with assert_deallocated(C, 0, 2, name='third name'):
+                    pass
+                assert_equal(gc.isenabled(), gc_current)
+
+
+@pytest.mark.skipif(IS_PYPY, reason="Test not meaningful on PyPy")
+def test_assert_deallocated_nodel():
+    class C:
+        pass
+    with pytest.raises(ReferenceError):
+        # Need to delete after using if in with-block context
+        # Note: assert_deallocated(C) needs to be assigned for the test
+        # to function correctly.  It is assigned to _, but _ itself is
+        # not referenced in the body of the with, it is only there for
+        # the refcount.
+        with assert_deallocated(C) as _:
+            pass
+
+
+@pytest.mark.skipif(IS_PYPY, reason="Test not meaningful on PyPy")
+def test_assert_deallocated_circular():
+    class C:
+        def __init__(self):
+            self._circular = self
+    with pytest.raises(ReferenceError):
+        # Circular reference, no automatic garbage collection
+        with assert_deallocated(C) as c:
+            del c
+
+
+@pytest.mark.skipif(IS_PYPY, reason="Test not meaningful on PyPy")
+def test_assert_deallocated_circular2():
+    class C:
+        def __init__(self):
+            self._circular = self
+    with pytest.raises(ReferenceError):
+        # Still circular reference, no automatic garbage collection
+        with assert_deallocated(C):
+            pass
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__pep440.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__pep440.py
new file mode 100644
index 0000000000000000000000000000000000000000..7f5b71c8f1e13b42de2e8e612a005dec409fc025
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__pep440.py
@@ -0,0 +1,67 @@
+from pytest import raises as assert_raises
+from scipy._lib._pep440 import Version, parse
+
+
+def test_main_versions():
+    assert Version('1.8.0') == Version('1.8.0')
+    for ver in ['1.9.0', '2.0.0', '1.8.1']:
+        assert Version('1.8.0') < Version(ver)
+
+    for ver in ['1.7.0', '1.7.1', '0.9.9']:
+        assert Version('1.8.0') > Version(ver)
+
+
+def test_version_1_point_10():
+    # regression test for gh-2998.
+    assert Version('1.9.0') < Version('1.10.0')
+    assert Version('1.11.0') < Version('1.11.1')
+    assert Version('1.11.0') == Version('1.11.0')
+    assert Version('1.99.11') < Version('1.99.12')
+
+
+def test_alpha_beta_rc():
+    assert Version('1.8.0rc1') == Version('1.8.0rc1')
+    for ver in ['1.8.0', '1.8.0rc2']:
+        assert Version('1.8.0rc1') < Version(ver)
+
+    for ver in ['1.8.0a2', '1.8.0b3', '1.7.2rc4']:
+        assert Version('1.8.0rc1') > Version(ver)
+
+    assert Version('1.8.0b1') > Version('1.8.0a2')
+
+
+def test_dev_version():
+    assert Version('1.9.0.dev+Unknown') < Version('1.9.0')
+    for ver in ['1.9.0', '1.9.0a1', '1.9.0b2', '1.9.0b2.dev+ffffffff', '1.9.0.dev1']:
+        assert Version('1.9.0.dev+f16acvda') < Version(ver)
+
+    assert Version('1.9.0.dev+f16acvda') == Version('1.9.0.dev+f16acvda')
+
+
+def test_dev_a_b_rc_mixed():
+    assert Version('1.9.0a2.dev+f16acvda') == Version('1.9.0a2.dev+f16acvda')
+    assert Version('1.9.0a2.dev+6acvda54') < Version('1.9.0a2')
+
+
+def test_dev0_version():
+    assert Version('1.9.0.dev0+Unknown') < Version('1.9.0')
+    for ver in ['1.9.0', '1.9.0a1', '1.9.0b2', '1.9.0b2.dev0+ffffffff']:
+        assert Version('1.9.0.dev0+f16acvda') < Version(ver)
+
+    assert Version('1.9.0.dev0+f16acvda') == Version('1.9.0.dev0+f16acvda')
+
+
+def test_dev0_a_b_rc_mixed():
+    assert Version('1.9.0a2.dev0+f16acvda') == Version('1.9.0a2.dev0+f16acvda')
+    assert Version('1.9.0a2.dev0+6acvda54') < Version('1.9.0a2')
+
+
+def test_raises():
+    for ver in ['1,9.0', '1.7.x']:
+        assert_raises(ValueError, Version, ver)
+
+def test_legacy_version():
+    # Non-PEP-440 version identifiers always compare less. For NumPy this only
+    # occurs on dev builds prior to 1.10.0 which are unsupported anyway.
+    assert parse('invalid') < Version('0.0.0')
+    assert parse('1.9.0-f16acvda') < Version('1.0.0')
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__testutils.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__testutils.py
new file mode 100644
index 0000000000000000000000000000000000000000..88db113d6d5a35c96ecc0a6a36ab42d74be49153
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__testutils.py
@@ -0,0 +1,32 @@
+import sys
+from scipy._lib._testutils import _parse_size, _get_mem_available
+import pytest
+
+
+def test__parse_size():
+    expected = {
+        '12': 12e6,
+        '12 b': 12,
+        '12k': 12e3,
+        '  12  M  ': 12e6,
+        '  12  G  ': 12e9,
+        ' 12Tb ': 12e12,
+        '12  Mib ': 12 * 1024.0**2,
+        '12Tib': 12 * 1024.0**4,
+    }
+
+    for inp, outp in sorted(expected.items()):
+        if outp is None:
+            with pytest.raises(ValueError):
+                _parse_size(inp)
+        else:
+            assert _parse_size(inp) == outp
+
+
+def test__mem_available():
+    # May return None on non-Linux platforms
+    available = _get_mem_available()
+    if sys.platform.startswith('linux'):
+        assert available >= 0
+    else:
+        assert available is None or available >= 0
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__util.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__util.py
new file mode 100644
index 0000000000000000000000000000000000000000..f78e36613f2a49a6e685a7775e117f80fe50affa
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test__util.py
@@ -0,0 +1,638 @@
+from multiprocessing import Pool
+from multiprocessing.pool import Pool as PWL
+import re
+import math
+import functools
+from fractions import Fraction
+
+import numpy as np
+from numpy.testing import assert_equal, assert_
+import pytest
+from pytest import raises as assert_raises
+from scipy.conftest import skip_xp_invalid_arg
+
+from scipy._lib._array_api import xp_assert_equal
+from scipy._lib._util import (_aligned_zeros, check_random_state, MapWrapper,
+                              getfullargspec_no_self, FullArgSpec,
+                              rng_integers, _validate_int, _rename_parameter,
+                              _contains_nan, _rng_html_rewrite, _workers_wrapper)
+import scipy._lib.array_api_extra as xpx
+from scipy._lib.array_api_extra.testing import lazy_xp_function
+from scipy import cluster, interpolate, linalg, optimize, sparse, spatial, stats
+
+
+lazy_xp_function(_contains_nan)
+
+
+@pytest.mark.slow
+def test__aligned_zeros():
+    niter = 10
+
+    def check(shape, dtype, order, align):
+        err_msg = repr((shape, dtype, order, align))
+        x = _aligned_zeros(shape, dtype, order, align=align)
+        if align is None:
+            align = np.dtype(dtype).alignment
+        assert_equal(x.__array_interface__['data'][0] % align, 0)
+        if hasattr(shape, '__len__'):
+            assert_equal(x.shape, shape, err_msg)
+        else:
+            assert_equal(x.shape, (shape,), err_msg)
+        assert_equal(x.dtype, dtype)
+        if order == "C":
+            assert_(x.flags.c_contiguous, err_msg)
+        elif order == "F":
+            if x.size > 0:
+                # Size-0 arrays get invalid flags on NumPy 1.5
+                assert_(x.flags.f_contiguous, err_msg)
+        elif order is None:
+            assert_(x.flags.c_contiguous, err_msg)
+        else:
+            raise ValueError()
+
+    # try various alignments
+    for align in [1, 2, 3, 4, 8, 16, 32, 64, None]:
+        for n in [0, 1, 3, 11]:
+            for order in ["C", "F", None]:
+                for dtype in [np.uint8, np.float64]:
+                    for shape in [n, (1, 2, 3, n)]:
+                        for j in range(niter):
+                            check(shape, dtype, order, align)
+
+
+def test_check_random_state():
+    # If seed is None, return the RandomState singleton used by np.random.
+    # If seed is an int, return a new RandomState instance seeded with seed.
+    # If seed is already a RandomState instance, return it.
+    # Otherwise raise ValueError.
+    rsi = check_random_state(1)
+    assert_equal(type(rsi), np.random.RandomState)
+    rsi = check_random_state(rsi)
+    assert_equal(type(rsi), np.random.RandomState)
+    rsi = check_random_state(None)
+    assert_equal(type(rsi), np.random.RandomState)
+    assert_raises(ValueError, check_random_state, 'a')
+    rg = np.random.Generator(np.random.PCG64())
+    rsi = check_random_state(rg)
+    assert_equal(type(rsi), np.random.Generator)
+
+
+def test_getfullargspec_no_self():
+    p = MapWrapper(1)
+    argspec = getfullargspec_no_self(p.__init__)
+    assert_equal(argspec, FullArgSpec(['pool'], None, None, (1,), [],
+                                      None, {}))
+    argspec = getfullargspec_no_self(p.__call__)
+    assert_equal(argspec, FullArgSpec(['func', 'iterable'], None, None, None,
+                                      [], None, {}))
+
+    class _rv_generic:
+        def _rvs(self, a, b=2, c=3, *args, size=None, **kwargs):
+            return None
+
+    rv_obj = _rv_generic()
+    argspec = getfullargspec_no_self(rv_obj._rvs)
+    assert_equal(argspec, FullArgSpec(['a', 'b', 'c'], 'args', 'kwargs',
+                                      (2, 3), ['size'], {'size': None}, {}))
+
+
+def test_mapwrapper_serial():
+    in_arg = np.arange(10.)
+    out_arg = np.sin(in_arg)
+
+    p = MapWrapper(1)
+    assert_(p._mapfunc is map)
+    assert_(p.pool is None)
+    assert_(p._own_pool is False)
+    out = list(p(np.sin, in_arg))
+    assert_equal(out, out_arg)
+
+    with assert_raises(RuntimeError):
+        p = MapWrapper(0)
+
+
+def test_pool():
+    with Pool(2) as p:
+        p.map(math.sin, [1, 2, 3, 4])
+
+
+def test_mapwrapper_parallel():
+    in_arg = np.arange(10.)
+    out_arg = np.sin(in_arg)
+
+    with MapWrapper(2) as p:
+        out = p(np.sin, in_arg)
+        assert_equal(list(out), out_arg)
+
+        assert_(p._own_pool is True)
+        assert_(isinstance(p.pool, PWL))
+        assert_(p._mapfunc is not None)
+
+    # the context manager should've closed the internal pool
+    # check that it has by asking it to calculate again.
+    with assert_raises(Exception) as excinfo:
+        p(np.sin, in_arg)
+
+    assert_(excinfo.type is ValueError)
+
+    # can also set a PoolWrapper up with a map-like callable instance
+    with Pool(2) as p:
+        q = MapWrapper(p.map)
+
+        assert_(q._own_pool is False)
+        q.close()
+
+        # closing the PoolWrapper shouldn't close the internal pool
+        # because it didn't create it
+        out = p.map(np.sin, in_arg)
+        assert_equal(list(out), out_arg)
+
+
+@_workers_wrapper
+def user_of_workers(x, b=1, workers=None):
+    assert workers is not None
+    assert isinstance(workers, MapWrapper)
+    return np.array(list(workers(np.sin, x * b)))
+
+
+def test__workers_wrapper():
+    arr = np.linspace(0, np.pi)
+    req = np.sin(arr * 2.0)
+
+    with Pool(2) as p:
+        v = user_of_workers(arr, workers=p.map, b=2)
+        assert_equal(v, req)
+
+    v = user_of_workers(arr, workers=None, b=2)
+    assert_equal(v, req)
+
+    v = user_of_workers(arr, workers=2, b=2)
+    assert_equal(v, req)
+
+    # assess if decorator works with partial functions
+    part_f = functools.partial(user_of_workers, b=2)
+    assert_equal(part_f(arr), req)
+
+    with Pool(2) as p:
+        part_f = functools.partial(user_of_workers, b=2, workers=p.map)
+        assert_equal(part_f(arr), req)
+
+
+def test_rng_integers():
+    rng = np.random.RandomState()
+
+    # test that numbers are inclusive of high point
+    arr = rng_integers(rng, low=2, high=5, size=100, endpoint=True)
+    assert np.max(arr) == 5
+    assert np.min(arr) == 2
+    assert arr.shape == (100, )
+
+    # test that numbers are inclusive of high point
+    arr = rng_integers(rng, low=5, size=100, endpoint=True)
+    assert np.max(arr) == 5
+    assert np.min(arr) == 0
+    assert arr.shape == (100, )
+
+    # test that numbers are exclusive of high point
+    arr = rng_integers(rng, low=2, high=5, size=100, endpoint=False)
+    assert np.max(arr) == 4
+    assert np.min(arr) == 2
+    assert arr.shape == (100, )
+
+    # test that numbers are exclusive of high point
+    arr = rng_integers(rng, low=5, size=100, endpoint=False)
+    assert np.max(arr) == 4
+    assert np.min(arr) == 0
+    assert arr.shape == (100, )
+
+    # now try with np.random.Generator
+    try:
+        rng = np.random.default_rng()
+    except AttributeError:
+        return
+
+    # test that numbers are inclusive of high point
+    arr = rng_integers(rng, low=2, high=5, size=100, endpoint=True)
+    assert np.max(arr) == 5
+    assert np.min(arr) == 2
+    assert arr.shape == (100, )
+
+    # test that numbers are inclusive of high point
+    arr = rng_integers(rng, low=5, size=100, endpoint=True)
+    assert np.max(arr) == 5
+    assert np.min(arr) == 0
+    assert arr.shape == (100, )
+
+    # test that numbers are exclusive of high point
+    arr = rng_integers(rng, low=2, high=5, size=100, endpoint=False)
+    assert np.max(arr) == 4
+    assert np.min(arr) == 2
+    assert arr.shape == (100, )
+
+    # test that numbers are exclusive of high point
+    arr = rng_integers(rng, low=5, size=100, endpoint=False)
+    assert np.max(arr) == 4
+    assert np.min(arr) == 0
+    assert arr.shape == (100, )
+
+
+class TestValidateInt:
+
+    @pytest.mark.parametrize('n', [4, np.uint8(4), np.int16(4), np.array(4)])
+    def test_validate_int(self, n):
+        n = _validate_int(n, 'n')
+        assert n == 4
+
+    @pytest.mark.parametrize('n', [4.0, np.array([4]), Fraction(4, 1)])
+    def test_validate_int_bad(self, n):
+        with pytest.raises(TypeError, match='n must be an integer'):
+            _validate_int(n, 'n')
+
+    def test_validate_int_below_min(self):
+        with pytest.raises(ValueError, match='n must be an integer not '
+                                             'less than 0'):
+            _validate_int(-1, 'n', 0)
+
+
+class TestRenameParameter:
+    # check that wrapper `_rename_parameter` for backward-compatible
+    # keyword renaming works correctly
+
+    # Example method/function that still accepts keyword `old`
+    @_rename_parameter("old", "new")
+    def old_keyword_still_accepted(self, new):
+        return new
+
+    # Example method/function for which keyword `old` is deprecated
+    @_rename_parameter("old", "new", dep_version="1.9.0")
+    def old_keyword_deprecated(self, new):
+        return new
+
+    def test_old_keyword_still_accepted(self):
+        # positional argument and both keyword work identically
+        res1 = self.old_keyword_still_accepted(10)
+        res2 = self.old_keyword_still_accepted(new=10)
+        res3 = self.old_keyword_still_accepted(old=10)
+        assert res1 == res2 == res3 == 10
+
+        # unexpected keyword raises an error
+        message = re.escape("old_keyword_still_accepted() got an unexpected")
+        with pytest.raises(TypeError, match=message):
+            self.old_keyword_still_accepted(unexpected=10)
+
+        # multiple values for the same parameter raises an error
+        message = re.escape("old_keyword_still_accepted() got multiple")
+        with pytest.raises(TypeError, match=message):
+            self.old_keyword_still_accepted(10, new=10)
+        with pytest.raises(TypeError, match=message):
+            self.old_keyword_still_accepted(10, old=10)
+        with pytest.raises(TypeError, match=message):
+            self.old_keyword_still_accepted(new=10, old=10)
+
+    @pytest.fixture
+    def kwarg_lock(self):
+        from threading import Lock
+        return Lock()
+
+    def test_old_keyword_deprecated(self, kwarg_lock):
+        # positional argument and both keyword work identically,
+        # but use of old keyword results in DeprecationWarning
+        dep_msg = "Use of keyword argument `old` is deprecated"
+        res1 = self.old_keyword_deprecated(10)
+        res2 = self.old_keyword_deprecated(new=10)
+        # pytest warning filter is not thread-safe, enforce serialization
+        with kwarg_lock:
+            with pytest.warns(DeprecationWarning, match=dep_msg):
+                    res3 = self.old_keyword_deprecated(old=10)
+        assert res1 == res2 == res3 == 10
+
+        # unexpected keyword raises an error
+        message = re.escape("old_keyword_deprecated() got an unexpected")
+        with pytest.raises(TypeError, match=message):
+            self.old_keyword_deprecated(unexpected=10)
+
+        # multiple values for the same parameter raises an error and,
+        # if old keyword is used, results in DeprecationWarning
+        message = re.escape("old_keyword_deprecated() got multiple")
+        with pytest.raises(TypeError, match=message):
+            self.old_keyword_deprecated(10, new=10)
+        with kwarg_lock:
+            with pytest.raises(TypeError, match=message), \
+                    pytest.warns(DeprecationWarning, match=dep_msg):
+                    # breakpoint()
+                    self.old_keyword_deprecated(10, old=10)
+        with kwarg_lock:
+            with pytest.raises(TypeError, match=message), \
+                    pytest.warns(DeprecationWarning, match=dep_msg):
+                    self.old_keyword_deprecated(new=10, old=10)
+
+
+class TestContainsNaN:
+    def test_policy(self):
+        data = np.array([1, 2, 3, np.nan])
+
+        assert _contains_nan(data)  # default policy is "propagate"
+        assert _contains_nan(data, nan_policy="propagate")
+        assert _contains_nan(data, nan_policy="omit")
+        assert not _contains_nan(data[:3])
+        assert not _contains_nan(data[:3], nan_policy="propagate")
+        assert not _contains_nan(data[:3], nan_policy="omit")
+
+        with pytest.raises(ValueError, match="The input contains nan values"):
+            _contains_nan(data, nan_policy="raise")
+        assert not _contains_nan(data[:3], nan_policy="raise")
+
+        with pytest.raises(ValueError, match="nan_policy must be one of"):
+            _contains_nan(data, nan_policy="nan")
+
+    def test_contains_nan(self):
+        # Special case: empty array
+        assert not _contains_nan(np.array([], dtype=float))
+
+        # Integer arrays cannot contain NaN
+        assert not _contains_nan(np.array([1, 2, 3]))
+        assert not _contains_nan(np.array([[1, 2], [3, 4]]))
+
+        assert not _contains_nan(np.array([1., 2., 3.]))
+        assert not _contains_nan(np.array([1., 2.j, 3.]))
+        assert _contains_nan(np.array([1., 2.j, np.nan]))
+        assert _contains_nan(np.array([1., 2., np.nan]))
+        assert _contains_nan(np.array([np.nan, 2., np.nan]))
+        assert not _contains_nan(np.array([[1., 2.], [3., 4.]]))
+        assert _contains_nan(np.array([[1., 2.], [3., np.nan]]))
+
+    @skip_xp_invalid_arg
+    def test_contains_nan_with_strings(self):
+        data1 = np.array([1, 2, "3", np.nan])  # converted to string "nan"
+        assert not _contains_nan(data1)
+
+        data2 = np.array([1, 2, "3", np.nan], dtype='object')
+        assert _contains_nan(data2)
+
+        data3 = np.array([["1", 2], [3, np.nan]])  # converted to string "nan"
+        assert not _contains_nan(data3)
+
+        data4 = np.array([["1", 2], [3, np.nan]], dtype='object')
+        assert _contains_nan(data4)
+
+    @pytest.mark.skip_xp_backends(eager_only=True,
+                                  reason="lazy backends tested separately")
+    @pytest.mark.parametrize("nan_policy", ['propagate', 'omit', 'raise'])
+    def test_array_api(self, xp, nan_policy):
+        rng = np.random.default_rng(932347235892482)
+        x0 = rng.random(size=(2, 3, 4))
+        x = xp.asarray(x0)
+        assert not _contains_nan(x, nan_policy)
+
+        x = xpx.at(x)[1, 2, 1].set(xp.nan)
+
+        if nan_policy == 'raise':
+            with pytest.raises(ValueError, match="The input contains nan values"):
+                _contains_nan(x, nan_policy)
+        elif nan_policy == 'omit':
+            assert _contains_nan(x, nan_policy, xp_omit_okay=True)
+        elif nan_policy == 'propagate':
+            assert _contains_nan(x, nan_policy)
+
+    @pytest.mark.skip_xp_backends("numpy", reason="lazy backends only")
+    @pytest.mark.skip_xp_backends("cupy", reason="lazy backends only")
+    @pytest.mark.skip_xp_backends("array_api_strict", reason="lazy backends only")
+    @pytest.mark.skip_xp_backends("torch", reason="lazy backends only")
+    def test_array_api_lazy(self, xp):
+        rng = np.random.default_rng(932347235892482)
+        x0 = rng.random(size=(2, 3, 4))
+        x = xp.asarray(x0)
+
+        xp_assert_equal(_contains_nan(x), xp.asarray(False))
+        xp_assert_equal(_contains_nan(x, "propagate"), xp.asarray(False))
+        xp_assert_equal(_contains_nan(x, "omit", xp_omit_okay=True), xp.asarray(False))
+        # Lazy arrays don't support "omit" and "raise" policies
+        match = "not supported for lazy arrays"
+        with pytest.raises(TypeError, match=match):
+            _contains_nan(x, "omit")
+        with pytest.raises(TypeError, match=match):
+            _contains_nan(x, "raise")
+
+        x = xpx.at(x)[1, 2, 1].set(np.nan)
+
+        xp_assert_equal(_contains_nan(x), xp.asarray(True))
+        xp_assert_equal(_contains_nan(x, "propagate"), xp.asarray(True))
+        xp_assert_equal(_contains_nan(x, "omit", xp_omit_okay=True), xp.asarray(True))
+        with pytest.raises(TypeError, match=match):
+            _contains_nan(x, "omit")
+        with pytest.raises(TypeError, match=match):
+            _contains_nan(x, "raise")
+
+
+def test__rng_html_rewrite():
+    def mock_str():
+        lines = [
+            'np.random.default_rng(8989843)',
+            'np.random.default_rng(seed)',
+            'np.random.default_rng(0x9a71b21474694f919882289dc1559ca)',
+            ' bob ',
+        ]
+        return lines
+
+    res = _rng_html_rewrite(mock_str)()
+    ref = [
+        'np.random.default_rng()',
+        'np.random.default_rng(seed)',
+        'np.random.default_rng()',
+        ' bob ',
+    ]
+
+    assert res == ref
+
+
+class TestTransitionToRNG:
+    def kmeans(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        return cluster.vq.kmeans2(rng.random(size=(20, 3)), 3, **kwargs)
+
+    def kmeans2(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        return cluster.vq.kmeans2(rng.random(size=(20, 3)), 3, **kwargs)
+
+    def barycentric(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        x1, x2, y1 = rng.random((3, 10))
+        f = interpolate.BarycentricInterpolator(x1, y1, **kwargs)
+        return f(x2)
+
+    def clarkson_woodruff_transform(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        return linalg.clarkson_woodruff_transform(rng.random((10, 10)), 3, **kwargs)
+
+    def basinhopping(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        return optimize.basinhopping(optimize.rosen, rng.random(3), **kwargs).x
+
+    def opt(self, fun, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        bounds = optimize.Bounds(-rng.random(3) * 10, rng.random(3) * 10)
+        return fun(optimize.rosen, bounds, **kwargs).x
+
+    def differential_evolution(self, **kwargs):
+        return self.opt(optimize.differential_evolution, **kwargs)
+
+    def dual_annealing(self, **kwargs):
+        return self.opt(optimize.dual_annealing, **kwargs)
+
+    def check_grad(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        x = rng.random(3)
+        return optimize.check_grad(optimize.rosen, optimize.rosen_der, x,
+                                   direction='random', **kwargs)
+
+    def random_array(self, **kwargs):
+        return sparse.random_array((10, 10), density=1.0, **kwargs).toarray()
+
+    def random(self, **kwargs):
+        return sparse.random(10, 10, density=1.0, **kwargs).toarray()
+
+    def rand(self, **kwargs):
+        return sparse.rand(10, 10, density=1.0, **kwargs).toarray()
+
+    def svds(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        A = rng.random((10, 10))
+        return sparse.linalg.svds(A, **kwargs)
+
+    def random_rotation(self, **kwargs):
+        return spatial.transform.Rotation.random(3, **kwargs).as_matrix()
+
+    def goodness_of_fit(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        data = rng.random(100)
+        return stats.goodness_of_fit(stats.laplace, data, **kwargs).pvalue
+
+    def permutation_test(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        data = tuple(rng.random((2, 100)))
+        def statistic(x, y, axis): return np.mean(x, axis=axis) - np.mean(y, axis=axis)
+        return stats.permutation_test(data, statistic, **kwargs).pvalue
+
+    def bootstrap(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        data = (rng.random(100),)
+        return stats.bootstrap(data, np.mean, **kwargs).confidence_interval
+
+    def dunnett(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        x, y, control = rng.random((3, 100))
+        return stats.dunnett(x, y, control=control, **kwargs).pvalue
+
+    def sobol_indices(self, **kwargs):
+        def f_ishigami(x): return (np.sin(x[0]) + 7 * np.sin(x[1]) ** 2
+                                   + 0.1 * (x[2] ** 4) * np.sin(x[0]))
+        dists = [stats.uniform(loc=-np.pi, scale=2 * np.pi),
+                 stats.uniform(loc=-np.pi, scale=2 * np.pi),
+                 stats.uniform(loc=-np.pi, scale=2 * np.pi)]
+        res = stats.sobol_indices(func=f_ishigami, n=1024, dists=dists, **kwargs)
+        return res.first_order
+
+    def qmc_engine(self, engine, **kwargs):
+        qrng = engine(d=1, **kwargs)
+        return qrng.random(4)
+
+    def halton(self, **kwargs):
+        return self.qmc_engine(stats.qmc.Halton, **kwargs)
+
+    def sobol(self, **kwargs):
+        return self.qmc_engine(stats.qmc.Sobol, **kwargs)
+
+    def latin_hypercube(self, **kwargs):
+        return self.qmc_engine(stats.qmc.LatinHypercube, **kwargs)
+
+    def poisson_disk(self, **kwargs):
+        return self.qmc_engine(stats.qmc.PoissonDisk, **kwargs)
+
+    def multivariate_normal_qmc(self, **kwargs):
+        X = stats.qmc.MultivariateNormalQMC([0], **kwargs)
+        return X.random(4)
+
+    def multinomial_qmc(self, **kwargs):
+        X = stats.qmc.MultinomialQMC([0.5, 0.5], 4, **kwargs)
+        return X.random(4)
+
+    def permutation_method(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        data = tuple(rng.random((2, 100)))
+        method = stats.PermutationMethod(**kwargs)
+        return stats.pearsonr(*data, method=method).pvalue
+
+    def bootstrap_method(self, **kwargs):
+        rng = np.random.default_rng(3458934594269824562)
+        data = tuple(rng.random((2, 100)))
+        res = stats.pearsonr(*data)
+        method = stats.BootstrapMethod(**kwargs)
+        return res.confidence_interval(method=method)
+
+    @pytest.mark.fail_slow(10)
+    @pytest.mark.slow
+    @pytest.mark.parametrize("method, arg_name", [
+        (kmeans, "seed"),
+        (kmeans2, "seed"),
+        (barycentric, "random_state"),
+        (clarkson_woodruff_transform, "seed"),
+        (basinhopping, "seed"),
+        (differential_evolution, "seed"),
+        (dual_annealing, "seed"),
+        (check_grad, "seed"),
+        (random_array, 'random_state'),
+        (random, 'random_state'),
+        (rand, 'random_state'),
+        (random_rotation, "random_state"),
+        (goodness_of_fit, "random_state"),
+        (permutation_test, "random_state"),
+        (bootstrap, "random_state"),
+        (permutation_method, "random_state"),
+        (bootstrap_method, "random_state"),
+        (dunnett, "random_state"),
+        (sobol_indices, "random_state"),
+        (halton, "seed"),
+        (sobol, "seed"),
+        (latin_hypercube, "seed"),
+        (poisson_disk, "seed"),
+        (multivariate_normal_qmc, "seed"),
+        (multinomial_qmc, "seed"),
+    ])
+    def test_rng_deterministic(self, method, arg_name):
+        np.random.seed(None)
+        seed = 2949672964
+
+        rng = np.random.default_rng(seed)
+        message = "got multiple values for argument now known as `rng`"
+        with pytest.raises(TypeError, match=message):
+            method(self, **{'rng': rng, arg_name: seed})
+
+        rng = np.random.default_rng(seed)
+        res1 = method(self, rng=rng)
+        res2 = method(self, rng=seed)
+        assert_equal(res2, res1)
+
+        if method.__name__ in {"dunnett", "sobol_indices"}:
+            # the two kwargs have essentially the same behavior for these functions
+            res3 = method(self, **{arg_name: seed})
+            assert_equal(res3, res1)
+            return
+
+        rng = np.random.RandomState(seed)
+        res1 = method(self, **{arg_name: rng})
+        res2 = method(self, **{arg_name: seed})
+
+        if method.__name__ in {"halton", "sobol", "latin_hypercube", "poisson_disk",
+                               "multivariate_normal_qmc", "multinomial_qmc"}:
+            # For these, passing `random_state=RandomState(seed)` is not the same as
+            # passing integer `seed`.
+            res1b = method(self, **{arg_name: np.random.RandomState(seed)})
+            assert_equal(res1b, res1)
+            res2b = method(self, **{arg_name: seed})
+            assert_equal(res2b, res2)
+            return
+
+        np.random.seed(seed)
+        res3 = method(self, **{arg_name: None})
+        assert_equal(res2, res1)
+        assert_equal(res3, res1)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_array_api.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_array_api.py
new file mode 100644
index 0000000000000000000000000000000000000000..cb7735debae5a18640aca3c6c6c330e7f1802e81
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_array_api.py
@@ -0,0 +1,400 @@
+import re
+
+import numpy as np
+import pytest
+
+from importlib import import_module
+
+from scipy._lib._array_api import (
+    SCIPY_ARRAY_API, array_namespace, _asarray, xp_copy, xp_assert_equal, is_numpy,
+    np_compat, xp_default_dtype, xp_result_type, is_torch,
+    xp_capabilities_table, _xp_copy_to_numpy
+)
+from scipy._lib._array_api_docs_tables import is_named_function_like_object
+from scipy._lib import array_api_extra as xpx
+from scipy._lib._array_api_no_0d import xp_assert_equal as xp_assert_equal_no_0d
+from scipy._lib.array_api_extra.testing import lazy_xp_function
+
+# Run all tests in this module in the Array API CI,
+# including those without the `xp` fixture
+pytestmark = pytest.mark.array_api_backends
+
+lazy_xp_function(_asarray)
+lazy_xp_function(xp_copy)
+
+
+@pytest.mark.skipif(not SCIPY_ARRAY_API,
+        reason="Array API test; set environment variable SCIPY_ARRAY_API=1 to run it")
+class TestArrayAPI:
+
+    def test_array_namespace(self):
+        x, y = np.array([0, 1, 2]), np.array([0, 1, 2])
+        xp = array_namespace(x, y)
+        assert 'array_api_compat.numpy' in xp.__name__
+
+    def test_asarray(self, xp):
+        x, y = _asarray([0, 1, 2], xp=xp), _asarray(np.arange(3), xp=xp)
+        ref = xp.asarray([0, 1, 2])
+        xp_assert_equal(x, ref)
+        xp_assert_equal(y, ref)
+
+    @pytest.mark.filterwarnings("ignore: the matrix subclass")
+    def test_raises(self):
+        msg = "of type `numpy.ma.MaskedArray` are not supported"
+        with pytest.raises(TypeError, match=msg):
+            array_namespace(np.ma.array(1), np.array(1))
+
+        msg = "of type `numpy.matrix` are not supported"
+        with pytest.raises(TypeError, match=msg):
+            array_namespace(np.array(1), np.matrix(1))
+
+        msg = "only boolean and numerical dtypes are supported"
+        with pytest.raises(TypeError, match=msg):
+            array_namespace([object()])
+        with pytest.raises(TypeError, match=msg):
+            array_namespace('abc')
+
+    @pytest.mark.skip_xp_backends(np_only=True, reason="Array-likes")
+    def test_array_likes(self, xp):
+        """Test that if all parameters of array_namespace are Array-likes,
+        the output is array_api_compat.numpy
+        """
+        assert array_namespace([0, 1, 2]) is xp
+        assert array_namespace((0, 1, 2)) is xp
+        assert array_namespace(1, 2, 3) is xp
+        assert array_namespace(1) is xp
+        assert array_namespace(np.int64(1)) is xp
+        assert array_namespace([0, 1, 2], 3) is xp
+        assert array_namespace() is xp
+        assert array_namespace(None) is xp
+        assert array_namespace(1, None) is xp
+        assert array_namespace(None, 1) is xp
+
+        # This only works when xp is numpy!
+        assert array_namespace(np.asarray([1, 2]), [3, 4]) is xp
+        assert array_namespace(np.int64(1), [3, 4]) is xp
+
+    def test_array_and_array_likes_mix(self, xp):
+        """Test that if there is at least one Array API object among
+        the parameters of array_namespace, and all other parameters
+        are scalars, the output is its namespace.
+
+        If there are non-scalar Array-Likes, raise as in array-api-compat.
+        """
+        x = xp.asarray(1)
+        assert array_namespace(x) is xp
+        assert array_namespace(x, 1) is xp
+        assert array_namespace(1, x) is xp
+        assert array_namespace(None, x) is xp
+
+        if is_numpy(xp):
+            assert array_namespace(x, [1, 2]) is xp
+        else:
+            with pytest.raises(TypeError, match="Multiple namespaces"):
+                array_namespace(x, [1, 2])
+            with pytest.raises(TypeError, match="Multiple namespaces"):
+                array_namespace(x, np.int64(1))
+            with pytest.raises(TypeError, match="Multiple namespaces"):
+                 # Subclass of float; matches array_api_compat behavior
+                array_namespace(x, np.float64(1))
+            with pytest.raises(TypeError, match="Multiple namespaces"):
+                # Subclass of complex; matches array_api_compat behavior
+                array_namespace(x, np.complex128(1))
+
+    def test_array_api_extra_hook(self):
+        """Test that the `array_namespace` function used by
+        array-api-extra has been overridden by scipy
+        """
+        msg = "only boolean and numerical dtypes are supported"
+        with pytest.raises(TypeError, match=msg):
+            xpx.atleast_nd("abc", ndim=0)
+
+    def test_jax_zero_gradient_array(self):
+        """Test array_namespace special case for JAX zero-gradient arrays, which are
+        numpy arrays but must be treated as JAX arrays.
+        See matching code and tests in array_api_compat.
+        """
+        jax = pytest.importorskip("jax")
+        xp = pytest.importorskip("jax.numpy")
+        # Create numpy array with dtype=jax.float0
+        jax_zero = jax.vmap(jax.grad(xp.float32, allow_int=True))(xp.arange(4))
+        assert array_namespace(jax_zero) is xp
+
+    def test_void_but_not_jax_zero_gradient_array(self):
+        """A void dtype that is not a jax.float0 must not be caught in the
+        special case for JAX zero-gradient arrays.
+        """
+        void = np.empty(0, dtype=np.dtype([]))
+        with pytest.raises(TypeError, match="only boolean and numerical dtypes"):
+            array_namespace(void)
+        with pytest.raises(TypeError, match="only boolean and numerical dtypes"):
+            array_namespace([void, void])
+
+    def test_copy(self, xp):
+        for _xp in [xp, None]:
+            x = xp.asarray([1, 2, 3])
+            y = xp_copy(x, xp=_xp)
+            # with numpy we'd want to use np.shared_memory, but that's not specified
+            # in the array-api
+            assert id(x) != id(y)
+            try:
+                y[0] = 10
+            except (TypeError, ValueError):
+                pass
+            else:
+                assert x[0] != y[0]
+
+    @pytest.mark.parametrize(
+        "dtype",
+        ["float32", "float64", "complex64", "complex128", "int32", "int64"],
+    )
+    @pytest.mark.parametrize(
+        "data", [[], 1, [1, 2, 3], [[1, 2], [2, 3]]],
+    )
+    def test_copy_to_numpy(self, xp, data, dtype):
+        xp_dtype = getattr(xp, dtype)
+        np_dtype = getattr(np, dtype)
+        x = xp.asarray(data, dtype=xp_dtype)
+        y = _xp_copy_to_numpy(x)
+        assert isinstance(y, np.ndarray)
+        assert y.dtype == np_dtype
+        assert x.shape == y.shape
+        np.testing.assert_equal(y, np.asarray(data, dtype=np_dtype))
+        if is_numpy(xp):
+            # Ensure y is a copy when xp is numpy.
+            assert id(x) != id(y)
+
+    
+    @pytest.mark.parametrize('dtype', ['int32', 'int64', 'float32', 'float64'])
+    @pytest.mark.parametrize('shape', [(), (3,)])
+    def test_strict_checks(self, xp, dtype, shape):
+        # Check that `_strict_check` behaves as expected
+        dtype = getattr(xp, dtype)
+        x = xp.broadcast_to(xp.asarray(1, dtype=dtype), shape)
+        x = x if shape else x[()]
+        y = np_compat.asarray(1)[()]
+
+        kwarg_names = ["check_namespace", "check_dtype", "check_shape", "check_0d"]
+        options = dict(zip(kwarg_names, [True, False, False, False]))
+        if is_numpy(xp):
+            xp_assert_equal(x, y, **options)
+        else:
+            with pytest.raises(
+                AssertionError,
+                match="Namespace of desired array does not match",
+            ):
+                xp_assert_equal(x, y, **options)
+            with pytest.raises(
+                AssertionError,
+                match="Namespace of actual and desired arrays do not match",
+            ):
+                xp_assert_equal(y, x, **options)
+
+        options = dict(zip(kwarg_names, [False, True, False, False]))
+        if y.dtype.name in str(x.dtype):
+            xp_assert_equal(x, y, **options)
+        else:
+            with pytest.raises(AssertionError, match="dtypes do not match."):
+                xp_assert_equal(x, y, **options)
+
+        options = dict(zip(kwarg_names, [False, False, True, False]))
+        if x.shape == y.shape:
+            xp_assert_equal(x, y, **options)
+        else:
+            with pytest.raises(AssertionError, match="Shapes do not match."):
+                xp_assert_equal(x, xp.asarray(y), **options)
+
+        options = dict(zip(kwarg_names, [False, False, False, True]))
+        if is_numpy(xp) and x.shape == y.shape:
+            xp_assert_equal(x, y, **options)
+        elif is_numpy(xp):
+            with pytest.raises(AssertionError, match="Array-ness does not match."):
+                xp_assert_equal(x, y, **options)
+
+    @pytest.mark.skip_xp_backends(np_only=True, reason="Scalars only exist in NumPy")
+    def test_check_scalar(self, xp):
+        # identity always passes
+        xp_assert_equal(xp.float64(0), xp.float64(0))
+        xp_assert_equal(xp.asarray(0.), xp.asarray(0.))
+        xp_assert_equal(xp.float64(0), xp.float64(0), check_0d=False)
+        xp_assert_equal(xp.asarray(0.), xp.asarray(0.), check_0d=False)
+
+        # Check default convention: 0d-arrays are distinguished from scalars
+        message = "Array-ness does not match:.*"
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal(xp.asarray(0.), xp.float64(0))
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal(xp.float64(0), xp.asarray(0.))
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal(xp.asarray(42), xp.int64(42))
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal(xp.int64(42), xp.asarray(42))
+
+        # with `check_0d=False`, scalars-vs-0d passes (if values match)
+        xp_assert_equal(xp.asarray(0.), xp.float64(0), check_0d=False)
+        xp_assert_equal(xp.float64(0), xp.asarray(0.), check_0d=False)
+        # also with regular python objects
+        xp_assert_equal(xp.asarray(0.), 0., check_0d=False)
+        xp_assert_equal(0., xp.asarray(0.), check_0d=False)
+        xp_assert_equal(xp.asarray(42), 42, check_0d=False)
+        xp_assert_equal(42, xp.asarray(42), check_0d=False)
+
+        # as an alternative to `check_0d=False`, explicitly expect scalar
+        xp_assert_equal(xp.float64(0), xp.asarray(0.)[()])
+
+    @pytest.mark.skip_xp_backends(np_only=True, reason="Scalars only exist in NumPy")
+    def test_check_scalar_no_0d(self, xp):
+        # identity passes, if first argument is not 0d (or check_0d=True)
+        xp_assert_equal_no_0d(xp.float64(0), xp.float64(0))
+        xp_assert_equal_no_0d(xp.float64(0), xp.float64(0), check_0d=True)
+        xp_assert_equal_no_0d(xp.asarray(0.), xp.asarray(0.), check_0d=True)
+
+        # by default, 0d values are forbidden as the first argument
+        message = "Result is a NumPy 0d-array.*"
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal_no_0d(xp.asarray(0.), xp.asarray(0.))
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal_no_0d(xp.asarray(0.), xp.float64(0))
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal_no_0d(xp.asarray(42), xp.int64(42))
+
+        # Check default convention: 0d-arrays are NOT distinguished from scalars
+        xp_assert_equal_no_0d(xp.float64(0), xp.asarray(0.))
+        xp_assert_equal_no_0d(xp.int64(42), xp.asarray(42))
+
+        # opt in to 0d-check remains possible
+        message = "Array-ness does not match:.*"
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal_no_0d(xp.asarray(0.), xp.float64(0), check_0d=True)
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal_no_0d(xp.float64(0), xp.asarray(0.), check_0d=True)
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal_no_0d(xp.asarray(42), xp.int64(0), check_0d=True)
+        with pytest.raises(AssertionError, match=message):
+            xp_assert_equal_no_0d(xp.int64(0), xp.asarray(42), check_0d=True)
+
+        # scalars-vs-0d passes (if values match) also with regular python objects
+        xp_assert_equal_no_0d(0., xp.asarray(0.))
+        xp_assert_equal_no_0d(42, xp.asarray(42))
+
+    def test_default_dtype(self, xp):
+        assert xp_default_dtype(xp) == xp.asarray(1.).dtype
+
+
+scalars = [1, 1., 1. + 1j]
+lists = [[1], [1.], [1. + 1j]]
+types = ('int8 int16 int32 int64 '
+         'uint8 uint16 uint32 uint64 '
+         'float32 float64 complex64 complex128').split()
+arrays = [np.asarray([1], dtype=getattr(np, t)) for t in types]
+
+
+def convert_type(x, xp):
+    # Convert NumPy array to xp-array
+    # Convert string to indicated dtype from xp
+    # Return Python scalars unchanged
+    if isinstance(x, np.ndarray):
+        return xp.asarray(x)
+    elif isinstance(x, str):
+        return getattr(xp, x)
+    return x
+
+
+def is_inexact(x, xp):
+    # Determine whether `x` is of inexact (real of complex floating) dtype
+    x = xp.asarray(x) if np.isscalar(x) or isinstance(x, list) else x
+    dtype = getattr(x, 'dtype', x)
+    return xp.isdtype(dtype, ('real floating', 'complex floating'))
+
+
+@pytest.mark.parametrize('x', scalars + lists + types + arrays)
+@pytest.mark.parametrize('y', scalars + lists + types + arrays)
+def test_xp_result_type_no_force(x, y, xp):
+    # When force_floating==False (default), behavior of `xp_result_type`
+    # should match that of `xp.result_type` on the same arguments after
+    # converting lists to arrays of type `xp`.
+    x = convert_type(x, xp)
+    y = convert_type(y, xp)
+    x_ref = xp.asarray(x) if isinstance(x, list) else x
+    y_ref = xp.asarray(y) if isinstance(y, list) else y
+
+    try:
+        dtype_ref = xp.result_type(x_ref, y_ref)
+        expected_error = None
+    except Exception as e:
+        expected_error = (type(e), str(e))
+
+    if expected_error is not None:
+        with pytest.raises(expected_error[0], match=re.escape(expected_error[1])):
+            xp_result_type(x, y, xp=xp)
+        return
+
+    dtype_res = xp_result_type(x, y, xp=xp)
+    assert dtype_res == dtype_ref
+
+
+@pytest.mark.parametrize('x', scalars + lists + types + arrays)
+@pytest.mark.parametrize('y', scalars + lists + types + arrays)
+def test_xp_result_type_force_floating(x, y, xp):
+    # When `force_floating==True`, behavior of `xp_result_type`
+    # should match that of `xp.result_type` with `1.0` appended to the set of
+    # arguments (after converting lists to arrays of type `xp`).
+    # If this raises a `TypeError`, which is the case when the result
+    # type is not defined by the standard, the result type should be
+    # the result type of any inexact (real or complex floating) arguments
+    # and the default floating point type.
+    if (is_torch(xp) and not(isinstance(x, str) or isinstance(y, str))
+            and np.isscalar(x) and np.isscalar(y)):
+        pytest.skip("See 3/27/2024 comment at  data-apis/array-api-compat#277")
+
+    x = convert_type(x, xp)
+    y = convert_type(y, xp)
+    x_ref = xp.asarray(x) if isinstance(x, list) else x
+    y_ref = xp.asarray(y) if isinstance(y, list) else y
+
+    expected_error = None
+    try:
+        dtype_ref = xp.result_type(x_ref, y_ref, 1.0)
+    except TypeError:
+        args = []
+        if is_inexact(x_ref, xp):
+            args.append(x_ref)
+        if is_inexact(y_ref, xp):
+            args.append(y_ref)
+        dtype_ref = xp.result_type(*args, xp.asarray(1.0))
+    except Exception as e:
+        expected_error = (type(e), str(e))
+
+    if expected_error is not None:
+        with pytest.raises(expected_error[0], match=expected_error[1]):
+            xp_result_type(x, y, xp=xp)
+        return
+
+    dtype_res = xp_result_type(x, y, force_floating=True, xp=xp)
+    assert dtype_res == dtype_ref
+
+# Test that the xp_capabilities decorator has been applied to all
+# functions and function-likes in the public API. Modules will be
+# added to the list of tested_modules below as decorator coverage
+# is added on a module by module basis. It remains for future work
+# to offer similar functionality to xp_capabilities for classes in
+# the public API.
+
+tested_modules = ["scipy.stats"]
+
+
+def collect_public_functions():
+    functions = []
+    for module_name in tested_modules:
+        module = import_module(module_name)
+        for name in module.__all__:
+            obj = getattr(module, name)
+            if not is_named_function_like_object(obj):
+                continue
+            functions.append(pytest.param(obj, id=f"{module_name}.{name}"))
+    return functions
+
+
+@pytest.mark.parametrize("func", collect_public_functions())
+def test_xp_capabilities_coverage(func):
+    assert func in xp_capabilities_table
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_bunch.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_bunch.py
new file mode 100644
index 0000000000000000000000000000000000000000..96008627e3afef540913071c95ea543c718a326c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_bunch.py
@@ -0,0 +1,169 @@
+import pytest
+import pickle
+from numpy.testing import assert_equal
+from scipy._lib._bunch import _make_tuple_bunch
+
+
+# `Result` is defined at the top level of the module so it can be
+# used to test pickling.
+Result = _make_tuple_bunch('Result', ['x', 'y', 'z'], ['w', 'beta'])
+
+
+class TestMakeTupleBunch:
+
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+    # Tests with Result
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+    def setup_method(self):
+        # Set up an instance of Result.
+        self.result = Result(x=1, y=2, z=3, w=99, beta=0.5)
+
+    def test_attribute_access(self):
+        assert_equal(self.result.x, 1)
+        assert_equal(self.result.y, 2)
+        assert_equal(self.result.z, 3)
+        assert_equal(self.result.w, 99)
+        assert_equal(self.result.beta, 0.5)
+
+    def test_indexing(self):
+        assert_equal(self.result[0], 1)
+        assert_equal(self.result[1], 2)
+        assert_equal(self.result[2], 3)
+        assert_equal(self.result[-1], 3)
+        with pytest.raises(IndexError, match='index out of range'):
+            self.result[3]
+
+    def test_unpacking(self):
+        x0, y0, z0 = self.result
+        assert_equal((x0, y0, z0), (1, 2, 3))
+        assert_equal(self.result, (1, 2, 3))
+
+    def test_slice(self):
+        assert_equal(self.result[1:], (2, 3))
+        assert_equal(self.result[::2], (1, 3))
+        assert_equal(self.result[::-1], (3, 2, 1))
+
+    def test_len(self):
+        assert_equal(len(self.result), 3)
+
+    def test_repr(self):
+        s = repr(self.result)
+        assert_equal(s, 'Result(x=1, y=2, z=3, w=99, beta=0.5)')
+
+    def test_hash(self):
+        assert_equal(hash(self.result), hash((1, 2, 3)))
+
+    def test_pickle(self):
+        s = pickle.dumps(self.result)
+        obj = pickle.loads(s)
+        assert isinstance(obj, Result)
+        assert_equal(obj.x, self.result.x)
+        assert_equal(obj.y, self.result.y)
+        assert_equal(obj.z, self.result.z)
+        assert_equal(obj.w, self.result.w)
+        assert_equal(obj.beta, self.result.beta)
+
+    def test_read_only_existing(self):
+        with pytest.raises(AttributeError, match="can't set attribute"):
+            self.result.x = -1
+
+    def test_read_only_new(self):
+        self.result.plate_of_shrimp = "lattice of coincidence"
+        assert self.result.plate_of_shrimp == "lattice of coincidence"
+
+    def test_constructor_missing_parameter(self):
+        with pytest.raises(TypeError, match='missing'):
+            # `w` is missing.
+            Result(x=1, y=2, z=3, beta=0.75)
+
+    def test_constructor_incorrect_parameter(self):
+        with pytest.raises(TypeError, match='unexpected'):
+            # `foo` is not an existing field.
+            Result(x=1, y=2, z=3, w=123, beta=0.75, foo=999)
+
+    def test_module(self):
+        m = 'scipy._lib.tests.test_bunch'
+        assert_equal(Result.__module__, m)
+        assert_equal(self.result.__module__, m)
+
+    def test_extra_fields_per_instance(self):
+        # This test exists to ensure that instances of the same class
+        # store their own values for the extra fields. That is, the values
+        # are stored per instance and not in the class.
+        result1 = Result(x=1, y=2, z=3, w=-1, beta=0.0)
+        result2 = Result(x=4, y=5, z=6, w=99, beta=1.0)
+        assert_equal(result1.w, -1)
+        assert_equal(result1.beta, 0.0)
+        # The rest of these checks aren't essential, but let's check
+        # them anyway.
+        assert_equal(result1[:], (1, 2, 3))
+        assert_equal(result2.w, 99)
+        assert_equal(result2.beta, 1.0)
+        assert_equal(result2[:], (4, 5, 6))
+
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+    # Other tests
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+    def test_extra_field_names_is_optional(self):
+        Square = _make_tuple_bunch('Square', ['width', 'height'])
+        sq = Square(width=1, height=2)
+        assert_equal(sq.width, 1)
+        assert_equal(sq.height, 2)
+        s = repr(sq)
+        assert_equal(s, 'Square(width=1, height=2)')
+
+    def test_tuple_like(self):
+        Tup = _make_tuple_bunch('Tup', ['a', 'b'])
+        tu = Tup(a=1, b=2)
+        assert isinstance(tu, tuple)
+        assert isinstance(tu + (1,), tuple)
+
+    def test_explicit_module(self):
+        m = 'some.module.name'
+        Foo = _make_tuple_bunch('Foo', ['x'], ['a', 'b'], module=m)
+        foo = Foo(x=1, a=355, b=113)
+        assert_equal(Foo.__module__, m)
+        assert_equal(foo.__module__, m)
+
+    def test_passes_polars_checks(self):
+        # gh-22450
+        Square = _make_tuple_bunch('Square', ['width', 'height'])
+        assert hasattr(Square, '_replace')
+        assert hasattr(Square, '_field_defaults')
+
+
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+    # Argument validation
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+    @pytest.mark.parametrize('args', [('123', ['a'], ['b']),
+                                      ('Foo', ['-3'], ['x']),
+                                      ('Foo', ['a'], ['+-*/'])])
+    def test_identifiers_not_allowed(self, args):
+        with pytest.raises(ValueError, match='identifiers'):
+            _make_tuple_bunch(*args)
+
+    @pytest.mark.parametrize('args', [('Foo', ['a', 'b', 'a'], ['x']),
+                                      ('Foo', ['a', 'b'], ['b', 'x'])])
+    def test_repeated_field_names(self, args):
+        with pytest.raises(ValueError, match='Duplicate'):
+            _make_tuple_bunch(*args)
+
+    @pytest.mark.parametrize('args', [('Foo', ['_a'], ['x']),
+                                      ('Foo', ['a'], ['_x'])])
+    def test_leading_underscore_not_allowed(self, args):
+        with pytest.raises(ValueError, match='underscore'):
+            _make_tuple_bunch(*args)
+
+    @pytest.mark.parametrize('args', [('Foo', ['def'], ['x']),
+                                      ('Foo', ['a'], ['or']),
+                                      ('and', ['a'], ['x'])])
+    def test_keyword_not_allowed_in_fields(self, args):
+        with pytest.raises(ValueError, match='keyword'):
+            _make_tuple_bunch(*args)
+
+    def test_at_least_one_field_name_required(self):
+        with pytest.raises(ValueError, match='at least one name'):
+            _make_tuple_bunch('Qwerty', [], ['a', 'b'])
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_ccallback.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_ccallback.py
new file mode 100644
index 0000000000000000000000000000000000000000..e8a2c97c6f67732f55eea6ed5cad297f5068a714
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_ccallback.py
@@ -0,0 +1,196 @@
+from numpy.testing import assert_equal, assert_
+from pytest import raises as assert_raises
+
+import time
+import pytest
+import ctypes
+import threading
+from scipy._lib import _ccallback_c as _test_ccallback_cython
+from scipy._lib import _test_ccallback
+from scipy._lib._ccallback import LowLevelCallable
+
+
+ERROR_VALUE = 2.0
+
+
+def callback_python(a, user_data=None):
+    if a == ERROR_VALUE:
+        raise ValueError("bad value")
+
+    if user_data is None:
+        return a + 1
+    else:
+        return a + user_data
+
+def _get_cffi_func(base, signature):
+    cffi = pytest.importorskip("cffi")
+
+    # Get function address
+    voidp = ctypes.cast(base, ctypes.c_void_p)
+    address = voidp.value
+
+    # Create corresponding cffi handle
+    ffi = cffi.FFI()
+    func = ffi.cast(signature, address)
+    return func
+
+
+def _get_ctypes_data():
+    value = ctypes.c_double(2.0)
+    return ctypes.cast(ctypes.pointer(value), ctypes.c_voidp)
+
+
+def _get_cffi_data():
+    cffi = pytest.importorskip("cffi")
+    ffi = cffi.FFI()
+    return ffi.new('double *', 2.0)
+
+
+CALLERS = {
+    'simple': _test_ccallback.test_call_simple,
+    'nodata': _test_ccallback.test_call_nodata,
+    'nonlocal': _test_ccallback.test_call_nonlocal,
+    'cython': _test_ccallback_cython.test_call_cython,
+}
+
+# These functions have signatures known to the callers
+FUNCS = {
+    'python': lambda: callback_python,
+    'capsule': lambda: _test_ccallback.test_get_plus1_capsule(),
+    'cython': lambda: LowLevelCallable.from_cython(_test_ccallback_cython,
+                                                   "plus1_cython"),
+    'ctypes': lambda: _test_ccallback_cython.plus1_ctypes,
+    'cffi': lambda: _get_cffi_func(_test_ccallback_cython.plus1_ctypes,
+                                   'double (*)(double, int *, void *)'),
+    'capsule_b': lambda: _test_ccallback.test_get_plus1b_capsule(),
+    'cython_b': lambda: LowLevelCallable.from_cython(_test_ccallback_cython,
+                                                     "plus1b_cython"),
+    'ctypes_b': lambda: _test_ccallback_cython.plus1b_ctypes,
+    'cffi_b': lambda: _get_cffi_func(_test_ccallback_cython.plus1b_ctypes,
+                                     'double (*)(double, double, int *, void *)'),
+}
+
+# These functions have signatures the callers don't know
+BAD_FUNCS = {
+    'capsule_bc': lambda: _test_ccallback.test_get_plus1bc_capsule(),
+    'cython_bc': lambda: LowLevelCallable.from_cython(_test_ccallback_cython,
+                                                      "plus1bc_cython"),
+    'ctypes_bc': lambda: _test_ccallback_cython.plus1bc_ctypes,
+    'cffi_bc': lambda: _get_cffi_func(
+        _test_ccallback_cython.plus1bc_ctypes,
+        'double (*)(double, double, double, int *, void *)'
+    ),
+}
+
+USER_DATAS = {
+    'ctypes': _get_ctypes_data,
+    'cffi': _get_cffi_data,
+    'capsule': _test_ccallback.test_get_data_capsule,
+}
+
+
+def test_callbacks():
+    def check(caller, func, user_data):
+        caller = CALLERS[caller]
+        func = FUNCS[func]()
+        user_data = USER_DATAS[user_data]()
+
+        if func is callback_python:
+            def func2(x):
+                return func(x, 2.0)
+        else:
+            func2 = LowLevelCallable(func, user_data)
+            func = LowLevelCallable(func)
+
+        # Test basic call
+        assert_equal(caller(func, 1.0), 2.0)
+
+        # Test 'bad' value resulting to an error
+        assert_raises(ValueError, caller, func, ERROR_VALUE)
+
+        # Test passing in user_data
+        assert_equal(caller(func2, 1.0), 3.0)
+
+    for caller in sorted(CALLERS.keys()):
+        for func in sorted(FUNCS.keys()):
+            for user_data in sorted(USER_DATAS.keys()):
+                check(caller, func, user_data)
+
+
+def test_bad_callbacks():
+    def check(caller, func, user_data):
+        caller = CALLERS[caller]
+        user_data = USER_DATAS[user_data]()
+        func = BAD_FUNCS[func]()
+
+        if func is callback_python:
+            def func2(x):
+                return func(x, 2.0)
+        else:
+            func2 = LowLevelCallable(func, user_data)
+            func = LowLevelCallable(func)
+
+        # Test that basic call fails
+        assert_raises(ValueError, caller, LowLevelCallable(func), 1.0)
+
+        # Test that passing in user_data also fails
+        assert_raises(ValueError, caller, func2, 1.0)
+
+        # Test error message
+        llfunc = LowLevelCallable(func)
+        try:
+            caller(llfunc, 1.0)
+        except ValueError as err:
+            msg = str(err)
+            assert_(llfunc.signature in msg, msg)
+            assert_('double (double, double, int *, void *)' in msg, msg)
+
+    for caller in sorted(CALLERS.keys()):
+        for func in sorted(BAD_FUNCS.keys()):
+            for user_data in sorted(USER_DATAS.keys()):
+                check(caller, func, user_data)
+
+
+def test_signature_override():
+    caller = _test_ccallback.test_call_simple
+    func = _test_ccallback.test_get_plus1_capsule()
+
+    llcallable = LowLevelCallable(func, signature="bad signature")
+    assert_equal(llcallable.signature, "bad signature")
+    assert_raises(ValueError, caller, llcallable, 3)
+
+    llcallable = LowLevelCallable(func, signature="double (double, int *, void *)")
+    assert_equal(llcallable.signature, "double (double, int *, void *)")
+    assert_equal(caller(llcallable, 3), 4)
+
+
+def test_threadsafety():
+    def callback(a, caller):
+        if a <= 0:
+            return 1
+        else:
+            res = caller(lambda x: callback(x, caller), a - 1)
+            return 2*res
+
+    def check(caller):
+        caller = CALLERS[caller]
+
+        results = []
+
+        count = 10
+
+        def run():
+            time.sleep(0.01)
+            r = caller(lambda x: callback(x, caller), count)
+            results.append(r)
+
+        threads = [threading.Thread(target=run) for j in range(20)]
+        for thread in threads:
+            thread.start()
+        for thread in threads:
+            thread.join()
+
+        assert_equal(results, [2.0**count]*len(threads))
+
+    for caller in CALLERS.keys():
+        check(caller)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_config.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_config.py
new file mode 100644
index 0000000000000000000000000000000000000000..b43d3f9f0da39a86b78cb2210cb21d670e5cf978
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_config.py
@@ -0,0 +1,44 @@
+"""
+Check the SciPy config is valid.
+"""
+import scipy
+import pytest
+from unittest.mock import patch
+
+pytestmark = pytest.mark.skipif(
+    not hasattr(scipy.__config__, "_built_with_meson"),
+    reason="Requires Meson builds",
+)
+
+
+class TestSciPyConfigs:
+    REQUIRED_CONFIG_KEYS = [
+        "Compilers",
+        "Machine Information",
+        "Python Information",
+    ]
+
+    @patch("scipy.__config__._check_pyyaml")
+    def test_pyyaml_not_found(self, mock_yaml_importer):
+        mock_yaml_importer.side_effect = ModuleNotFoundError()
+        with pytest.warns(UserWarning):
+            scipy.show_config()
+
+    def test_dict_mode(self):
+        config = scipy.show_config(mode="dicts")
+
+        assert isinstance(config, dict)
+        assert all([key in config for key in self.REQUIRED_CONFIG_KEYS]), (
+            "Required key missing,"
+            " see index of `False` with `REQUIRED_CONFIG_KEYS`"
+        )
+
+    def test_invalid_mode(self):
+        with pytest.raises(AttributeError):
+            scipy.show_config(mode="foo")
+
+    def test_warn_to_add_tests(self):
+        assert len(scipy.__config__.DisplayModes) == 2, (
+            "New mode detected,"
+            " please add UT if applicable and increment this count"
+        )
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_deprecation.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_deprecation.py
new file mode 100644
index 0000000000000000000000000000000000000000..36d4b671117ba54fa612e7de504382c238dc18ff
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_deprecation.py
@@ -0,0 +1,10 @@
+import pytest
+
+@pytest.mark.thread_unsafe(reason="deprecate_cython_api is not thread-safe")
+def test_cython_api_deprecation():
+    match = ("`scipy._lib._test_deprecation_def.foo_deprecated` "
+             "is deprecated, use `foo` instead!\n"
+             "Deprecated in Scipy 42.0.0")
+    with pytest.warns(DeprecationWarning, match=match):
+        from .. import _test_deprecation_call
+    assert _test_deprecation_call.call() == (1, 1)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_doccer.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_doccer.py
new file mode 100644
index 0000000000000000000000000000000000000000..d351b12da33e0f873e71b6ab6c11fa3aff5e9430
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_doccer.py
@@ -0,0 +1,144 @@
+''' Some tests for the documenting decorator and support functions '''
+
+import sys
+import warnings
+import pytest
+from numpy.testing import assert_equal
+
+from scipy._lib import doccer
+
+# python -OO strips docstrings
+DOCSTRINGS_STRIPPED = sys.flags.optimize > 1
+
+docstring = \
+"""Docstring
+    %(strtest1)s
+        %(strtest2)s
+     %(strtest3)s
+"""
+param_doc1 = \
+"""Another test
+   with some indent"""
+
+param_doc2 = \
+"""Another test, one line"""
+
+param_doc3 = \
+"""    Another test
+       with some indent"""
+
+doc_dict = {'strtest1':param_doc1,
+            'strtest2':param_doc2,
+            'strtest3':param_doc3}
+
+filled_docstring = \
+"""Docstring
+    Another test
+       with some indent
+        Another test, one line
+     Another test
+       with some indent
+"""
+
+
+def test_unindent():
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", category=DeprecationWarning)
+        assert_equal(doccer.unindent_string(param_doc1), param_doc1)
+        assert_equal(doccer.unindent_string(param_doc2), param_doc2)
+        assert_equal(doccer.unindent_string(param_doc3), param_doc1)
+
+
+def test_unindent_dict():
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", category=DeprecationWarning)
+        d2 = doccer.unindent_dict(doc_dict)
+    assert_equal(d2['strtest1'], doc_dict['strtest1'])
+    assert_equal(d2['strtest2'], doc_dict['strtest2'])
+    assert_equal(d2['strtest3'], doc_dict['strtest1'])
+
+
+def test_docformat():
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", category=DeprecationWarning)
+        udd = doccer.unindent_dict(doc_dict)
+        formatted = doccer.docformat(docstring, udd)
+        assert_equal(formatted, filled_docstring)
+        single_doc = 'Single line doc %(strtest1)s'
+        formatted = doccer.docformat(single_doc, doc_dict)
+        # Note - initial indent of format string does not
+        # affect subsequent indent of inserted parameter
+        assert_equal(formatted, """Single line doc Another test
+   with some indent""")
+
+
+@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstrings stripped")
+def test_decorator():
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", category=DeprecationWarning)
+        # with unindentation of parameters
+        decorator = doccer.filldoc(doc_dict, True)
+
+        @decorator
+        def func():
+            """ Docstring
+            %(strtest3)s
+            """
+
+        def expected():
+            """ Docstring
+            Another test
+               with some indent
+            """
+        assert_equal(func.__doc__, expected.__doc__)
+
+        # without unindentation of parameters
+
+        # The docstring should be unindented for Python 3.13+
+        # because of https://github.com/python/cpython/issues/81283
+        decorator = doccer.filldoc(doc_dict, False if \
+                                   sys.version_info < (3, 13) else True)
+
+        @decorator
+        def func():
+            """ Docstring
+            %(strtest3)s
+            """
+        def expected():
+            """ Docstring
+                Another test
+                   with some indent
+            """
+        assert_equal(func.__doc__, expected.__doc__)
+
+
+@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstrings stripped")
+def test_inherit_docstring_from():
+
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", category=DeprecationWarning)
+
+        class Foo:
+            def func(self):
+                '''Do something useful.'''
+                return
+
+            def func2(self):
+                '''Something else.'''
+
+        class Bar(Foo):
+            @doccer.inherit_docstring_from(Foo)
+            def func(self):
+                '''%(super)sABC'''
+                return
+
+            @doccer.inherit_docstring_from(Foo)
+            def func2(self):
+                # No docstring.
+                return
+
+    assert_equal(Bar.func.__doc__, Foo.func.__doc__ + 'ABC')
+    assert_equal(Bar.func2.__doc__, Foo.func2.__doc__)
+    bar = Bar()
+    assert_equal(bar.func.__doc__, Foo.func.__doc__ + 'ABC')
+    assert_equal(bar.func2.__doc__, Foo.func2.__doc__)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_import_cycles.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_import_cycles.py
new file mode 100644
index 0000000000000000000000000000000000000000..d1d7c2bfca4976019b77bfbbfbc0cc4ca96a6962
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_import_cycles.py
@@ -0,0 +1,26 @@
+import multiprocessing
+import subprocess
+import sys
+
+import pytest
+
+from .test_public_api import PUBLIC_MODULES
+
+# Regression tests for gh-6793.
+# Check that all modules are importable in a new Python process.
+# This is not necessarily true if there are import cycles present.
+
+
+def _check_single_module(module):
+    pid = subprocess.Popen([sys.executable, '-X', 'faulthandler', '-c',
+                            f'import {module}'])
+    assert pid.wait() == 0, f'Failed to import {module}'
+
+
+@pytest.mark.fail_slow(40)
+@pytest.mark.slow
+def test_public_modules_importable_2():
+    # Ensure we use max 6 processes, to limit peak resource usage (memory, file handles)
+    # on resource-constrained systems (e.g., RISC-V - see gh-24163).
+    with multiprocessing.Pool(processes=6) as pool:
+        pool.map(_check_single_module, PUBLIC_MODULES)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_public_api.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_public_api.py
new file mode 100644
index 0000000000000000000000000000000000000000..dfafb4f223364fd566a83bf3425e8077f96dafad
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_public_api.py
@@ -0,0 +1,433 @@
+"""
+This test script is adopted from:
+    https://github.com/numpy/numpy/blob/main/numpy/tests/test_public_api.py
+"""
+
+import pkgutil
+import types
+import importlib
+import warnings
+from importlib import import_module
+
+import pytest
+
+import scipy
+
+from scipy._lib._public_api import PUBLIC_MODULES
+from scipy.conftest import xp_available_backends
+
+
+def test_dir_testing():
+    """Assert that output of dir has only one "testing/tester"
+    attribute without duplicate"""
+    assert len(dir(scipy)) == len(set(dir(scipy)))
+
+
+# The PRIVATE_BUT_PRESENT_MODULES list contains modules that lacked underscores
+# in their name and hence looked public, but weren't meant to be. All these
+# namespace were deprecated in the 1.8.0 release - see "clear split between
+# public and private API" in the 1.8.0 release notes.
+# These private modules support will be removed in SciPy v2.0.0, as the
+# deprecation messages emitted by each of these modules say.
+PRIVATE_BUT_PRESENT_MODULES = [
+    'scipy.constants.codata',
+    'scipy.constants.constants',
+    'scipy.fftpack.basic',
+    'scipy.fftpack.convolve',
+    'scipy.fftpack.helper',
+    'scipy.fftpack.pseudo_diffs',
+    'scipy.fftpack.realtransforms',
+    'scipy.integrate.dop',
+    'scipy.integrate.odepack',
+    'scipy.integrate.quadpack',
+    'scipy.integrate.vode',
+    'scipy.interpolate.dfitpack',
+    'scipy.interpolate.fitpack',
+    'scipy.interpolate.fitpack2',
+    'scipy.interpolate.interpnd',
+    'scipy.interpolate.interpolate',
+    'scipy.interpolate.ndgriddata',
+    'scipy.interpolate.polyint',
+    'scipy.interpolate.rbf',
+    'scipy.io.arff.arffread',
+    'scipy.io.harwell_boeing',
+    'scipy.io.idl',
+    'scipy.io.matlab.byteordercodes',
+    'scipy.io.matlab.mio',
+    'scipy.io.matlab.mio4',
+    'scipy.io.matlab.mio5',
+    'scipy.io.matlab.mio5_params',
+    'scipy.io.matlab.mio5_utils',
+    'scipy.io.matlab.mio_utils',
+    'scipy.io.matlab.miobase',
+    'scipy.io.matlab.streams',
+    'scipy.io.mmio',
+    'scipy.io.netcdf',
+    'scipy.linalg.basic',
+    'scipy.linalg.decomp',
+    'scipy.linalg.decomp_cholesky',
+    'scipy.linalg.decomp_lu',
+    'scipy.linalg.decomp_qr',
+    'scipy.linalg.decomp_schur',
+    'scipy.linalg.decomp_svd',
+    'scipy.linalg.matfuncs',
+    'scipy.linalg.misc',
+    'scipy.linalg.special_matrices',
+    'scipy.misc',
+    'scipy.misc.common',
+    'scipy.misc.doccer',
+    'scipy.ndimage.filters',
+    'scipy.ndimage.fourier',
+    'scipy.ndimage.interpolation',
+    'scipy.ndimage.measurements',
+    'scipy.ndimage.morphology',
+    'scipy.odr.models',
+    'scipy.odr.odrpack',
+    'scipy.optimize.cobyla',
+    'scipy.optimize.cython_optimize',
+    'scipy.optimize.lbfgsb',
+    'scipy.optimize.linesearch',
+    'scipy.optimize.minpack',
+    'scipy.optimize.minpack2',
+    'scipy.optimize.moduleTNC',
+    'scipy.optimize.nonlin',
+    'scipy.optimize.optimize',
+    'scipy.optimize.slsqp',
+    'scipy.optimize.tnc',
+    'scipy.optimize.zeros',
+    'scipy.signal.bsplines',
+    'scipy.signal.filter_design',
+    'scipy.signal.fir_filter_design',
+    'scipy.signal.lti_conversion',
+    'scipy.signal.ltisys',
+    'scipy.signal.signaltools',
+    'scipy.signal.spectral',
+    'scipy.signal.spline',
+    'scipy.signal.waveforms',
+    'scipy.signal.wavelets',
+    'scipy.signal.windows.windows',
+    'scipy.sparse.base',
+    'scipy.sparse.bsr',
+    'scipy.sparse.compressed',
+    'scipy.sparse.construct',
+    'scipy.sparse.coo',
+    'scipy.sparse.csc',
+    'scipy.sparse.csr',
+    'scipy.sparse.data',
+    'scipy.sparse.dia',
+    'scipy.sparse.dok',
+    'scipy.sparse.extract',
+    'scipy.sparse.lil',
+    'scipy.sparse.linalg.dsolve',
+    'scipy.sparse.linalg.eigen',
+    'scipy.sparse.linalg.interface',
+    'scipy.sparse.linalg.isolve',
+    'scipy.sparse.linalg.matfuncs',
+    'scipy.sparse.sparsetools',
+    'scipy.sparse.spfuncs',
+    'scipy.sparse.sputils',
+    'scipy.spatial.ckdtree',
+    'scipy.spatial.kdtree',
+    'scipy.spatial.qhull',
+    'scipy.spatial.transform.rotation',
+    'scipy.special.add_newdocs',
+    'scipy.special.basic',
+    'scipy.special.cython_special',
+    'scipy.special.orthogonal',
+    'scipy.special.sf_error',
+    'scipy.special.specfun',
+    'scipy.special.spfun_stats',
+    'scipy.stats.biasedurn',
+    'scipy.stats.kde',
+    'scipy.stats.morestats',
+    'scipy.stats.mstats_basic',
+    'scipy.stats.mstats_extras',
+    'scipy.stats.mvn',
+    'scipy.stats.stats',
+]
+
+
+def is_unexpected(name):
+    """Check if this needs to be considered."""
+    if '._' in name or '.tests' in name or '.setup' in name:
+        return False
+
+    if name in PUBLIC_MODULES:
+        return False
+
+    if name in PRIVATE_BUT_PRESENT_MODULES:
+        return False
+
+    return True
+
+
+SKIP_LIST = [
+    'scipy.conftest',
+    'scipy.version',
+    'scipy.special.libsf_error_state',
+    'scipy.integrate.lsoda'
+]
+
+
+# XXX: this test does more than it says on the tin - in using `pkgutil.walk_packages`,
+# it will raise if it encounters any exceptions which are not handled by `ignore_errors`
+# while attempting to import each discovered package.
+# For now, `ignore_errors` only ignores what is necessary, but this could be expanded -
+# for example, to all errors from private modules or git subpackages - if desired.
+@pytest.mark.thread_unsafe(
+    reason=("crashes in pkgutil.walk_packages, see "
+            "https://github.com/data-apis/array-api-compat/issues/343"))
+def test_all_modules_are_expected():
+    """
+    Test that we don't add anything that looks like a new public module by
+    accident.  Check is based on filenames.
+    """
+
+    def ignore_errors(name):
+        # if versions of other array libraries are installed which are incompatible
+        # with the installed NumPy version, there can be errors on importing
+        # `array_api_compat`. This should only raise if SciPy is configured with
+        # that library as an available backend.
+        backends = {'cupy', 'torch', 'dask.array'}
+        for backend in backends:
+            path = f'array_api_compat.{backend}'
+            if path in name and backend not in xp_available_backends:
+                return
+        raise
+
+    modnames = []
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings("ignore", "scipy.misc", DeprecationWarning)
+        for _, modname, _ in pkgutil.walk_packages(path=scipy.__path__,
+                                                   prefix=scipy.__name__ + '.',
+                                                   onerror=ignore_errors):
+            if is_unexpected(modname) and modname not in SKIP_LIST:
+                # We have a name that is new.  If that's on purpose, add it to
+                # PUBLIC_MODULES.  We don't expect to have to add anything to
+                # PRIVATE_BUT_PRESENT_MODULES.  Use an underscore in the name!
+                modnames.append(modname)
+
+    if modnames:
+        raise AssertionError(f'Found unexpected modules: {modnames}')
+
+
+# Stuff that clearly shouldn't be in the API and is detected by the next test
+# below
+SKIP_LIST_2 = [
+    'scipy.char',
+    'scipy.rec',
+    'scipy.emath',
+    'scipy.math',
+    'scipy.random',
+    'scipy.ctypeslib',
+    'scipy.ma',
+    'scipy.integrate.lsoda'
+]
+
+
+def test_all_modules_are_expected_2():
+    """
+    Method checking all objects. The pkgutil-based method in
+    `test_all_modules_are_expected` does not catch imports into a namespace,
+    only filenames.
+    """
+
+    def find_unexpected_members(mod_name):
+        members = []
+        module = importlib.import_module(mod_name)
+        if hasattr(module, '__all__'):
+            objnames = module.__all__
+        else:
+            objnames = dir(module)
+
+        for objname in objnames:
+            if not objname.startswith('_'):
+                fullobjname = mod_name + '.' + objname
+                if isinstance(getattr(module, objname), types.ModuleType):
+                    if is_unexpected(fullobjname) and fullobjname not in SKIP_LIST_2:
+                        members.append(fullobjname)
+
+        return members
+    with warnings.catch_warnings():
+        warnings.filterwarnings("ignore",  "scipy.misc", DeprecationWarning)
+        unexpected_members = find_unexpected_members("scipy")
+
+    for modname in PUBLIC_MODULES:
+        unexpected_members.extend(find_unexpected_members(modname))
+
+    if unexpected_members:
+        raise AssertionError("Found unexpected object(s) that look like "
+                             f"modules: {unexpected_members}")
+
+
+def test_api_importable():
+    """
+    Check that all submodules listed higher up in this file can be imported
+    Note that if a PRIVATE_BUT_PRESENT_MODULES entry goes missing, it may
+    simply need to be removed from the list (deprecation may or may not be
+    needed - apply common sense).
+    """
+    def check_importable(module_name):
+        try:
+            importlib.import_module(module_name)
+        except (ImportError, AttributeError):
+            return False
+
+        return True
+
+    module_names = []
+    for module_name in PUBLIC_MODULES:
+        if not check_importable(module_name):
+            module_names.append(module_name)
+
+    if module_names:
+        raise AssertionError("Modules in the public API that cannot be "
+                             f"imported: {module_names}")
+
+    with warnings.catch_warnings(record=True):
+        warnings.simplefilter('always', category=DeprecationWarning)
+        warnings.simplefilter('always', category=ImportWarning)
+        for module_name in PRIVATE_BUT_PRESENT_MODULES:
+            if not check_importable(module_name):
+                module_names.append(module_name)
+
+    if module_names:
+        raise AssertionError("Modules that are not really public but looked "
+                             "public and can not be imported: "
+                             f"{module_names}")
+
+
+@pytest.mark.parametrize(("module_name", "correct_module"),
+                         [('scipy.constants.codata', None),
+                          ('scipy.constants.constants', None),
+                          ('scipy.fftpack.basic', None),
+                          ('scipy.fftpack.helper', None),
+                          ('scipy.fftpack.pseudo_diffs', None),
+                          ('scipy.fftpack.realtransforms', None),
+                          ('scipy.integrate.dop', None),
+                          ('scipy.integrate.odepack', None),
+                          ('scipy.integrate.quadpack', None),
+                          ('scipy.integrate.vode', None),
+                          ('scipy.interpolate.dfitpack', None),
+                          ('scipy.interpolate.fitpack', None),
+                          ('scipy.interpolate.fitpack2', None),
+                          ('scipy.interpolate.interpnd', None),
+                          ('scipy.interpolate.interpolate', None),
+                          ('scipy.interpolate.ndgriddata', None),
+                          ('scipy.interpolate.polyint', None),
+                          ('scipy.interpolate.rbf', None),
+                          ('scipy.io.harwell_boeing', None),
+                          ('scipy.io.idl', None),
+                          ('scipy.io.mmio', None),
+                          ('scipy.io.netcdf', None),
+                          ('scipy.io.arff.arffread', 'arff'),
+                          ('scipy.io.matlab.byteordercodes', 'matlab'),
+                          ('scipy.io.matlab.mio_utils', 'matlab'),
+                          ('scipy.io.matlab.mio', 'matlab'),
+                          ('scipy.io.matlab.mio4', 'matlab'),
+                          ('scipy.io.matlab.mio5_params', 'matlab'),
+                          ('scipy.io.matlab.mio5_utils', 'matlab'),
+                          ('scipy.io.matlab.mio5', 'matlab'),
+                          ('scipy.io.matlab.miobase', 'matlab'),
+                          ('scipy.io.matlab.streams', 'matlab'),
+                          ('scipy.linalg.basic', None),
+                          ('scipy.linalg.decomp', None),
+                          ('scipy.linalg.decomp_cholesky', None),
+                          ('scipy.linalg.decomp_lu', None),
+                          ('scipy.linalg.decomp_qr', None),
+                          ('scipy.linalg.decomp_schur', None),
+                          ('scipy.linalg.decomp_svd', None),
+                          ('scipy.linalg.matfuncs', None),
+                          ('scipy.linalg.misc', None),
+                          ('scipy.linalg.special_matrices', None),
+                          ('scipy.ndimage.filters', None),
+                          ('scipy.ndimage.fourier', None),
+                          ('scipy.ndimage.interpolation', None),
+                          ('scipy.ndimage.measurements', None),
+                          ('scipy.ndimage.morphology', None),
+                          ('scipy.optimize.cobyla', None),
+                          ('scipy.optimize.lbfgsb', None),
+                          ('scipy.optimize.linesearch', None),
+                          ('scipy.optimize.minpack', None),
+                          ('scipy.optimize.minpack2', None),
+                          ('scipy.optimize.moduleTNC', None),
+                          ('scipy.optimize.nonlin', None),
+                          ('scipy.optimize.optimize', None),
+                          ('scipy.optimize.slsqp', None),
+                          ('scipy.optimize.tnc', None),
+                          ('scipy.optimize.zeros', None),
+                          ('scipy.signal.bsplines', None),
+                          ('scipy.signal.filter_design', None),
+                          ('scipy.signal.fir_filter_design', None),
+                          ('scipy.signal.lti_conversion', None),
+                          ('scipy.signal.ltisys', None),
+                          ('scipy.signal.signaltools', None),
+                          ('scipy.signal.spectral', None),
+                          ('scipy.signal.spline', None),
+                          ('scipy.signal.waveforms', None),
+                          ('scipy.signal.wavelets', None),
+                          ('scipy.signal.windows.windows', 'windows'),
+                          ('scipy.sparse.base', None),
+                          ('scipy.sparse.bsr', None),
+                          ('scipy.sparse.compressed', None),
+                          ('scipy.sparse.construct', None),
+                          ('scipy.sparse.coo', None),
+                          ('scipy.sparse.csc', None),
+                          ('scipy.sparse.csr', None),
+                          ('scipy.sparse.data', None),
+                          ('scipy.sparse.dia', None),
+                          ('scipy.sparse.dok', None),
+                          ('scipy.sparse.extract', None),
+                          ('scipy.sparse.lil', None),
+                          ('scipy.sparse.linalg.dsolve', 'linalg'),
+                          ('scipy.sparse.linalg.eigen', 'linalg'),
+                          ('scipy.sparse.linalg.interface', 'linalg'),
+                          ('scipy.sparse.linalg.isolve', 'linalg'),
+                          ('scipy.sparse.linalg.matfuncs', 'linalg'),
+                          ('scipy.sparse.sparsetools', None),
+                          ('scipy.sparse.spfuncs', None),
+                          ('scipy.sparse.sputils', None),
+                          ('scipy.spatial.ckdtree', None),
+                          ('scipy.spatial.kdtree', None),
+                          ('scipy.spatial.qhull', None),
+                          ('scipy.spatial.transform.rotation', 'transform'),
+                          ('scipy.special.add_newdocs', None),
+                          ('scipy.special.basic', None),
+                          ('scipy.special.orthogonal', None),
+                          ('scipy.special.sf_error', None),
+                          ('scipy.special.specfun', None),
+                          ('scipy.special.spfun_stats', None),
+                          ('scipy.stats.biasedurn', None),
+                          ('scipy.stats.kde', None),
+                          ('scipy.stats.morestats', None),
+                          ('scipy.stats.mstats_basic', 'mstats'),
+                          ('scipy.stats.mstats_extras', 'mstats'),
+                          ('scipy.stats.mvn', None),
+                          ('scipy.stats.stats', None)])
+def test_private_but_present_deprecation(module_name, correct_module):
+    # gh-18279, gh-17572, gh-17771 noted that deprecation warnings
+    # for imports from private modules
+    # were misleading. Check that this is resolved.
+    module = import_module(module_name)
+    if correct_module is None:
+        import_name = f'scipy.{module_name.split(".")[1]}'
+    else:
+        import_name = f'scipy.{module_name.split(".")[1]}.{correct_module}'
+
+    correct_import = import_module(import_name)
+
+    # Attributes that were formerly in `module_name` can still be imported from
+    # `module_name`, albeit with a deprecation warning.
+    for attr_name in module.__all__:
+        # ensure attribute is present where the warning is pointing
+        assert getattr(correct_import, attr_name, None) is not None
+        message = f"Please import `{attr_name}` from the `{import_name}`..."
+        with pytest.deprecated_call(match=message):
+            getattr(module, attr_name)
+
+    # Attributes that were not in `module_name` get an error notifying the user
+    # that the attribute is not in `module_name` and that `module_name` is deprecated.
+    message = f"`{module_name}` is deprecated..."
+    with pytest.raises(AttributeError, match=message):
+        getattr(module, "ekki")
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_scipy_version.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_scipy_version.py
new file mode 100644
index 0000000000000000000000000000000000000000..68e1a43c3fb329b6a4274ba76b53a215738da6ad
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_scipy_version.py
@@ -0,0 +1,28 @@
+import re
+
+import scipy
+import scipy.version
+
+
+def test_valid_scipy_version():
+    # Verify that the SciPy version is a valid one (no .post suffix or other
+    # nonsense). See NumPy issue gh-6431 for an issue caused by an invalid
+    # version.
+    version_pattern = r"^[0-9]+\.[0-9]+\.[0-9]+(|a[0-9]|b[0-9]|rc[0-9])"
+    dev_suffix = r"((.dev0)|(\.dev0+\+git[0-9]{8}.[0-9a-f]{7}))"
+    if scipy.version.release:
+        res = re.match(version_pattern, scipy.__version__)
+    else:
+        res = re.match(version_pattern + dev_suffix, scipy.__version__)
+
+    assert res is not None
+    assert scipy.__version__
+
+
+def test_version_submodule_members():
+    """`scipy.version` may not be quite public, but we install it.
+
+    So check that we don't silently change its contents.
+    """
+    for attr in ('version', 'full_version', 'short_version', 'git_revision', 'release'):
+        assert hasattr(scipy.version, attr)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_tmpdirs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_tmpdirs.py
new file mode 100644
index 0000000000000000000000000000000000000000..3ee90319aa4c7b6d73c64f0f16eadc1ab070c7ec
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_tmpdirs.py
@@ -0,0 +1,48 @@
+""" Test tmpdirs module """
+from os import getcwd
+from os.path import realpath, abspath, dirname, isfile, join as pjoin, exists
+
+from scipy._lib._tmpdirs import tempdir, in_tempdir, in_dir
+
+from numpy.testing import assert_, assert_equal
+
+import pytest
+
+
+MY_PATH = abspath(__file__)
+MY_DIR = dirname(MY_PATH)
+
+
+@pytest.mark.thread_unsafe(reason="tempdir is not thread-safe")
+def test_tempdir():
+    with tempdir() as tmpdir:
+        fname = pjoin(tmpdir, 'example_file.txt')
+        with open(fname, "w") as fobj:
+            fobj.write('a string\\n')
+    assert_(not exists(tmpdir))
+
+
+@pytest.mark.thread_unsafe(reason="in_tempdir is not thread-safe")
+def test_in_tempdir():
+    my_cwd = getcwd()
+    with in_tempdir() as tmpdir:
+        with open('test.txt', "w") as f:
+            f.write('some text')
+        assert_(isfile('test.txt'))
+        assert_(isfile(pjoin(tmpdir, 'test.txt')))
+    assert_(not exists(tmpdir))
+    assert_equal(getcwd(), my_cwd)
+
+
+@pytest.mark.thread_unsafe(reason="in_dir is not thread-safe")
+def test_given_directory():
+    # Test InGivenDirectory
+    cwd = getcwd()
+    with in_dir() as tmpdir:
+        assert_equal(tmpdir, abspath(cwd))
+        assert_equal(tmpdir, abspath(getcwd()))
+    with in_dir(MY_DIR) as tmpdir:
+        assert_equal(tmpdir, MY_DIR)
+        assert_equal(realpath(MY_DIR), realpath(abspath(getcwd())))
+    # We were deleting the given directory! Check not so now.
+    assert_(isfile(MY_PATH))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_warnings.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_warnings.py
new file mode 100644
index 0000000000000000000000000000000000000000..2dd96428fe4106da2e90b65718ad78752d28cd0c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/tests/test_warnings.py
@@ -0,0 +1,137 @@
+"""
+Tests which scan for certain occurrences in the code, they may not find
+all of these occurrences but should catch almost all. This file was adapted
+from NumPy.
+"""
+
+
+import os
+from pathlib import Path
+import ast
+import tokenize
+
+import scipy
+
+import pytest
+
+
+class ParseCall(ast.NodeVisitor):
+    def __init__(self):
+        self.ls = []
+
+    def visit_Attribute(self, node):
+        ast.NodeVisitor.generic_visit(self, node)
+        self.ls.append(node.attr)
+
+    def visit_Name(self, node):
+        self.ls.append(node.id)
+
+
+class FindFuncs(ast.NodeVisitor):
+    def __init__(self, filename):
+        super().__init__()
+        self.__filename = filename
+        self.bad_filters = []
+        self.bad_stacklevels = []
+
+    def visit_Call(self, node):
+        p = ParseCall()
+        p.visit(node.func)
+        ast.NodeVisitor.generic_visit(self, node)
+
+        if p.ls[-1] == 'simplefilter' or p.ls[-1] == 'filterwarnings':
+            # get first argument of the `args` node of the filter call
+            match node.args[0]:
+                case ast.Constant() as c:
+                    argtext = c.value
+                case ast.JoinedStr() as js:
+                    # if we get an f-string, discard the templated pieces, which
+                    # are likely the type or specific message; we're interested
+                    # in the action, which is less likely to use a template
+                    argtext = "".join(
+                        x.value for x in js.values if isinstance(x, ast.Constant)
+                    )
+                case _:
+                    raise ValueError("unknown ast node type")
+            # check if filter is set to ignore outside of test code
+            if argtext == "ignore" and "tests" not in self.__filename.parts:
+                self.bad_filters.append(
+                    f"{self.__filename}:{node.lineno}")
+
+        if p.ls[-1] == 'warn' and (
+                len(p.ls) == 1 or p.ls[-2] == 'warnings'):
+
+            if self.__filename == "_lib/tests/test_warnings.py":
+                # This file
+                return
+
+            # See if stacklevel exists:
+            if len(node.args) == 3:
+                return
+            args = {kw.arg for kw in node.keywords}
+            if "stacklevel" not in args:
+                self.bad_stacklevels.append(
+                    f"{self.__filename}:{node.lineno}")
+
+
+@pytest.fixture(scope="session")
+def warning_calls():
+    # combined "ignore" and stacklevel error
+    base = Path(scipy.__file__).parent
+
+    bad_filters = []
+    bad_stacklevels = []
+
+    for path in base.rglob("*.py"):
+        # use tokenize to auto-detect encoding on systems where no
+        # default encoding is defined (e.g., LANG='C')
+        with tokenize.open(str(path)) as file:
+            tree = ast.parse(file.read(), filename=str(path))
+            finder = FindFuncs(path.relative_to(base))
+            finder.visit(tree)
+            bad_filters.extend(finder.bad_filters)
+            bad_stacklevels.extend(finder.bad_stacklevels)
+
+    return bad_filters, bad_stacklevels
+
+
+@pytest.mark.fail_slow(40)
+@pytest.mark.slow
+def test_warning_calls_filters(warning_calls):
+    bad_filters, bad_stacklevels = warning_calls
+
+    # We try not to add filters in the code base, because those filters aren't
+    # thread-safe. We aim to only filter in tests with
+    # warnings.catch_warnings. However, in some cases it may prove
+    # necessary to filter out warnings, because we can't (easily) fix the root
+    # cause for them and we don't want users to see some warnings when they use
+    # SciPy correctly. So we list exceptions here.  Add new entries only if
+    # there's a good reason.
+    allowed_filters = (
+        os.path.join('datasets', '_fetchers.py'),
+        os.path.join('datasets', '__init__.py'),
+        os.path.join('optimize', '_optimize.py'),
+        os.path.join('optimize', '_constraints.py'),
+        os.path.join('optimize', '_nnls.py'),
+        os.path.join('signal', '_ltisys.py'),
+        os.path.join('sparse', '__init__.py'),  # np.matrix pending-deprecation
+        os.path.join('special', '_basic.py'),  # gh-21801
+        os.path.join('stats', '_discrete_distns.py'),  # gh-14901
+        os.path.join('stats', '_continuous_distns.py'),
+        os.path.join('stats', '_binned_statistic.py'),  # gh-19345
+        os.path.join('stats', '_stats_py.py'),  # gh-20743
+        os.path.join('stats', '_variation.py'),  # gh-22827
+        os.path.join('stats', 'tests', 'test_axis_nan_policy.py'),  # gh-20694
+        os.path.join('_lib', '_util.py'),  # gh-19341
+        os.path.join('sparse', 'linalg', '_dsolve', 'linsolve.py'),  # gh-17924
+        "conftest.py",
+    )
+    bad_filters = [item for item in bad_filters if item.split(':')[0] not in
+                   allowed_filters]
+
+    if bad_filters:
+        raise AssertionError(
+            "Warning ignore filters should not be used outside of tests.\n"
+            "Found in:\n    {}".format(
+                "\n    ".join(bad_filters)))
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/uarray.py b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/uarray.py
new file mode 100644
index 0000000000000000000000000000000000000000..b29fc713efb3e836cc179ac87ce41f87b51870ef
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/_lib/uarray.py
@@ -0,0 +1,31 @@
+"""`uarray` provides functions for generating multimethods that dispatch to
+multiple different backends
+
+This should be imported, rather than `_uarray` so that an installed version could
+be used instead, if available. This means that users can call
+`uarray.set_backend` directly instead of going through SciPy.
+
+"""
+
+
+# Prefer an installed version of uarray, if available
+try:
+    import uarray as _uarray
+except ImportError:
+    _has_uarray = False
+else:
+    from scipy._lib._pep440 import Version as _Version
+
+    _has_uarray = _Version(_uarray.__version__) >= _Version("0.8")
+    del _uarray
+    del _Version
+
+
+if _has_uarray:
+    from uarray import *  # noqa: F403
+    from uarray import _Function
+else:
+    from ._uarray import *  # noqa: F403
+    from ._uarray import _Function  # noqa: F401
+
+del _has_uarray
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/._vq.py b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/._vq.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..7b7784969a573d05cc6b98ee9066c42720156d1d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/__init__.py
@@ -0,0 +1,31 @@
+"""
+=========================================
+Clustering package (:mod:`scipy.cluster`)
+=========================================
+
+.. currentmodule:: scipy.cluster
+
+Clustering algorithms are useful in information theory, target detection,
+communications, compression, and other areas. The `vq` module only
+supports vector quantization and the k-means algorithms.
+
+The `hierarchy` module provides functions for hierarchical and
+agglomerative clustering.  Its features include generating hierarchical
+clusters from distance matrices,
+calculating statistics on clusters, cutting linkages
+to generate flat clusters, and visualizing clusters with dendrograms.
+
+.. toctree::
+   :maxdepth: 1
+
+   cluster.vq
+   cluster.hierarchy
+
+"""
+__all__ = ['vq', 'hierarchy']
+
+from . import vq, hierarchy
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/_hierarchy.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/_hierarchy.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..39078fb4760f067f40f12a52a2c9bb38324f286f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/_hierarchy.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cf409258500f0a6516cf22d3525e9089df61f9f007d73f4d5b91ec75de542241
+size 220624
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/_optimal_leaf_ordering.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/_optimal_leaf_ordering.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..2d00beab6edaa0e2ef5c2f4239ecd7cbe85243ff
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/_optimal_leaf_ordering.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ed8c4b8b229d97de5ba8d51a919a91915bd171859677c63f5523ab36577874bf
+size 151904
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/_vq.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/_vq.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..1ce063c4a7931505924a98c30e5f21647d6df0d2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/_vq.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7a2e2b6a4a58469f57e8d3c77b7bfc8bfe1aed8f4c98c4f0866e65444c83ee1b
+size 111912
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/hierarchy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/hierarchy.py
new file mode 100644
index 0000000000000000000000000000000000000000..c94986afb9fdf0756de991fa3c5de86f994d6e52
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/hierarchy.py
@@ -0,0 +1,4338 @@
+"""
+Hierarchical clustering (:mod:`scipy.cluster.hierarchy`)
+========================================================
+
+.. currentmodule:: scipy.cluster.hierarchy
+
+These functions cut hierarchical clusterings into flat clusterings
+or find the roots of the forest formed by a cut by providing the flat
+cluster ids of each observation.
+
+.. autosummary::
+   :toctree: generated/
+
+   fcluster
+   fclusterdata
+   leaders
+
+These are routines for agglomerative clustering.
+
+.. autosummary::
+   :toctree: generated/
+
+   linkage
+   single
+   complete
+   average
+   weighted
+   centroid
+   median
+   ward
+
+These routines compute statistics on hierarchies.
+
+.. autosummary::
+   :toctree: generated/
+
+   cophenet
+   from_mlab_linkage
+   inconsistent
+   maxinconsts
+   maxdists
+   maxRstat
+   to_mlab_linkage
+
+Routines for visualizing flat clusters.
+
+.. autosummary::
+   :toctree: generated/
+
+   dendrogram
+
+These are data structures and routines for representing hierarchies as
+tree objects.
+
+.. autosummary::
+   :toctree: generated/
+
+   ClusterNode
+   leaves_list
+   to_tree
+   cut_tree
+   optimal_leaf_ordering
+
+These are predicates for checking the validity of linkage and
+inconsistency matrices as well as for checking isomorphism of two
+flat cluster assignments.
+
+.. autosummary::
+   :toctree: generated/
+
+   is_valid_im
+   is_valid_linkage
+   is_isomorphic
+   is_monotonic
+   correspond
+   num_obs_linkage
+
+Utility routines for plotting:
+
+.. autosummary::
+   :toctree: generated/
+
+   set_link_color_palette
+
+Utility classes:
+
+.. autosummary::
+   :toctree: generated/
+
+   DisjointSet -- data structure for incremental connectivity queries
+
+"""
+# Copyright (C) Damian Eads, 2007-2008. New BSD License.
+
+# hierarchy.py (derived from cluster.py, http://scipy-cluster.googlecode.com)
+#
+# Author: Damian Eads
+# Date:   September 22, 2007
+#
+# Copyright (c) 2007, 2008, Damian Eads
+#
+# All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#   - Redistributions of source code must retain the above
+#     copyright notice, this list of conditions and the
+#     following disclaimer.
+#   - Redistributions in binary form must reproduce the above copyright
+#     notice, this list of conditions and the following disclaimer
+#     in the documentation and/or other materials provided with the
+#     distribution.
+#   - Neither the name of the author nor the names of its
+#     contributors may be used to endorse or promote products derived
+#     from this software without specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+# A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+# OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+import warnings
+import bisect
+from collections import deque
+
+import numpy as np
+from . import _hierarchy, _optimal_leaf_ordering
+import scipy.spatial.distance as distance
+from scipy._lib._array_api import (_asarray, array_namespace, is_dask,
+                                   is_lazy_array, xp_capabilities, xp_copy)
+from scipy._lib._disjoint_set import DisjointSet
+import scipy._lib.array_api_extra as xpx
+
+
+_LINKAGE_METHODS = {'single': 0, 'complete': 1, 'average': 2, 'centroid': 3,
+                    'median': 4, 'ward': 5, 'weighted': 6}
+_EUCLIDEAN_METHODS = ('centroid', 'median', 'ward')
+
+__all__ = ['ClusterNode', 'DisjointSet', 'average', 'centroid', 'complete',
+           'cophenet', 'correspond', 'cut_tree', 'dendrogram', 'fcluster',
+           'fclusterdata', 'from_mlab_linkage', 'inconsistent',
+           'is_isomorphic', 'is_monotonic', 'is_valid_im', 'is_valid_linkage',
+           'leaders', 'leaves_list', 'linkage', 'maxRstat', 'maxdists',
+           'maxinconsts', 'median', 'num_obs_linkage', 'optimal_leaf_ordering',
+           'set_link_color_palette', 'single', 'to_mlab_linkage', 'to_tree',
+           'ward', 'weighted']
+
+
+class ClusterWarning(UserWarning):
+    pass
+
+
+def _warning(s):
+    warnings.warn(f'scipy.cluster: {s}', ClusterWarning, stacklevel=3)
+
+
+def int_floor(arr, xp):
+    # array_api_strict is strict about not allowing `int()` on a float array.
+    # That's typically not needed, here it is - so explicitly convert
+    return int(xp.asarray(arr, dtype=xp.int64))
+
+
+lazy_cython = xp_capabilities(
+    cpu_only=True, reason="Cython code",
+    warnings=[("dask.array", "merges chunks")])
+
+
+@lazy_cython
+def single(y):
+    """
+    Perform single/min/nearest linkage on the condensed distance matrix ``y``.
+
+    Parameters
+    ----------
+    y : ndarray
+        The upper triangular of the distance matrix. The result of
+        ``pdist`` is returned in this form.
+
+    Returns
+    -------
+    Z : ndarray
+        The linkage matrix.
+
+    See Also
+    --------
+    linkage : for advanced creation of hierarchical clusterings.
+    scipy.spatial.distance.pdist : pairwise distance metrics
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import single, fcluster
+    >>> from scipy.spatial.distance import pdist
+
+    First, we need a toy dataset to play with::
+
+        x x    x x
+        x        x
+
+        x        x
+        x x    x x
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    Then, we get a condensed distance matrix from this dataset:
+
+    >>> y = pdist(X)
+
+    Finally, we can perform the clustering:
+
+    >>> Z = single(y)
+    >>> Z
+    array([[ 0.,  1.,  1.,  2.],
+           [ 2., 12.,  1.,  3.],
+           [ 3.,  4.,  1.,  2.],
+           [ 5., 14.,  1.,  3.],
+           [ 6.,  7.,  1.,  2.],
+           [ 8., 16.,  1.,  3.],
+           [ 9., 10.,  1.,  2.],
+           [11., 18.,  1.,  3.],
+           [13., 15.,  2.,  6.],
+           [17., 20.,  2.,  9.],
+           [19., 21.,  2., 12.]])
+
+    The linkage matrix ``Z`` represents a dendrogram - see
+    `scipy.cluster.hierarchy.linkage` for a detailed explanation of its
+    contents.
+
+    We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster
+    each initial point would belong given a distance threshold:
+
+    >>> fcluster(Z, 0.9, criterion='distance')
+    array([ 7,  8,  9, 10, 11, 12,  4,  5,  6,  1,  2,  3], dtype=int32)
+    >>> fcluster(Z, 1, criterion='distance')
+    array([3, 3, 3, 4, 4, 4, 2, 2, 2, 1, 1, 1], dtype=int32)
+    >>> fcluster(Z, 2, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
+
+    Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a
+    plot of the dendrogram.
+    """
+    return linkage(y, method='single', metric='euclidean')
+
+
+@lazy_cython
+def complete(y):
+    """
+    Perform complete/max/farthest point linkage on a condensed distance matrix.
+
+    Parameters
+    ----------
+    y : ndarray
+        The upper triangular of the distance matrix. The result of
+        ``pdist`` is returned in this form.
+
+    Returns
+    -------
+    Z : ndarray
+        A linkage matrix containing the hierarchical clustering. See
+        the `linkage` function documentation for more information
+        on its structure.
+
+    See Also
+    --------
+    linkage : for advanced creation of hierarchical clusterings.
+    scipy.spatial.distance.pdist : pairwise distance metrics
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import complete, fcluster
+    >>> from scipy.spatial.distance import pdist
+
+    First, we need a toy dataset to play with::
+
+        x x    x x
+        x        x
+
+        x        x
+        x x    x x
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    Then, we get a condensed distance matrix from this dataset:
+
+    >>> y = pdist(X)
+
+    Finally, we can perform the clustering:
+
+    >>> Z = complete(y)
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.41421356,  3.        ],
+           [ 5.        , 13.        ,  1.41421356,  3.        ],
+           [ 8.        , 14.        ,  1.41421356,  3.        ],
+           [11.        , 15.        ,  1.41421356,  3.        ],
+           [16.        , 17.        ,  4.12310563,  6.        ],
+           [18.        , 19.        ,  4.12310563,  6.        ],
+           [20.        , 21.        ,  5.65685425, 12.        ]])
+
+    The linkage matrix ``Z`` represents a dendrogram - see
+    `scipy.cluster.hierarchy.linkage` for a detailed explanation of its
+    contents.
+
+    We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster
+    each initial point would belong given a distance threshold:
+
+    >>> fcluster(Z, 0.9, criterion='distance')
+    array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12], dtype=int32)
+    >>> fcluster(Z, 1.5, criterion='distance')
+    array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
+    >>> fcluster(Z, 4.5, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], dtype=int32)
+    >>> fcluster(Z, 6, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
+
+    Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a
+    plot of the dendrogram.
+    """
+    return linkage(y, method='complete', metric='euclidean')
+
+
+@lazy_cython
+def average(y):
+    """
+    Perform average/UPGMA linkage on a condensed distance matrix.
+
+    Parameters
+    ----------
+    y : ndarray
+        The upper triangular of the distance matrix. The result of
+        ``pdist`` is returned in this form.
+
+    Returns
+    -------
+    Z : ndarray
+        A linkage matrix containing the hierarchical clustering. See
+        `linkage` for more information on its structure.
+
+    See Also
+    --------
+    linkage : for advanced creation of hierarchical clusterings.
+    scipy.spatial.distance.pdist : pairwise distance metrics
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import average, fcluster
+    >>> from scipy.spatial.distance import pdist
+
+    First, we need a toy dataset to play with::
+
+        x x    x x
+        x        x
+
+        x        x
+        x x    x x
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    Then, we get a condensed distance matrix from this dataset:
+
+    >>> y = pdist(X)
+
+    Finally, we can perform the clustering:
+
+    >>> Z = average(y)
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.20710678,  3.        ],
+           [ 5.        , 13.        ,  1.20710678,  3.        ],
+           [ 8.        , 14.        ,  1.20710678,  3.        ],
+           [11.        , 15.        ,  1.20710678,  3.        ],
+           [16.        , 17.        ,  3.39675184,  6.        ],
+           [18.        , 19.        ,  3.39675184,  6.        ],
+           [20.        , 21.        ,  4.09206523, 12.        ]])
+
+    The linkage matrix ``Z`` represents a dendrogram - see
+    `scipy.cluster.hierarchy.linkage` for a detailed explanation of its
+    contents.
+
+    We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster
+    each initial point would belong given a distance threshold:
+
+    >>> fcluster(Z, 0.9, criterion='distance')
+    array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12], dtype=int32)
+    >>> fcluster(Z, 1.5, criterion='distance')
+    array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
+    >>> fcluster(Z, 4, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], dtype=int32)
+    >>> fcluster(Z, 6, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
+
+    Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a
+    plot of the dendrogram.
+
+    """
+    return linkage(y, method='average', metric='euclidean')
+
+
+@lazy_cython
+def weighted(y):
+    """
+    Perform weighted/WPGMA linkage on the condensed distance matrix.
+
+    See `linkage` for more information on the return
+    structure and algorithm.
+
+    Parameters
+    ----------
+    y : ndarray
+        The upper triangular of the distance matrix. The result of
+        ``pdist`` is returned in this form.
+
+    Returns
+    -------
+    Z : ndarray
+        A linkage matrix containing the hierarchical clustering. See
+        `linkage` for more information on its structure.
+
+    See Also
+    --------
+    linkage : for advanced creation of hierarchical clusterings.
+    scipy.spatial.distance.pdist : pairwise distance metrics
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import weighted, fcluster
+    >>> from scipy.spatial.distance import pdist
+
+    First, we need a toy dataset to play with::
+
+        x x    x x
+        x        x
+
+        x        x
+        x x    x x
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    Then, we get a condensed distance matrix from this dataset:
+
+    >>> y = pdist(X)
+
+    Finally, we can perform the clustering:
+
+    >>> Z = weighted(y)
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 9.        , 11.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.20710678,  3.        ],
+           [ 8.        , 13.        ,  1.20710678,  3.        ],
+           [ 5.        , 14.        ,  1.20710678,  3.        ],
+           [10.        , 15.        ,  1.20710678,  3.        ],
+           [18.        , 19.        ,  3.05595762,  6.        ],
+           [16.        , 17.        ,  3.32379407,  6.        ],
+           [20.        , 21.        ,  4.06357713, 12.        ]])
+
+    The linkage matrix ``Z`` represents a dendrogram - see
+    `scipy.cluster.hierarchy.linkage` for a detailed explanation of its
+    contents.
+
+    We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster
+    each initial point would belong given a distance threshold:
+
+    >>> fcluster(Z, 0.9, criterion='distance')
+    array([ 7,  8,  9,  1,  2,  3, 10, 11, 12,  4,  6,  5], dtype=int32)
+    >>> fcluster(Z, 1.5, criterion='distance')
+    array([3, 3, 3, 1, 1, 1, 4, 4, 4, 2, 2, 2], dtype=int32)
+    >>> fcluster(Z, 4, criterion='distance')
+    array([2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1], dtype=int32)
+    >>> fcluster(Z, 6, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
+
+    Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a
+    plot of the dendrogram.
+
+    """
+    return linkage(y, method='weighted', metric='euclidean')
+
+
+@lazy_cython
+def centroid(y):
+    """
+    Perform centroid/UPGMC linkage.
+
+    See `linkage` for more information on the input matrix,
+    return structure, and algorithm.
+
+    The following are common calling conventions:
+
+    1. ``Z = centroid(y)``
+
+       Performs centroid/UPGMC linkage on the condensed distance
+       matrix ``y``.
+
+    2. ``Z = centroid(X)``
+
+       Performs centroid/UPGMC linkage on the observation matrix ``X``
+       using Euclidean distance as the distance metric.
+
+    Parameters
+    ----------
+    y : ndarray
+        A condensed distance matrix. A condensed
+        distance matrix is a flat array containing the upper
+        triangular of the distance matrix. This is the form that
+        ``pdist`` returns. Alternatively, a collection of
+        m observation vectors in n dimensions may be passed as
+        an m by n array.
+
+    Returns
+    -------
+    Z : ndarray
+        A linkage matrix containing the hierarchical clustering. See
+        the `linkage` function documentation for more information
+        on its structure.
+
+    See Also
+    --------
+    linkage : for advanced creation of hierarchical clusterings.
+    scipy.spatial.distance.pdist : pairwise distance metrics
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import centroid, fcluster
+    >>> from scipy.spatial.distance import pdist
+
+    First, we need a toy dataset to play with::
+
+        x x    x x
+        x        x
+
+        x        x
+        x x    x x
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    Then, we get a condensed distance matrix from this dataset:
+
+    >>> y = pdist(X)
+
+    Finally, we can perform the clustering:
+
+    >>> Z = centroid(y)
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.11803399,  3.        ],
+           [ 5.        , 13.        ,  1.11803399,  3.        ],
+           [ 8.        , 15.        ,  1.11803399,  3.        ],
+           [11.        , 14.        ,  1.11803399,  3.        ],
+           [18.        , 19.        ,  3.33333333,  6.        ],
+           [16.        , 17.        ,  3.33333333,  6.        ],
+           [20.        , 21.        ,  3.33333333, 12.        ]]) # may vary
+
+    The linkage matrix ``Z`` represents a dendrogram - see
+    `scipy.cluster.hierarchy.linkage` for a detailed explanation of its
+    contents.
+
+    We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster
+    each initial point would belong given a distance threshold:
+
+    >>> fcluster(Z, 0.9, criterion='distance')
+    array([ 7,  8,  9, 10, 11, 12,  1,  2,  3,  4,  5,  6], dtype=int32) # may vary
+    >>> fcluster(Z, 1.1, criterion='distance')
+    array([5, 5, 6, 7, 7, 8, 1, 1, 2, 3, 3, 4], dtype=int32) # may vary
+    >>> fcluster(Z, 2, criterion='distance')
+    array([3, 3, 3, 4, 4, 4, 1, 1, 1, 2, 2, 2], dtype=int32) # may vary
+    >>> fcluster(Z, 4, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
+
+    Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a
+    plot of the dendrogram.
+
+    """
+    return linkage(y, method='centroid', metric='euclidean')
+
+
+@lazy_cython
+def median(y):
+    """
+    Perform median/WPGMC linkage.
+
+    See `linkage` for more information on the return structure
+    and algorithm.
+
+     The following are common calling conventions:
+
+     1. ``Z = median(y)``
+
+        Performs median/WPGMC linkage on the condensed distance matrix
+        ``y``.  See ``linkage`` for more information on the return
+        structure and algorithm.
+
+     2. ``Z = median(X)``
+
+        Performs median/WPGMC linkage on the observation matrix ``X``
+        using Euclidean distance as the distance metric. See `linkage`
+        for more information on the return structure and algorithm.
+
+    Parameters
+    ----------
+    y : ndarray
+        A condensed distance matrix. A condensed
+        distance matrix is a flat array containing the upper
+        triangular of the distance matrix. This is the form that
+        ``pdist`` returns.  Alternatively, a collection of
+        m observation vectors in n dimensions may be passed as
+        an m by n array.
+
+    Returns
+    -------
+    Z : ndarray
+        The hierarchical clustering encoded as a linkage matrix.
+
+    See Also
+    --------
+    linkage : for advanced creation of hierarchical clusterings.
+    scipy.spatial.distance.pdist : pairwise distance metrics
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import median, fcluster
+    >>> from scipy.spatial.distance import pdist
+
+    First, we need a toy dataset to play with::
+
+        x x    x x
+        x        x
+
+        x        x
+        x x    x x
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    Then, we get a condensed distance matrix from this dataset:
+
+    >>> y = pdist(X)
+
+    Finally, we can perform the clustering:
+
+    >>> Z = median(y)
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.11803399,  3.        ],
+           [ 5.        , 13.        ,  1.11803399,  3.        ],
+           [ 8.        , 15.        ,  1.11803399,  3.        ],
+           [11.        , 14.        ,  1.11803399,  3.        ],
+           [18.        , 19.        ,  3.        ,  6.        ],
+           [16.        , 17.        ,  3.5       ,  6.        ],
+           [20.        , 21.        ,  3.25      , 12.        ]])
+
+    The linkage matrix ``Z`` represents a dendrogram - see
+    `scipy.cluster.hierarchy.linkage` for a detailed explanation of its
+    contents.
+
+    We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster
+    each initial point would belong given a distance threshold:
+
+    >>> fcluster(Z, 0.9, criterion='distance')
+    array([ 7,  8,  9, 10, 11, 12,  1,  2,  3,  4,  5,  6], dtype=int32)
+    >>> fcluster(Z, 1.1, criterion='distance')
+    array([5, 5, 6, 7, 7, 8, 1, 1, 2, 3, 3, 4], dtype=int32)
+    >>> fcluster(Z, 2, criterion='distance')
+    array([3, 3, 3, 4, 4, 4, 1, 1, 1, 2, 2, 2], dtype=int32)
+    >>> fcluster(Z, 4, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
+
+    Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a
+    plot of the dendrogram.
+
+    """
+    return linkage(y, method='median', metric='euclidean')
+
+
+@lazy_cython
+def ward(y):
+    """
+    Perform Ward's linkage on a condensed distance matrix.
+
+    See `linkage` for more information on the return structure
+    and algorithm.
+
+    The following are common calling conventions:
+
+    1. ``Z = ward(y)``
+       Performs Ward's linkage on the condensed distance matrix ``y``.
+
+    2. ``Z = ward(X)``
+       Performs Ward's linkage on the observation matrix ``X`` using
+       Euclidean distance as the distance metric.
+
+    Parameters
+    ----------
+    y : ndarray
+        A condensed distance matrix. A condensed
+        distance matrix is a flat array containing the upper
+        triangular of the distance matrix. This is the form that
+        ``pdist`` returns.  Alternatively, a collection of
+        m observation vectors in n dimensions may be passed as
+        an m by n array.
+
+    Returns
+    -------
+    Z : ndarray
+        The hierarchical clustering encoded as a linkage matrix. See
+        `linkage` for more information on the return structure and
+        algorithm.
+
+    See Also
+    --------
+    linkage : for advanced creation of hierarchical clusterings.
+    scipy.spatial.distance.pdist : pairwise distance metrics
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import ward, fcluster
+    >>> from scipy.spatial.distance import pdist
+
+    First, we need a toy dataset to play with::
+
+        x x    x x
+        x        x
+
+        x        x
+        x x    x x
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    Then, we get a condensed distance matrix from this dataset:
+
+    >>> y = pdist(X)
+
+    Finally, we can perform the clustering:
+
+    >>> Z = ward(y)
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.29099445,  3.        ],
+           [ 5.        , 13.        ,  1.29099445,  3.        ],
+           [ 8.        , 14.        ,  1.29099445,  3.        ],
+           [11.        , 15.        ,  1.29099445,  3.        ],
+           [16.        , 17.        ,  5.77350269,  6.        ],
+           [18.        , 19.        ,  5.77350269,  6.        ],
+           [20.        , 21.        ,  8.16496581, 12.        ]])
+
+    The linkage matrix ``Z`` represents a dendrogram - see
+    `scipy.cluster.hierarchy.linkage` for a detailed explanation of its
+    contents.
+
+    We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster
+    each initial point would belong given a distance threshold:
+
+    >>> fcluster(Z, 0.9, criterion='distance')
+    array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12], dtype=int32)
+    >>> fcluster(Z, 1.1, criterion='distance')
+    array([1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8], dtype=int32)
+    >>> fcluster(Z, 3, criterion='distance')
+    array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
+    >>> fcluster(Z, 9, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
+
+    Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a
+    plot of the dendrogram.
+
+    """
+    return linkage(y, method='ward', metric='euclidean')
+
+
+@lazy_cython
+def linkage(y, method='single', metric='euclidean', optimal_ordering=False):
+    """
+    Perform hierarchical/agglomerative clustering.
+
+    The input y may be either a 1-D condensed distance matrix
+    or a 2-D array of observation vectors.
+
+    If y is a 1-D condensed distance matrix,
+    then y must be a :math:`\\binom{n}{2}` sized
+    vector, where n is the number of original observations paired
+    in the distance matrix. The behavior of this function is very
+    similar to the MATLAB linkage function.
+
+    A :math:`(n-1)` by 4 matrix ``Z`` is returned. At the
+    :math:`i`-th iteration, clusters with indices ``Z[i, 0]`` and
+    ``Z[i, 1]`` are combined to form cluster :math:`n + i`. A
+    cluster with an index less than :math:`n` corresponds to one of
+    the :math:`n` original observations. The distance between
+    clusters ``Z[i, 0]`` and ``Z[i, 1]`` is given by ``Z[i, 2]``. The
+    fourth value ``Z[i, 3]`` represents the number of original
+    observations in the newly formed cluster.
+
+    The following linkage methods are used to compute the distance
+    :math:`d(s, t)` between two clusters :math:`s` and
+    :math:`t`. The algorithm begins with a forest of clusters that
+    have yet to be used in the hierarchy being formed. When two
+    clusters :math:`s` and :math:`t` from this forest are combined
+    into a single cluster :math:`u`, :math:`s` and :math:`t` are
+    removed from the forest, and :math:`u` is added to the
+    forest. When only one cluster remains in the forest, the algorithm
+    stops, and this cluster becomes the root.
+
+    A distance matrix is maintained at each iteration. The ``d[i,j]``
+    entry corresponds to the distance between cluster :math:`i` and
+    :math:`j` in the original forest.
+
+    At each iteration, the algorithm must update the distance matrix
+    to reflect the distance of the newly formed cluster u with the
+    remaining clusters in the forest.
+
+    Suppose there are :math:`|u|` original observations
+    :math:`u[0], \\ldots, u[|u|-1]` in cluster :math:`u` and
+    :math:`|v|` original objects :math:`v[0], \\ldots, v[|v|-1]` in
+    cluster :math:`v`. Recall, :math:`s` and :math:`t` are
+    combined to form cluster :math:`u`. Let :math:`v` be any
+    remaining cluster in the forest that is not :math:`u`.
+
+    The following are methods for calculating the distance between the
+    newly formed cluster :math:`u` and each :math:`v`.
+
+      * method='single' assigns
+
+        .. math::
+           d(u,v) = \\min(dist(u[i],v[j]))
+
+        for all points :math:`i` in cluster :math:`u` and
+        :math:`j` in cluster :math:`v`. This is also known as the
+        Nearest Point Algorithm.
+
+      * method='complete' assigns
+
+        .. math::
+           d(u, v) = \\max(dist(u[i],v[j]))
+
+        for all points :math:`i` in cluster u and :math:`j` in
+        cluster :math:`v`. This is also known by the Farthest Point
+        Algorithm or Voor Hees Algorithm.
+
+      * method='average' assigns
+
+        .. math::
+           d(u,v) = \\sum_{ij} \\frac{d(u[i], v[j])}
+                                   {(|u|*|v|)}
+
+        for all points :math:`i` and :math:`j` where :math:`|u|`
+        and :math:`|v|` are the cardinalities of clusters :math:`u`
+        and :math:`v`, respectively. This is also called the UPGMA
+        algorithm.
+
+      * method='weighted' assigns
+
+        .. math::
+           d(u,v) = (dist(s,v) + dist(t,v))/2
+
+        where cluster u was formed with cluster s and t and v
+        is a remaining cluster in the forest (also called WPGMA).
+
+      * method='centroid' assigns
+
+        .. math::
+           dist(s,t) = ||c_s-c_t||_2
+
+        where :math:`c_s` and :math:`c_t` are the centroids of
+        clusters :math:`s` and :math:`t`, respectively. When two
+        clusters :math:`s` and :math:`t` are combined into a new
+        cluster :math:`u`, the new centroid is computed over all the
+        original objects in clusters :math:`s` and :math:`t`. The
+        distance then becomes the Euclidean distance between the
+        centroid of :math:`u` and the centroid of a remaining cluster
+        :math:`v` in the forest. This is also known as the UPGMC
+        algorithm.
+
+      * method='median' assigns :math:`d(s,t)` like the ``centroid``
+        method. When two clusters :math:`s` and :math:`t` are combined
+        into a new cluster :math:`u`, the average of centroids s and t
+        give the new centroid :math:`u`. This is also known as the
+        WPGMC algorithm.
+
+      * method='ward' uses the Ward variance minimization algorithm.
+        The new entry :math:`d(u,v)` is computed as follows,
+
+        .. math::
+
+           d(u,v) = \\sqrt{\\frac{|v|+|s|}
+                               {T}d(v,s)^2
+                        + \\frac{|v|+|t|}
+                               {T}d(v,t)^2
+                        - \\frac{|v|}
+                               {T}d(s,t)^2}
+
+        where :math:`u` is the newly joined cluster consisting of
+        clusters :math:`s` and :math:`t`, :math:`v` is an unused
+        cluster in the forest, :math:`T=|v|+|s|+|t|`, and
+        :math:`|*|` is the cardinality of its argument. This is also
+        known as the incremental algorithm.
+
+    Warning: When the minimum distance pair in the forest is chosen, there
+    may be two or more pairs with the same minimum distance. This
+    implementation may choose a different minimum than the MATLAB
+    version.
+
+    Parameters
+    ----------
+    y : ndarray
+        A condensed distance matrix. A condensed distance matrix
+        is a flat array containing the upper triangular of the distance matrix.
+        This is the form that ``pdist`` returns. Alternatively, a collection of
+        :math:`m` observation vectors in :math:`n` dimensions may be passed as
+        an :math:`m` by :math:`n` array. All elements of the condensed distance
+        matrix must be finite, i.e., no NaNs or infs.
+    method : str, optional
+        The linkage algorithm to use. See the ``Linkage Methods`` section below
+        for full descriptions.
+    metric : str or function, optional
+        The distance metric to use in the case that y is a collection of
+        observation vectors; ignored otherwise. See the ``pdist``
+        function for a list of valid distance metrics. A custom distance
+        function can also be used.
+    optimal_ordering : bool, optional
+        If True, the linkage matrix will be reordered so that the distance
+        between successive leaves is minimal. This results in a more intuitive
+        tree structure when the data are visualized. defaults to False, because
+        this algorithm can be slow, particularly on large datasets [2]_. See
+        also the `optimal_leaf_ordering` function.
+
+        .. versionadded:: 1.0.0
+
+    Returns
+    -------
+    Z : ndarray
+        The hierarchical clustering encoded as a linkage matrix.
+
+    Notes
+    -----
+    1. For method 'single', an optimized algorithm based on minimum spanning
+       tree is implemented. It has time complexity :math:`O(n^2)`.
+       For methods 'complete', 'average', 'weighted' and 'ward', an algorithm
+       called nearest-neighbors chain is implemented. It also has time
+       complexity :math:`O(n^2)`.
+       For other methods, a naive algorithm is implemented with :math:`O(n^3)`
+       time complexity.
+       All algorithms use :math:`O(n^2)` memory.
+       Refer to [1]_ for details about the algorithms.
+    2. Methods 'centroid', 'median', and 'ward' are correctly defined only if
+       Euclidean pairwise metric is used. If `y` is passed as precomputed
+       pairwise distances, then it is the user's responsibility to assure that
+       these distances are in fact Euclidean, otherwise the produced result
+       will be incorrect.
+
+    See Also
+    --------
+    scipy.spatial.distance.pdist : pairwise distance metrics
+
+    References
+    ----------
+    .. [1] Daniel Mullner, "Modern hierarchical, agglomerative clustering
+           algorithms", :arXiv:`1109.2378v1`.
+    .. [2] Ziv Bar-Joseph, David K. Gifford, Tommi S. Jaakkola, "Fast optimal
+           leaf ordering for hierarchical clustering", 2001. Bioinformatics
+           :doi:`10.1093/bioinformatics/17.suppl_1.S22`
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import dendrogram, linkage
+    >>> from matplotlib import pyplot as plt
+    >>> X = [[i] for i in [2, 8, 0, 4, 1, 9, 9, 0]]
+
+    >>> Z = linkage(X, 'ward')
+    >>> fig = plt.figure(figsize=(25, 10))
+    >>> dn = dendrogram(Z)
+
+    >>> Z = linkage(X, 'single')
+    >>> fig = plt.figure(figsize=(25, 10))
+    >>> dn = dendrogram(Z)
+    >>> plt.show()
+    """
+    xp = array_namespace(y)
+    y = _asarray(y, order='C', dtype=xp.float64, xp=xp)
+    lazy = is_lazy_array(y)
+
+    if method not in _LINKAGE_METHODS:
+        raise ValueError(f"Invalid method: {method}")
+
+    if method in _EUCLIDEAN_METHODS and metric != 'euclidean' and y.ndim == 2:
+        msg = f"`method={method}` requires the distance metric to be Euclidean"
+        raise ValueError(msg)
+
+    if y.ndim == 1:
+        distance.is_valid_y(y, throw=True, name='y')
+    elif y.ndim == 2:
+        if (not lazy and y.shape[0] == y.shape[1]
+            and xp.all(xpx.isclose(xp.linalg.diagonal(y), 0))
+            and xp.all(y >= 0) and xp.all(xpx.isclose(y, y.T))):
+            warnings.warn('The symmetric non-negative hollow observation '
+                          'matrix looks suspiciously like an uncondensed '
+                          'distance matrix',
+                          ClusterWarning, stacklevel=2)
+        y = distance.pdist(y, metric)
+    else:
+        raise ValueError("`y` must be 1 or 2 dimensional.")
+
+    if not lazy and not xp.all(xp.isfinite(y)):
+        raise ValueError("The condensed distance matrix must contain only "
+                         "finite values.")
+
+    n = distance.num_obs_y(y)
+    method_code = _LINKAGE_METHODS[method]
+
+    def cy_linkage(y, validate):
+        if validate and not np.all(np.isfinite(y)):
+            raise ValueError("The condensed distance matrix must contain only "
+                            "finite values.")            
+
+        if method == 'single':
+            return _hierarchy.mst_single_linkage(y, n)
+        elif method in ('complete', 'average', 'weighted', 'ward'):
+            return _hierarchy.nn_chain(y, n, method_code)
+        else:
+            return _hierarchy.fast_linkage(y, n, method_code)
+
+    result = xpx.lazy_apply(cy_linkage, y, validate=lazy,
+                            shape=(n - 1, 4), dtype=xp.float64,
+                            as_numpy=True, xp=xp)
+
+    if optimal_ordering:
+        return optimal_leaf_ordering(result, y)
+    else:
+        return result
+
+
+class ClusterNode:
+    """
+    A tree node class for representing a cluster.
+
+    Leaf nodes correspond to original observations, while non-leaf nodes
+    correspond to non-singleton clusters.
+
+    The `to_tree` function converts a matrix returned by the linkage
+    function into an easy-to-use tree representation.
+
+    All parameter names are also attributes.
+
+    Parameters
+    ----------
+    id : int
+        The node id.
+    left : ClusterNode instance, optional
+        The left child tree node.
+    right : ClusterNode instance, optional
+        The right child tree node.
+    dist : float, optional
+        Distance for this cluster in the linkage matrix.
+    count : int, optional
+        The number of samples in this cluster.
+
+    See Also
+    --------
+    to_tree : for converting a linkage matrix ``Z`` into a tree object.
+
+    """
+
+    def __init__(self, id, left=None, right=None, dist=0.0, count=1):
+        if id < 0:
+            raise ValueError('The id must be non-negative.')
+        if dist < 0:
+            raise ValueError('The distance must be non-negative.')
+        if (left is None and right is not None) or \
+           (left is not None and right is None):
+            raise ValueError('Only full or proper binary trees are permitted.'
+                             '  This node has one child.')
+        if count < 1:
+            raise ValueError('A cluster must contain at least one original '
+                             'observation.')
+        self.id = id
+        self.left = left
+        self.right = right
+        self.dist = dist
+        if self.left is None:
+            self.count = count
+        else:
+            self.count = left.count + right.count
+
+    def __lt__(self, node):
+        if not isinstance(node, ClusterNode):
+            raise ValueError("Can't compare ClusterNode "
+                             f"to type {type(node)}")
+        return self.dist < node.dist
+
+    def __gt__(self, node):
+        if not isinstance(node, ClusterNode):
+            raise ValueError("Can't compare ClusterNode "
+                             f"to type {type(node)}")
+        return self.dist > node.dist
+
+    def __eq__(self, node):
+        if not isinstance(node, ClusterNode):
+            raise ValueError("Can't compare ClusterNode "
+                             f"to type {type(node)}")
+        return self.dist == node.dist
+
+    def get_id(self):
+        """
+        The identifier of the target node.
+
+        For ``0 <= i < n``, `i` corresponds to original observation i.
+        For ``n <= i < 2n-1``, `i` corresponds to non-singleton cluster formed
+        at iteration ``i-n``.
+
+        Returns
+        -------
+        id : int
+            The identifier of the target node.
+
+        """
+        return self.id
+
+    def get_count(self):
+        """
+        The number of leaf nodes (original observations) belonging to
+        the cluster node nd. If the target node is a leaf, 1 is
+        returned.
+
+        Returns
+        -------
+        get_count : int
+            The number of leaf nodes below the target node.
+
+        """
+        return self.count
+
+    def get_left(self):
+        """
+        Return a reference to the left child tree object.
+
+        Returns
+        -------
+        left : ClusterNode
+            The left child of the target node. If the node is a leaf,
+            None is returned.
+
+        """
+        return self.left
+
+    def get_right(self):
+        """
+        Return a reference to the right child tree object.
+
+        Returns
+        -------
+        right : ClusterNode
+            The left child of the target node. If the node is a leaf,
+            None is returned.
+
+        """
+        return self.right
+
+    def is_leaf(self):
+        """
+        Return True if the target node is a leaf.
+
+        Returns
+        -------
+        leafness : bool
+            True if the target node is a leaf node.
+
+        """
+        return self.left is None
+
+    def pre_order(self, func=(lambda x: x.id)):
+        """
+        Perform pre-order traversal without recursive function calls.
+
+        When a leaf node is first encountered, ``func`` is called with
+        the leaf node as its argument, and its result is appended to
+        the list.
+
+        For example, the statement::
+
+           ids = root.pre_order(lambda x: x.id)
+
+        returns a list of the node ids corresponding to the leaf nodes
+        of the tree as they appear from left to right.
+
+        Parameters
+        ----------
+        func : function
+            Applied to each leaf ClusterNode object in the pre-order traversal.
+            Given the ``i``-th leaf node in the pre-order traversal ``n[i]``,
+            the result of ``func(n[i])`` is stored in ``L[i]``. If not
+            provided, the index of the original observation to which the node
+            corresponds is used.
+
+        Returns
+        -------
+        L : list
+            The pre-order traversal.
+
+        """
+        # Do a preorder traversal, caching the result. To avoid having to do
+        # recursion, we'll store the previous index we've visited in a vector.
+        n = self.count
+
+        curNode = [None] * (2 * n)
+        lvisited = set()
+        rvisited = set()
+        curNode[0] = self
+        k = 0
+        preorder = []
+        while k >= 0:
+            nd = curNode[k]
+            ndid = nd.id
+            if nd.is_leaf():
+                preorder.append(func(nd))
+                k = k - 1
+            else:
+                if ndid not in lvisited:
+                    curNode[k + 1] = nd.left
+                    lvisited.add(ndid)
+                    k = k + 1
+                elif ndid not in rvisited:
+                    curNode[k + 1] = nd.right
+                    rvisited.add(ndid)
+                    k = k + 1
+                # If we've visited the left and right of this non-leaf
+                # node already, go up in the tree.
+                else:
+                    k = k - 1
+
+        return preorder
+
+
+_cnode_bare = ClusterNode(0)
+_cnode_type = type(ClusterNode)
+
+
+def _order_cluster_tree(Z):
+    """
+    Return clustering nodes in bottom-up order by distance.
+
+    Parameters
+    ----------
+    Z : scipy.cluster.linkage array
+        The linkage matrix.
+
+    Returns
+    -------
+    nodes : list
+        A list of ClusterNode objects.
+    """
+    q = deque()
+    tree = to_tree(Z)
+    q.append(tree)
+    nodes = []
+
+    while q:
+        node = q.popleft()
+        if not node.is_leaf():
+            bisect.insort_left(nodes, node)
+            q.append(node.get_right())
+            q.append(node.get_left())
+    return nodes
+
+
+@xp_capabilities(np_only=True, reason="non-standard indexing")
+def cut_tree(Z, n_clusters=None, height=None):
+    """
+    Given a linkage matrix Z, return the cut tree.
+
+    Parameters
+    ----------
+    Z : scipy.cluster.linkage array
+        The linkage matrix.
+    n_clusters : array_like, optional
+        Number of clusters in the tree at the cut point.
+    height : array_like, optional
+        The height at which to cut the tree. Only possible for ultrametric
+        trees.
+
+    Returns
+    -------
+    cutree : array
+        An array indicating group membership at each agglomeration step. I.e.,
+        for a full cut tree, in the first column each data point is in its own
+        cluster. At the next step, two nodes are merged. Finally, all
+        singleton and non-singleton clusters are in one group. If `n_clusters`
+        or `height` are given, the columns correspond to the columns of
+        `n_clusters` or `height`.
+
+    Examples
+    --------
+    >>> from scipy import cluster
+    >>> import numpy as np
+    >>> from numpy.random import default_rng
+    >>> rng = default_rng()
+    >>> X = rng.random((50, 4))
+    >>> Z = cluster.hierarchy.ward(X)
+    >>> cutree = cluster.hierarchy.cut_tree(Z, n_clusters=[5, 10])
+    >>> cutree[:10]
+    array([[0, 0],
+           [1, 1],
+           [2, 2],
+           [3, 3],
+           [3, 4],
+           [2, 2],
+           [0, 0],
+           [1, 5],
+           [3, 6],
+           [4, 7]])  # random
+
+    """
+    xp = array_namespace(Z)
+    nobs = num_obs_linkage(Z)
+    nodes = _order_cluster_tree(Z)
+
+    if height is not None and n_clusters is not None:
+        raise ValueError("At least one of either height or n_clusters "
+                         "must be None")
+    elif height is None and n_clusters is None:  # return the full cut tree
+        cols_idx = xp.arange(nobs)
+    elif height is not None:
+        height = xp.asarray(height)
+        heights = xp.asarray([x.dist for x in nodes])
+        cols_idx = xp.searchsorted(heights, height)
+    else:
+        n_clusters = xp.asarray(n_clusters)
+        cols_idx = nobs - xp.searchsorted(xp.arange(nobs), n_clusters)
+
+    try:
+        n_cols = len(cols_idx)
+    except TypeError:  # scalar
+        n_cols = 1
+        cols_idx = xp.asarray([cols_idx])
+
+    groups = xp.zeros((n_cols, nobs), dtype=xp.int64)
+    last_group = xp.arange(nobs)
+    if 0 in cols_idx:
+        groups[0] = last_group
+
+    for i, node in enumerate(nodes):
+        idx = node.pre_order()
+        this_group = xp_copy(last_group, xp=xp)
+        # TODO ARRAY_API complex indexing not supported
+        this_group[idx] = xp.min(last_group[idx])
+        this_group[this_group > xp.max(last_group[idx])] -= 1
+        if i + 1 in cols_idx:
+            groups[np.nonzero(i + 1 == cols_idx)[0]] = this_group
+        last_group = this_group
+
+    return groups.T
+
+
+@xp_capabilities(jax_jit=False, allow_dask_compute=True)
+def to_tree(Z, rd=False):
+    """
+    Convert a linkage matrix into an easy-to-use tree object.
+
+    The reference to the root `ClusterNode` object is returned (by default).
+
+    Each `ClusterNode` object has a ``left``, ``right``, ``dist``, ``id``,
+    and ``count`` attribute. The left and right attributes point to
+    ClusterNode objects that were combined to generate the cluster.
+    If both are None then the `ClusterNode` object is a leaf node, its count
+    must be 1, and its distance is meaningless but set to 0.
+
+    *Note: This function is provided for the convenience of the library
+    user. ClusterNodes are not used as input to any of the functions in this
+    library.*
+
+    Parameters
+    ----------
+    Z : ndarray
+        The linkage matrix in proper form (see the `linkage`
+        function documentation).
+    rd : bool, optional
+        When False (default), a reference to the root `ClusterNode` object is
+        returned.  Otherwise, a tuple ``(r, d)`` is returned. ``r`` is a
+        reference to the root node while ``d`` is a list of `ClusterNode`
+        objects - one per original entry in the linkage matrix plus entries
+        for all clustering steps. If a cluster id is
+        less than the number of samples ``n`` in the data that the linkage
+        matrix describes, then it corresponds to a singleton cluster (leaf
+        node).
+        See `linkage` for more information on the assignment of cluster ids
+        to clusters.
+
+    Returns
+    -------
+    tree : ClusterNode or tuple (ClusterNode, list of ClusterNode)
+        If ``rd`` is False, a `ClusterNode`.
+        If ``rd`` is True, a list of length ``2*n - 1``, with ``n`` the number
+        of samples.  See the description of `rd` above for more details.
+
+    See Also
+    --------
+    linkage, is_valid_linkage, ClusterNode
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster import hierarchy
+    >>> rng = np.random.default_rng()
+    >>> x = rng.random((5, 2))
+    >>> Z = hierarchy.linkage(x)
+    >>> hierarchy.to_tree(Z)
+    >> rootnode, nodelist = hierarchy.to_tree(Z, rd=True)
+    >>> rootnode
+    >> len(nodelist)
+    9
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, order='C', xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', materialize=True, xp=xp)
+
+    # Number of original objects is equal to the number of rows plus 1.
+    n = Z.shape[0] + 1
+
+    # Create a list full of None's to store the node objects
+    d = [None] * (n * 2 - 1)
+
+    # Create the nodes corresponding to the n original objects.
+    for i in range(0, n):
+        d[i] = ClusterNode(i)
+
+    nd = None
+
+    for i in range(Z.shape[0]):
+        row = Z[i, :]
+
+        fi = int_floor(row[0], xp)
+        fj = int_floor(row[1], xp)
+        if fi > i + n:
+            raise ValueError('Corrupt matrix Z. Index to derivative cluster '
+                              f'is used before it is formed. See row {fi}, '
+                              'column 0')
+        if fj > i + n:
+            raise ValueError('Corrupt matrix Z. Index to derivative cluster '
+                              f'is used before it is formed. See row {fj}, '
+                              'column 1')
+
+        nd = ClusterNode(i + n, d[fi], d[fj], row[2])
+        #                ^ id   ^ left ^ right ^ dist
+        if row[3] != nd.count:
+            raise ValueError(f'Corrupt matrix Z. The count Z[{i},3] is '
+                              'incorrect.')
+        d[n + i] = nd
+
+    if rd:
+        return (nd, d)
+    else:
+        return nd
+
+
+@lazy_cython
+def optimal_leaf_ordering(Z, y, metric='euclidean'):
+    """
+    Given a linkage matrix Z and distance, reorder the cut tree.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The hierarchical clustering encoded as a linkage matrix. See
+        `linkage` for more information on the return structure and
+        algorithm.
+    y : ndarray
+        The condensed distance matrix from which Z was generated.
+        Alternatively, a collection of m observation vectors in n
+        dimensions may be passed as an m by n array.
+    metric : str or function, optional
+        The distance metric to use in the case that y is a collection of
+        observation vectors; ignored otherwise. See the ``pdist``
+        function for a list of valid distance metrics. A custom distance
+        function can also be used.
+
+    Returns
+    -------
+    Z_ordered : ndarray
+        A copy of the linkage matrix Z, reordered to minimize the distance
+        between adjacent leaves.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster import hierarchy
+    >>> rng = np.random.default_rng()
+    >>> X = rng.standard_normal((10, 10))
+    >>> Z = hierarchy.ward(X)
+    >>> hierarchy.leaves_list(Z)
+    array([0, 3, 1, 9, 2, 5, 7, 4, 6, 8], dtype=int32)
+    >>> hierarchy.leaves_list(hierarchy.optimal_leaf_ordering(Z, X))
+    array([3, 0, 2, 5, 7, 4, 8, 6, 9, 1], dtype=int32)
+
+    """
+    xp = array_namespace(Z, y)
+    Z = _asarray(Z, order='C', xp=xp)
+    y = _asarray(y, order='C', dtype=xp.float64, xp=xp)
+    lazy = is_lazy_array(Z)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+
+    if y.ndim == 1:
+        distance.is_valid_y(y, throw=True, name='y')
+    elif y.ndim == 2:
+        if (not lazy and y.shape[0] == y.shape[1]
+            and xp.all(xpx.isclose(xp.linalg.diagonal(y), 0))
+            and xp.all(y >= 0) and xp.all(xpx.isclose(y, y.T))):
+            warnings.warn('The symmetric non-negative hollow observation '
+                          'matrix looks suspiciously like an uncondensed '
+                          'distance matrix',
+                          ClusterWarning, stacklevel=2)
+        y = distance.pdist(y, metric)
+    else:
+        raise ValueError("`y` must be 1 or 2 dimensional.")
+    if not lazy and not xp.all(xp.isfinite(y)):
+        raise ValueError("The condensed distance matrix must contain only "
+                         "finite values.")
+
+    # The function name is prominently visible on the user-facing Dask dashboard;
+    # make sure it is meaningful.
+    def cy_optimal_leaf_ordering(Z, y, validate):
+        if validate:
+            _is_valid_linkage(Z, throw=True, name='Z', xp=np)
+            if not np.all(np.isfinite(y)):
+                raise ValueError("The condensed distance matrix must contain only "
+                                 "finite values.")
+        return _optimal_leaf_ordering.optimal_leaf_ordering(Z, y)
+
+    return xpx.lazy_apply(cy_optimal_leaf_ordering, Z, y, validate=lazy,
+                          shape=Z.shape, dtype=Z.dtype, as_numpy=True, xp=xp)
+
+
+@lazy_cython
+def cophenet(Z, Y=None):
+    """
+    Calculate the cophenetic distances between each observation in
+    the hierarchical clustering defined by the linkage ``Z``.
+
+    Suppose ``p`` and ``q`` are original observations in
+    disjoint clusters ``s`` and ``t``, respectively and
+    ``s`` and ``t`` are joined by a direct parent cluster
+    ``u``. The cophenetic distance between observations
+    ``i`` and ``j`` is simply the distance between
+    clusters ``s`` and ``t``.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The hierarchical clustering encoded as an array
+        (see `linkage` function).
+    Y : ndarray (optional)
+        Calculates the cophenetic correlation coefficient ``c`` of a
+        hierarchical clustering defined by the linkage matrix `Z`
+        of a set of :math:`n` observations in :math:`m`
+        dimensions. `Y` is the condensed distance matrix from which
+        `Z` was generated.
+
+    Returns
+    -------
+    c : ndarray
+        The cophentic correlation distance (if ``Y`` is passed).
+    d : ndarray
+        The cophenetic distance matrix in condensed form. The
+        :math:`ij` th entry is the cophenetic distance between
+        original observations :math:`i` and :math:`j`.
+
+    See Also
+    --------
+    linkage :
+        for a description of what a linkage matrix is.
+    scipy.spatial.distance.squareform :
+        transforming condensed matrices into square ones.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import single, cophenet
+    >>> from scipy.spatial.distance import pdist, squareform
+
+    Given a dataset ``X`` and a linkage matrix ``Z``, the cophenetic distance
+    between two points of ``X`` is the distance between the largest two
+    distinct clusters that each of the points:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    ``X`` corresponds to this dataset ::
+
+        x x    x x
+        x        x
+
+        x        x
+        x x    x x
+
+    >>> Z = single(pdist(X))
+    >>> Z
+    array([[ 0.,  1.,  1.,  2.],
+           [ 2., 12.,  1.,  3.],
+           [ 3.,  4.,  1.,  2.],
+           [ 5., 14.,  1.,  3.],
+           [ 6.,  7.,  1.,  2.],
+           [ 8., 16.,  1.,  3.],
+           [ 9., 10.,  1.,  2.],
+           [11., 18.,  1.,  3.],
+           [13., 15.,  2.,  6.],
+           [17., 20.,  2.,  9.],
+           [19., 21.,  2., 12.]])
+    >>> cophenet(Z)
+    array([1., 1., 2., 2., 2., 2., 2., 2., 2., 2., 2., 1., 2., 2., 2., 2., 2.,
+           2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 1., 1., 2., 2.,
+           2., 2., 2., 2., 1., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2.,
+           1., 1., 2., 2., 2., 1., 2., 2., 2., 2., 2., 2., 1., 1., 1.])
+
+    The output of the `scipy.cluster.hierarchy.cophenet` method is
+    represented in condensed form. We can use
+    `scipy.spatial.distance.squareform` to see the output as a
+    regular matrix (where each element ``ij`` denotes the cophenetic distance
+    between each ``i``, ``j`` pair of points in ``X``):
+
+    >>> squareform(cophenet(Z))
+    array([[0., 1., 1., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
+           [1., 0., 1., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
+           [1., 1., 0., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
+           [2., 2., 2., 0., 1., 1., 2., 2., 2., 2., 2., 2.],
+           [2., 2., 2., 1., 0., 1., 2., 2., 2., 2., 2., 2.],
+           [2., 2., 2., 1., 1., 0., 2., 2., 2., 2., 2., 2.],
+           [2., 2., 2., 2., 2., 2., 0., 1., 1., 2., 2., 2.],
+           [2., 2., 2., 2., 2., 2., 1., 0., 1., 2., 2., 2.],
+           [2., 2., 2., 2., 2., 2., 1., 1., 0., 2., 2., 2.],
+           [2., 2., 2., 2., 2., 2., 2., 2., 2., 0., 1., 1.],
+           [2., 2., 2., 2., 2., 2., 2., 2., 2., 1., 0., 1.],
+           [2., 2., 2., 2., 2., 2., 2., 2., 2., 1., 1., 0.]])
+
+    In this example, the cophenetic distance between points on ``X`` that are
+    very close (i.e., in the same corner) is 1. For other pairs of points is 2,
+    because the points will be located in clusters at different
+    corners - thus, the distance between these clusters will be larger.
+
+    """
+    xp = array_namespace(Z, Y)
+    # Ensure float64 C-contiguous array. Cython code doesn't deal with striding.
+    Z = _asarray(Z, order='C', dtype=xp.float64, xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+
+    def cy_cophenet(Z, validate):
+        if validate:
+            _is_valid_linkage(Z, throw=True, name='Z', xp=np)
+        n = Z.shape[0] + 1
+        zz = np.zeros((n * (n-1)) // 2, dtype=np.float64)
+        _hierarchy.cophenetic_distances(Z, zz, n)
+        return zz
+    
+    n = Z.shape[0] + 1
+    zz = xpx.lazy_apply(cy_cophenet, Z, validate=is_lazy_array(Z),
+                        shape=((n * (n-1)) // 2, ), dtype=xp.float64,
+                        as_numpy=True, xp=xp)
+                        
+    if Y is None:
+        return zz
+
+    Y = _asarray(Y, order='C', xp=xp)
+    distance.is_valid_y(Y, throw=True, name='Y')
+
+    z = xp.mean(zz)
+    y = xp.mean(Y)
+    Yy = Y - y
+    Zz = zz - z
+    numerator = (Yy * Zz)
+    denomA = Yy**2
+    denomB = Zz**2
+    c = xp.sum(numerator) / xp.sqrt(xp.sum(denomA) * xp.sum(denomB))
+    return (c, zz)
+
+
+@lazy_cython
+def inconsistent(Z, d=2):
+    r"""
+    Calculate inconsistency statistics on a linkage matrix.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The :math:`(n-1)` by 4 matrix encoding the linkage (hierarchical
+        clustering).  See `linkage` documentation for more information on its
+        form.
+    d : int, optional
+        The number of links up to `d` levels below each non-singleton cluster.
+
+    Returns
+    -------
+    R : ndarray
+        A :math:`(n-1)` by 4 matrix where the ``i``'th row contains the link
+        statistics for the non-singleton cluster ``i``. The link statistics are
+        computed over the link heights for links :math:`d` levels below the
+        cluster ``i``. ``R[i,0]`` and ``R[i,1]`` are the mean and standard
+        deviation of the link heights, respectively; ``R[i,2]`` is the number
+        of links included in the calculation; and ``R[i,3]`` is the
+        inconsistency coefficient,
+
+        .. math:: \frac{\mathtt{Z[i,2]} - \mathtt{R[i,0]}} {R[i,1]}
+
+    Notes
+    -----
+    This function behaves similarly to the MATLAB(TM) ``inconsistent``
+    function.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import inconsistent, linkage
+    >>> from matplotlib import pyplot as plt
+    >>> X = [[i] for i in [2, 8, 0, 4, 1, 9, 9, 0]]
+    >>> Z = linkage(X, 'ward')
+    >>> print(Z)
+    [[ 5.          6.          0.          2.        ]
+     [ 2.          7.          0.          2.        ]
+     [ 0.          4.          1.          2.        ]
+     [ 1.          8.          1.15470054  3.        ]
+     [ 9.         10.          2.12132034  4.        ]
+     [ 3.         12.          4.11096096  5.        ]
+     [11.         13.         14.07183949  8.        ]]
+    >>> inconsistent(Z)
+    array([[ 0.        ,  0.        ,  1.        ,  0.        ],
+           [ 0.        ,  0.        ,  1.        ,  0.        ],
+           [ 1.        ,  0.        ,  1.        ,  0.        ],
+           [ 0.57735027,  0.81649658,  2.        ,  0.70710678],
+           [ 1.04044011,  1.06123822,  3.        ,  1.01850858],
+           [ 3.11614065,  1.40688837,  2.        ,  0.70710678],
+           [ 6.44583366,  6.76770586,  3.        ,  1.12682288]])
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, order='C', dtype=xp.float64, xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+
+    if d != np.floor(d) or d < 0:
+        raise ValueError('The second argument d must be a nonnegative '
+                         'integer value.')
+
+    def cy_inconsistent(Z, d, validate):
+        if validate:
+            _is_valid_linkage(Z, throw=True, name='Z', xp=np)
+        R = np.zeros((Z.shape[0], 4), dtype=np.float64)
+        n = Z.shape[0] + 1
+        _hierarchy.inconsistent(Z, R, n, d)
+        return R
+
+    return xpx.lazy_apply(cy_inconsistent, Z, d=int(d), validate=is_lazy_array(Z),
+                          shape=(Z.shape[0], 4), dtype=xp.float64,
+                          as_numpy=True, xp=xp)
+
+
+@lazy_cython
+def from_mlab_linkage(Z):
+    """
+    Convert a linkage matrix generated by MATLAB(TM) to a new
+    linkage matrix compatible with this module.
+
+    The conversion does two things:
+
+     * the indices are converted from ``1..N`` to ``0..(N-1)`` form,
+       and
+
+     * a fourth column ``Z[:,3]`` is added where ``Z[i,3]`` represents the
+       number of original observations (leaves) in the non-singleton
+       cluster ``i``.
+
+    This function is useful when loading in linkages from legacy data
+    files generated by MATLAB.
+
+    Parameters
+    ----------
+    Z : ndarray
+        A linkage matrix generated by MATLAB(TM).
+
+    Returns
+    -------
+    ZS : ndarray
+        A linkage matrix compatible with ``scipy.cluster.hierarchy``.
+
+    See Also
+    --------
+    linkage : for a description of what a linkage matrix is.
+    to_mlab_linkage : transform from SciPy to MATLAB format.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster.hierarchy import ward, from_mlab_linkage
+
+    Given a linkage matrix in MATLAB format ``mZ``, we can use
+    `scipy.cluster.hierarchy.from_mlab_linkage` to import
+    it into SciPy format:
+
+    >>> mZ = np.array([[1, 2, 1], [4, 5, 1], [7, 8, 1],
+    ...                [10, 11, 1], [3, 13, 1.29099445],
+    ...                [6, 14, 1.29099445],
+    ...                [9, 15, 1.29099445],
+    ...                [12, 16, 1.29099445],
+    ...                [17, 18, 5.77350269],
+    ...                [19, 20, 5.77350269],
+    ...                [21, 22,  8.16496581]])
+
+    >>> Z = from_mlab_linkage(mZ)
+    >>> Z
+    array([[  0.        ,   1.        ,   1.        ,   2.        ],
+           [  3.        ,   4.        ,   1.        ,   2.        ],
+           [  6.        ,   7.        ,   1.        ,   2.        ],
+           [  9.        ,  10.        ,   1.        ,   2.        ],
+           [  2.        ,  12.        ,   1.29099445,   3.        ],
+           [  5.        ,  13.        ,   1.29099445,   3.        ],
+           [  8.        ,  14.        ,   1.29099445,   3.        ],
+           [ 11.        ,  15.        ,   1.29099445,   3.        ],
+           [ 16.        ,  17.        ,   5.77350269,   6.        ],
+           [ 18.        ,  19.        ,   5.77350269,   6.        ],
+           [ 20.        ,  21.        ,   8.16496581,  12.        ]])
+
+    As expected, the linkage matrix ``Z`` returned includes an
+    additional column counting the number of original samples in
+    each cluster. Also, all cluster indices are reduced by 1
+    (MATLAB format uses 1-indexing, whereas SciPy uses 0-indexing).
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, dtype=xp.float64, order='C', xp=xp)
+
+    # If it's empty, return it.
+    if Z.shape in ((), (0, )):
+        return xp_copy(Z, xp=xp)
+
+    if Z.ndim != 2:
+        raise ValueError("The linkage array must be rectangular.")
+
+    # If it contains no rows, return it.
+    n = Z.shape[0]
+    if n == 0:
+        return xp_copy(Z, xp=xp)
+
+    lazy = is_lazy_array(Z)
+
+    if not lazy and xp.min(Z[:, :2]) != 1.0 and xp.max(Z[:, :2]) != 2 * n:
+        raise ValueError('The format of the indices is not 1..N')
+
+    res = xp.empty((Z.shape[0], Z.shape[1] + 1), dtype=Z.dtype)
+    res = xpx.at(res)[:, :2].set(Z[:, :2] - 1.0)
+    res = xpx.at(res)[:, 2:-1].set(Z[:, 2:])
+
+    def cy_from_mlab_linkage(Zpart, validate):
+        n = Zpart.shape[0]
+        if validate and np.min(Zpart[:, :2]) != 0.0 and np.max(Zpart[:, :2]) != 2 * n:
+            raise ValueError('The format of the indices is not 1..N')
+
+        if not Zpart.flags.writeable:
+            Zpart = Zpart.copy()  # xp=jax.numpy
+
+        CS = np.zeros((n,))
+        _hierarchy.calculate_cluster_sizes(Zpart, CS, n + 1)
+        return CS
+
+    CS = xpx.lazy_apply(cy_from_mlab_linkage, res[:, :-1], validate=lazy,
+                        shape=(res.shape[0],), dtype=xp.float64,
+                        as_numpy=True, xp=xp)
+
+    return xpx.at(res)[:, -1].set(CS)
+
+
+@xp_capabilities()
+def to_mlab_linkage(Z):
+    """
+    Convert a linkage matrix to a MATLAB(TM) compatible one.
+
+    Converts a linkage matrix ``Z`` generated by the linkage function
+    of this module to a MATLAB(TM) compatible one. The return linkage
+    matrix has the last column removed and the cluster indices are
+    converted to ``1..N`` indexing.
+
+    Parameters
+    ----------
+    Z : ndarray
+        A linkage matrix generated by ``scipy.cluster.hierarchy``.
+
+    Returns
+    -------
+    to_mlab_linkage : ndarray
+        A linkage matrix compatible with MATLAB(TM)'s hierarchical
+        clustering functions.
+
+        The return linkage matrix has the last column removed
+        and the cluster indices are converted to ``1..N`` indexing.
+
+    See Also
+    --------
+    linkage : for a description of what a linkage matrix is.
+    from_mlab_linkage : transform from Matlab to SciPy format.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import ward, to_mlab_linkage
+    >>> from scipy.spatial.distance import pdist
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = ward(pdist(X))
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.29099445,  3.        ],
+           [ 5.        , 13.        ,  1.29099445,  3.        ],
+           [ 8.        , 14.        ,  1.29099445,  3.        ],
+           [11.        , 15.        ,  1.29099445,  3.        ],
+           [16.        , 17.        ,  5.77350269,  6.        ],
+           [18.        , 19.        ,  5.77350269,  6.        ],
+           [20.        , 21.        ,  8.16496581, 12.        ]])
+
+    After a linkage matrix ``Z`` has been created, we can use
+    `scipy.cluster.hierarchy.to_mlab_linkage` to convert it
+    into MATLAB format:
+
+    >>> mZ = to_mlab_linkage(Z)
+    >>> mZ
+    array([[  1.        ,   2.        ,   1.        ],
+           [  4.        ,   5.        ,   1.        ],
+           [  7.        ,   8.        ,   1.        ],
+           [ 10.        ,  11.        ,   1.        ],
+           [  3.        ,  13.        ,   1.29099445],
+           [  6.        ,  14.        ,   1.29099445],
+           [  9.        ,  15.        ,   1.29099445],
+           [ 12.        ,  16.        ,   1.29099445],
+           [ 17.        ,  18.        ,   5.77350269],
+           [ 19.        ,  20.        ,   5.77350269],
+           [ 21.        ,  22.        ,   8.16496581]])
+
+    The new linkage matrix ``mZ`` uses 1-indexing for all the
+    clusters (instead of 0-indexing). Also, the last column of
+    the original linkage matrix has been dropped.
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, dtype=xp.float64, xp=xp)
+    if Z.shape in ((), (0, )):
+        return xp_copy(Z, xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+
+    return xp.concat((Z[:, :2] + 1.0, Z[:, 2:3]), axis=1)
+
+
+@xp_capabilities()
+def is_monotonic(Z):
+    """
+    Return True if the linkage passed is monotonic.
+
+    The linkage is monotonic if for every cluster :math:`s` and :math:`t`
+    joined, the distance between them is no less than the distance
+    between any previously joined clusters.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The linkage matrix to check for monotonicity.
+
+    Returns
+    -------
+    b : bool
+        A boolean indicating whether the linkage is monotonic.
+
+    See Also
+    --------
+    linkage : for a description of what a linkage matrix is.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import median, ward, is_monotonic
+    >>> from scipy.spatial.distance import pdist
+
+    By definition, some hierarchical clustering algorithms - such as
+    `scipy.cluster.hierarchy.ward` - produce monotonic assignments of
+    samples to clusters; however, this is not always true for other
+    hierarchical methods - e.g. `scipy.cluster.hierarchy.median`.
+
+    Given a linkage matrix ``Z`` (as the result of a hierarchical clustering
+    method) we can test programmatically whether it has the monotonicity
+    property or not, using `scipy.cluster.hierarchy.is_monotonic`:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = ward(pdist(X))
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.29099445,  3.        ],
+           [ 5.        , 13.        ,  1.29099445,  3.        ],
+           [ 8.        , 14.        ,  1.29099445,  3.        ],
+           [11.        , 15.        ,  1.29099445,  3.        ],
+           [16.        , 17.        ,  5.77350269,  6.        ],
+           [18.        , 19.        ,  5.77350269,  6.        ],
+           [20.        , 21.        ,  8.16496581, 12.        ]])
+    >>> is_monotonic(Z)
+    True
+
+    >>> Z = median(pdist(X))
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.11803399,  3.        ],
+           [ 5.        , 13.        ,  1.11803399,  3.        ],
+           [ 8.        , 15.        ,  1.11803399,  3.        ],
+           [11.        , 14.        ,  1.11803399,  3.        ],
+           [18.        , 19.        ,  3.        ,  6.        ],
+           [16.        , 17.        ,  3.5       ,  6.        ],
+           [20.        , 21.        ,  3.25      , 12.        ]])
+    >>> is_monotonic(Z)
+    False
+
+    Note that this method is equivalent to just verifying that the distances
+    in the third column of the linkage matrix appear in a monotonically
+    increasing order.
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+
+    # We expect the i'th value to be greater than its successor.
+    return xp.all(Z[1:, 2] >= Z[:-1, 2])
+
+
+@xp_capabilities(warnings=[("dask.array", "see notes"), ("jax.numpy", "see notes")])
+def is_valid_im(R, warning=False, throw=False, name=None):
+    """Return True if the inconsistency matrix passed is valid.
+
+    It must be a :math:`n` by 4 array of doubles. The standard
+    deviations ``R[:,1]`` must be nonnegative. The link counts
+    ``R[:,2]`` must be positive and no greater than :math:`n-1`.
+
+    Parameters
+    ----------
+    R : ndarray
+        The inconsistency matrix to check for validity.
+    warning : bool, optional
+        When True, issues a Python warning if the linkage
+        matrix passed is invalid.
+    throw : bool, optional
+        When True, throws a Python exception if the linkage
+        matrix passed is invalid.
+    name : str, optional
+        This string refers to the variable name of the invalid
+        linkage matrix.
+
+    Returns
+    -------
+    b : bool
+        True if the inconsistency matrix is valid; False otherwise.
+
+    Notes
+    -----
+    *Array API support (experimental):* If the input is a lazy Array (e.g. Dask
+    or JAX), the return value may be a 0-dimensional bool Array. When warning=True
+    or throw=True, calling this function materializes the array.
+
+    See Also
+    --------
+    linkage : for a description of what a linkage matrix is.
+    inconsistent : for the creation of a inconsistency matrix.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import ward, inconsistent, is_valid_im
+    >>> from scipy.spatial.distance import pdist
+
+    Given a data set ``X``, we can apply a clustering method to obtain a
+    linkage matrix ``Z``. `scipy.cluster.hierarchy.inconsistent` can
+    be also used to obtain the inconsistency matrix ``R`` associated to
+    this clustering process:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = ward(pdist(X))
+    >>> R = inconsistent(Z)
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.29099445,  3.        ],
+           [ 5.        , 13.        ,  1.29099445,  3.        ],
+           [ 8.        , 14.        ,  1.29099445,  3.        ],
+           [11.        , 15.        ,  1.29099445,  3.        ],
+           [16.        , 17.        ,  5.77350269,  6.        ],
+           [18.        , 19.        ,  5.77350269,  6.        ],
+           [20.        , 21.        ,  8.16496581, 12.        ]])
+    >>> R
+    array([[1.        , 0.        , 1.        , 0.        ],
+           [1.        , 0.        , 1.        , 0.        ],
+           [1.        , 0.        , 1.        , 0.        ],
+           [1.        , 0.        , 1.        , 0.        ],
+           [1.14549722, 0.20576415, 2.        , 0.70710678],
+           [1.14549722, 0.20576415, 2.        , 0.70710678],
+           [1.14549722, 0.20576415, 2.        , 0.70710678],
+           [1.14549722, 0.20576415, 2.        , 0.70710678],
+           [2.78516386, 2.58797734, 3.        , 1.15470054],
+           [2.78516386, 2.58797734, 3.        , 1.15470054],
+           [6.57065706, 1.38071187, 3.        , 1.15470054]])
+
+    Now we can use `scipy.cluster.hierarchy.is_valid_im` to verify that
+    ``R`` is correct:
+
+    >>> is_valid_im(R)
+    True
+
+    However, if ``R`` is wrongly constructed (e.g., one of the standard
+    deviations is set to a negative value), then the check will fail:
+
+    >>> R[-1,1] = R[-1,1] * -1
+    >>> is_valid_im(R)
+    False
+
+    """
+    xp = array_namespace(R)
+    R = _asarray(R, xp=xp)
+    return _is_valid_im(R, warning=warning, throw=throw, name=name,
+                        materialize=True, xp=xp)
+
+
+def _is_valid_im(R, warning=False, throw=False, name=None, materialize=False, *, xp):
+    """Variant of `is_valid_im` to be called internally by other scipy functions,
+    which by default does not materialize lazy input arrays (Dask, JAX, etc.) when
+    warning=True or throw=True.
+    """
+    name_str = f"{name!r} " if name else ''
+    try:
+        if R.dtype != xp.float64:
+            raise TypeError(f'Inconsistency matrix {name_str}must contain doubles '
+                            '(double).')
+        if len(R.shape) != 2:
+            raise ValueError(f'Inconsistency matrix {name_str}must have shape=2 (i.e. '
+                             'be two-dimensional).')
+        if R.shape[1] != 4:
+            raise ValueError(f'Inconsistency matrix {name_str}'
+                             'must have 4 columns.')
+        if R.shape[0] < 1:
+            raise ValueError(f'Inconsistency matrix {name_str}'
+                             'must have at least one row.')
+    except (TypeError, ValueError) as e:
+        if throw:
+            raise
+        if warning:
+            _warning(str(e))
+        return False
+
+    return _lazy_valid_checks(
+        (xp.any(R[:, 0] < 0),
+         f'Inconsistency matrix {name_str} contains negative link height means.'),
+        (xp.any(R[:, 1] < 0),
+         f'Inconsistency matrix {name_str} contains negative link height standard '
+         'deviations.'),
+        (xp.any(R[:, 2] < 0),
+         f'Inconsistency matrix {name_str} contains negative link counts.'),
+        throw=throw, warning=warning, materialize=materialize, xp=xp
+    )
+
+
+@xp_capabilities(warnings=[("dask.array", "see notes"), ("jax.numpy", "see notes")])
+def is_valid_linkage(Z, warning=False, throw=False, name=None):
+    """
+    Check the validity of a linkage matrix.
+
+    A linkage matrix is valid if it is a 2-D array (type double)
+    with :math:`n` rows and 4 columns. The first two columns must contain
+    indices between 0 and :math:`2n-1`. For a given row ``i``, the following
+    two expressions have to hold:
+
+    .. math::
+
+        0 \\leq \\mathtt{Z[i,0]} \\leq i+n-1
+        0 \\leq Z[i,1] \\leq i+n-1
+
+    I.e., a cluster cannot join another cluster unless the cluster being joined
+    has been generated.
+
+    The fourth column of `Z` represents the number of original observations
+    in a cluster, so a valid ``Z[i, 3]`` value may not exceed the number of
+    original observations.
+
+    Parameters
+    ----------
+    Z : array_like
+        Linkage matrix.
+    warning : bool, optional
+        When True, issues a Python warning if the linkage
+        matrix passed is invalid.
+    throw : bool, optional
+        When True, throws a Python exception if the linkage
+        matrix passed is invalid.
+    name : str, optional
+        This string refers to the variable name of the invalid
+        linkage matrix.
+
+    Returns
+    -------
+    b : bool
+        True if the inconsistency matrix is valid; False otherwise.
+
+    Notes
+    -----
+    *Array API support (experimental):* If the input is a lazy Array (e.g. Dask
+    or JAX), the return value may be a 0-dimensional bool Array. When warning=True
+    or throw=True, calling this function materializes the array.
+
+    See Also
+    --------
+    linkage: for a description of what a linkage matrix is.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import ward, is_valid_linkage
+    >>> from scipy.spatial.distance import pdist
+
+    All linkage matrices generated by the clustering methods in this module
+    will be valid (i.e., they will have the appropriate dimensions and the two
+    required expressions will hold for all the rows).
+
+    We can check this using `scipy.cluster.hierarchy.is_valid_linkage`:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = ward(pdist(X))
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.29099445,  3.        ],
+           [ 5.        , 13.        ,  1.29099445,  3.        ],
+           [ 8.        , 14.        ,  1.29099445,  3.        ],
+           [11.        , 15.        ,  1.29099445,  3.        ],
+           [16.        , 17.        ,  5.77350269,  6.        ],
+           [18.        , 19.        ,  5.77350269,  6.        ],
+           [20.        , 21.        ,  8.16496581, 12.        ]])
+    >>> is_valid_linkage(Z)
+    True
+
+    However, if we create a linkage matrix in a wrong way - or if we modify
+    a valid one in a way that any of the required expressions don't hold
+    anymore, then the check will fail:
+
+    >>> Z[3][1] = 20    # the cluster number 20 is not defined at this point
+    >>> is_valid_linkage(Z)
+    False
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, xp=xp)
+    return _is_valid_linkage(Z, warning=warning, throw=throw,
+                             name=name, materialize=True, xp=xp)
+
+
+def _is_valid_linkage(Z, warning=False, throw=False, name=None,
+                      materialize=False, *, xp):
+    """Variant of `is_valid_linkage` to be called internally by other scipy functions,
+    which by default does not materialize lazy input arrays (Dask, JAX, etc.) when
+    warning=True or throw=True.
+    """
+    name_str = f"{name!r} " if name else ''
+    try:
+        if Z.dtype != xp.float64:
+            raise TypeError(f'Linkage matrix {name_str}must contain doubles.')
+        if len(Z.shape) != 2:
+            raise ValueError(f'Linkage matrix {name_str}must have shape=2 (i.e. be'
+                             ' two-dimensional).')
+        if Z.shape[1] != 4:
+            raise ValueError(f'Linkage matrix {name_str}must have 4 columns.')
+        if Z.shape[0] == 0:
+            raise ValueError('Linkage must be computed on at least two '
+                             'observations.')
+    except (TypeError, ValueError) as e:
+        if throw:
+            raise
+        if warning:
+            _warning(str(e))
+        return False
+
+    n = Z.shape[0]
+    if n < 2:
+        return True
+
+    return _lazy_valid_checks(
+        (xp.any(Z[:, :2] < 0),
+         f'Linkage {name_str}contains negative indices.'),
+        (xp.any(Z[:, 2] < 0),
+         f'Linkage {name_str}contains negative distances.'),
+        (xp.any(Z[:, 3] < 0),
+         f'Linkage {name_str}contains negative counts.'),
+        (xp.any(Z[:, 3] > n + 1),
+         f'Linkage {name_str}contains excessive observations in a cluster'),
+        (xp.any(xp.max(Z[:, :2], axis=1) >= xp.arange(n + 1, 2 * n + 1, dtype=Z.dtype)),
+         f'Linkage {name_str}uses non-singleton cluster before it is formed.'),
+        (xpx.nunique(Z[:, :2]) < n * 2,
+         f'Linkage {name_str}uses the same cluster more than once.'),
+        throw=throw, warning=warning, materialize=materialize, xp=xp
+    )
+
+
+def _lazy_valid_checks(*args, throw=False, warning=False, materialize=False, xp):
+    """Validate a set of conditions on the contents of possibly lazy arrays.
+
+    Parameters
+    ----------
+    args : tuples of (Array, str)
+        The first element of each tuple must be a 0-dimensional Array
+        that evaluates to bool; the second element must be the message to convey
+        if the  first element evaluates to True.
+    throw: bool
+        Set to True to `raise ValueError(args[i][1])` if `args[i][0]` is True.
+    warning: bool
+        Set to True to issue a warning with message `args[i][1]` if `args[i][0]`
+        is True.
+    materialize: bool
+        Set to True to force materialization of lazy arrays when throw=True or
+        warning=True. If the inputs are lazy and materialize=False, ignore the
+        `throw` and `warning` flags.
+    xp: module
+        Array API namespace
+
+    Returns
+    -------
+    If xp is an eager backend (e.g. numpy) and all conditions are False, return True.
+    If throw is True, raise. Otherwise, return False.
+
+    If xp is a lazy backend (e.g. Dask or JAX), return a 0-dimensional bool Array.
+    """
+    conds = xp.concat([xp.reshape(cond, (1, )) for cond, _ in args])
+
+    lazy = is_lazy_array(conds)
+    if not throw and not warning or (lazy and not materialize):
+        out = ~xp.any(conds)
+        return out if lazy else bool(out)
+
+    if is_dask(xp):
+        # Only materialize the graph once, instead of once per check
+        conds = conds.compute()
+
+    # Don't call np.asarray(conds), as it would be blocked by the device transfer
+    # guard on CuPy and PyTorch and the densification guard on Sparse, whereas
+    # bool() will not.
+    conds = [bool(cond) for cond in conds]
+
+    for cond, (_, msg) in zip(conds, args):
+        if throw and cond:
+            raise ValueError(msg)
+        elif warning and cond:
+            warnings.warn(msg, ClusterWarning, stacklevel=3)
+
+    return not any(conds)
+
+
+@xp_capabilities()
+def num_obs_linkage(Z):
+    """
+    Return the number of original observations of the linkage matrix passed.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The linkage matrix on which to perform the operation.
+
+    Returns
+    -------
+    n : int
+        The number of original observations in the linkage.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import ward, num_obs_linkage
+    >>> from scipy.spatial.distance import pdist
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = ward(pdist(X))
+
+    ``Z`` is a linkage matrix obtained after using the Ward clustering method
+    with ``X``, a dataset with 12 data points.
+
+    >>> num_obs_linkage(Z)
+    12
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+    return Z.shape[0] + 1
+
+
+@xp_capabilities()
+def correspond(Z, Y):
+    """
+    Check for correspondence between linkage and condensed distance matrices.
+
+    They must have the same number of original observations for
+    the check to succeed.
+
+    This function is useful as a sanity check in algorithms that make
+    extensive use of linkage and distance matrices that must
+    correspond to the same set of original observations.
+
+    Parameters
+    ----------
+    Z : array_like
+        The linkage matrix to check for correspondence.
+    Y : array_like
+        The condensed distance matrix to check for correspondence.
+
+    Returns
+    -------
+    b : bool
+        A boolean indicating whether the linkage matrix and distance
+        matrix could possibly correspond to one another.
+
+    See Also
+    --------
+    linkage : for a description of what a linkage matrix is.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import ward, correspond
+    >>> from scipy.spatial.distance import pdist
+
+    This method can be used to check if a given linkage matrix ``Z`` has been
+    obtained from the application of a cluster method over a dataset ``X``:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+    >>> X_condensed = pdist(X)
+    >>> Z = ward(X_condensed)
+
+    Here, we can compare ``Z`` and ``X`` (in condensed form):
+
+    >>> correspond(Z, X_condensed)
+    True
+
+    """
+    xp = array_namespace(Z, Y)
+    Z = _asarray(Z, xp=xp)
+    Y = _asarray(Y, xp=xp)
+    _is_valid_linkage(Z, throw=True, xp=xp)
+    distance.is_valid_y(Y, throw=True)
+    return distance.num_obs_y(Y) == num_obs_linkage(Z)
+
+
+@xp_capabilities(cpu_only=True, reason="Cython code",
+                 jax_jit=False, allow_dask_compute=True)
+def fcluster(Z, t, criterion='inconsistent', depth=2, R=None, monocrit=None):
+    """
+    Form flat clusters from the hierarchical clustering defined by
+    the given linkage matrix.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The hierarchical clustering encoded with the matrix returned
+        by the `linkage` function.
+    t : scalar
+        For criteria 'inconsistent', 'distance' or 'monocrit',
+         this is the threshold to apply when forming flat clusters.
+        For 'maxclust' or 'maxclust_monocrit' criteria,
+         this would be max number of clusters requested.
+    criterion : str, optional
+        The criterion to use in forming flat clusters. This can
+        be any of the following values:
+
+          ``inconsistent`` :
+              If a cluster node and all its
+              descendants have an inconsistent value less than or equal
+              to `t`, then all its leaf descendants belong to the
+              same flat cluster. When no non-singleton cluster meets
+              this criterion, every node is assigned to its own
+              cluster. (Default)
+
+          ``distance`` :
+              Forms flat clusters so that the original
+              observations in each flat cluster have no greater a
+              cophenetic distance than `t`.
+
+          ``maxclust`` :
+              Finds a minimum threshold ``r`` so that
+              the cophenetic distance between any two original
+              observations in the same flat cluster is no more than
+              ``r`` and no more than `t` flat clusters are formed.
+
+          ``monocrit`` :
+              Forms a flat cluster from a cluster node c
+              with index i when ``monocrit[j] <= t``.
+
+              For example, to threshold on the maximum mean distance
+              as computed in the inconsistency matrix R with a
+              threshold of 0.8 do::
+
+                  MR = maxRstat(Z, R, 3)
+                  fcluster(Z, t=0.8, criterion='monocrit', monocrit=MR)
+
+          ``maxclust_monocrit`` :
+              Forms a flat cluster from a
+              non-singleton cluster node ``c`` when ``monocrit[i] <=
+              r`` for all cluster indices ``i`` below and including
+              ``c``. ``r`` is minimized such that no more than ``t``
+              flat clusters are formed. monocrit must be
+              monotonic. For example, to minimize the threshold t on
+              maximum inconsistency values so that no more than 3 flat
+              clusters are formed, do::
+
+                  MI = maxinconsts(Z, R)
+                  fcluster(Z, t=3, criterion='maxclust_monocrit', monocrit=MI)
+    depth : int, optional
+        The maximum depth to perform the inconsistency calculation.
+        It has no meaning for the other criteria. Default is 2.
+    R : ndarray, optional
+        The inconsistency matrix to use for the ``'inconsistent'``
+        criterion. This matrix is computed if not provided.
+    monocrit : ndarray, optional
+        An array of length n-1. `monocrit[i]` is the
+        statistics upon which non-singleton i is thresholded. The
+        monocrit vector must be monotonic, i.e., given a node c with
+        index i, for all node indices j corresponding to nodes
+        below c, ``monocrit[i] >= monocrit[j]``.
+
+    Returns
+    -------
+    fcluster : ndarray
+        An array of length ``n``. ``T[i]`` is the flat cluster number to
+        which original observation ``i`` belongs.
+
+    See Also
+    --------
+    linkage : for information about hierarchical clustering methods work.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import ward, fcluster
+    >>> from scipy.spatial.distance import pdist
+
+    All cluster linkage methods - e.g., `scipy.cluster.hierarchy.ward`
+    generate a linkage matrix ``Z`` as their output:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = ward(pdist(X))
+
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.29099445,  3.        ],
+           [ 5.        , 13.        ,  1.29099445,  3.        ],
+           [ 8.        , 14.        ,  1.29099445,  3.        ],
+           [11.        , 15.        ,  1.29099445,  3.        ],
+           [16.        , 17.        ,  5.77350269,  6.        ],
+           [18.        , 19.        ,  5.77350269,  6.        ],
+           [20.        , 21.        ,  8.16496581, 12.        ]])
+
+    This matrix represents a dendrogram, where the first and second elements
+    are the two clusters merged at each step, the third element is the
+    distance between these clusters, and the fourth element is the size of
+    the new cluster - the number of original data points included.
+
+    `scipy.cluster.hierarchy.fcluster` can be used to flatten the
+    dendrogram, obtaining as a result an assignation of the original data
+    points to single clusters.
+
+    This assignation mostly depends on a distance threshold ``t`` - the maximum
+    inter-cluster distance allowed:
+
+    >>> fcluster(Z, t=0.9, criterion='distance')
+    array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12], dtype=int32)
+
+    >>> fcluster(Z, t=1.1, criterion='distance')
+    array([1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8], dtype=int32)
+
+    >>> fcluster(Z, t=3, criterion='distance')
+    array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
+
+    >>> fcluster(Z, t=9, criterion='distance')
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
+
+    In the first case, the threshold ``t`` is too small to allow any two
+    samples in the data to form a cluster, so 12 different clusters are
+    returned.
+
+    In the second case, the threshold is large enough to allow the first
+    4 points to be merged with their nearest neighbors. So, here, only 8
+    clusters are returned.
+
+    The third case, with a much higher threshold, allows for up to 8 data
+    points to be connected - so 4 clusters are returned here.
+
+    Lastly, the threshold of the fourth case is large enough to allow for
+    all data points to be merged together - so a single cluster is returned.
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, order='C', dtype=xp.float64, xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', materialize=True, xp=xp)
+
+    n = Z.shape[0] + 1
+    T = np.zeros((n,), dtype='i')
+
+    if monocrit is not None:
+        monocrit = np.asarray(monocrit, order='C', dtype=np.float64)
+
+    Z = np.asarray(Z)
+    monocrit = np.asarray(monocrit)
+    if criterion == 'inconsistent':
+        if R is None:
+            R = inconsistent(Z, depth)
+        else:
+            R = _asarray(R, order='C', dtype=xp.float64, xp=xp)
+            _is_valid_im(R, throw=True, name='R', materialize=True, xp=xp)
+            # Since the C code does not support striding using strides.
+            # The dimensions are used instead.
+            R = np.asarray(R)
+        _hierarchy.cluster_in(Z, R, T, float(t), int(n))
+    elif criterion == 'distance':
+        _hierarchy.cluster_dist(Z, T, float(t), int(n))
+    elif criterion == 'maxclust':
+        _hierarchy.cluster_maxclust_dist(Z, T, int(n), t)
+    elif criterion == 'monocrit':
+        _hierarchy.cluster_monocrit(Z, monocrit, T, float(t), int(n))
+    elif criterion == 'maxclust_monocrit':
+        _hierarchy.cluster_maxclust_monocrit(Z, monocrit, T, int(n), int(t))
+    else:
+        raise ValueError(f'Invalid cluster formation criterion: {str(criterion)}')
+    return xp.asarray(T)
+
+
+@xp_capabilities(cpu_only=True, reason="Cython code",
+                 jax_jit=False, allow_dask_compute=True)
+def fclusterdata(X, t, criterion='inconsistent',
+                 metric='euclidean', depth=2, method='single', R=None):
+    """
+    Cluster observation data using a given metric.
+
+    Clusters the original observations in the n-by-m data
+    matrix X (n observations in m dimensions), using the euclidean
+    distance metric to calculate distances between original observations,
+    performs hierarchical clustering using the single linkage algorithm,
+    and forms flat clusters using the inconsistency method with `t` as the
+    cut-off threshold.
+
+    A 1-D array ``T`` of length ``n`` is returned. ``T[i]`` is
+    the index of the flat cluster to which the original observation ``i``
+    belongs.
+
+    Parameters
+    ----------
+    X : (N, M) ndarray
+        N by M data matrix with N observations in M dimensions.
+    t : scalar
+        For criteria 'inconsistent', 'distance' or 'monocrit',
+         this is the threshold to apply when forming flat clusters.
+        For 'maxclust' or 'maxclust_monocrit' criteria,
+         this would be max number of clusters requested.
+    criterion : str, optional
+        Specifies the criterion for forming flat clusters. Valid
+        values are 'inconsistent' (default), 'distance', or 'maxclust'
+        cluster formation algorithms. See `fcluster` for descriptions.
+    metric : str or function, optional
+        The distance metric for calculating pairwise distances. See
+        ``distance.pdist`` for descriptions and linkage to verify
+        compatibility with the linkage method.
+    depth : int, optional
+        The maximum depth for the inconsistency calculation. See
+        `inconsistent` for more information.
+    method : str, optional
+        The linkage method to use (single, complete, average,
+        weighted, median centroid, ward). See `linkage` for more
+        information. Default is "single".
+    R : ndarray, optional
+        The inconsistency matrix. It will be computed if necessary
+        if it is not passed.
+
+    Returns
+    -------
+    fclusterdata : ndarray
+        A vector of length n. T[i] is the flat cluster number to
+        which original observation i belongs.
+
+    See Also
+    --------
+    scipy.spatial.distance.pdist : pairwise distance metrics
+
+    Notes
+    -----
+    This function is similar to the MATLAB function ``clusterdata``.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import fclusterdata
+
+    This is a convenience method that abstracts all the steps to perform in a
+    typical SciPy's hierarchical clustering workflow.
+
+    * Transform the input data into a condensed matrix with
+      `scipy.spatial.distance.pdist`.
+
+    * Apply a clustering method.
+
+    * Obtain flat clusters at a user defined distance threshold ``t`` using
+      `scipy.cluster.hierarchy.fcluster`.
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> fclusterdata(X, t=1)
+    array([3, 3, 3, 4, 4, 4, 2, 2, 2, 1, 1, 1], dtype=int32)
+
+    The output here (for the dataset ``X``, distance threshold ``t``, and the
+    default settings) is four clusters with three data points each.
+
+    """
+    xp = array_namespace(X)
+    X = _asarray(X, order='C', dtype=xp.float64, xp=xp)
+
+    if X.ndim != 2:
+        raise TypeError('The observation matrix X must be an n by m array.')
+
+    Y = distance.pdist(X, metric=metric)
+    Z = linkage(Y, method=method)
+    if R is None:
+        R = inconsistent(Z, d=depth)
+    else:
+        R = _asarray(R, order='C', xp=xp)
+    T = fcluster(Z, criterion=criterion, depth=depth, R=R, t=t)
+    return T
+
+
+@lazy_cython
+def leaves_list(Z):
+    """
+    Return a list of leaf node ids.
+
+    The return corresponds to the observation vector index as it appears
+    in the tree from left to right. Z is a linkage matrix.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The hierarchical clustering encoded as a matrix.  `Z` is
+        a linkage matrix.  See `linkage` for more information.
+
+    Returns
+    -------
+    leaves_list : ndarray
+        The list of leaf node ids.
+
+    See Also
+    --------
+    dendrogram : for information about dendrogram structure.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import ward, dendrogram, leaves_list
+    >>> from scipy.spatial.distance import pdist
+    >>> from matplotlib import pyplot as plt
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = ward(pdist(X))
+
+    The linkage matrix ``Z`` represents a dendrogram, that is, a tree that
+    encodes the structure of the clustering performed.
+    `scipy.cluster.hierarchy.leaves_list` shows the mapping between
+    indices in the ``X`` dataset and leaves in the dendrogram:
+
+    >>> leaves_list(Z)
+    array([ 2,  0,  1,  5,  3,  4,  8,  6,  7, 11,  9, 10], dtype=int32)
+
+    >>> fig = plt.figure(figsize=(25, 10))
+    >>> dn = dendrogram(Z)
+    >>> plt.show()
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, order='C', xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+
+    def cy_leaves_list(Z, validate):
+        if validate:
+            _is_valid_linkage(Z, throw=True, name='Z', xp=np)
+        n = Z.shape[0] + 1
+        ML = np.zeros((n,), dtype=np.int32)
+        _hierarchy.prelist(Z, ML, n)
+        return ML
+
+    n = Z.shape[0] + 1
+    return xpx.lazy_apply(cy_leaves_list, Z, validate=is_lazy_array(Z),
+                          shape=(n, ), dtype=xp.int32,
+                          as_numpy=True, xp=xp)
+
+
+# Maps number of leaves to text size.
+#
+# p <= 20, size="12"
+# 20 < p <= 30, size="10"
+# 30 < p <= 50, size="8"
+# 50 < p <= np.inf, size="6"
+
+_dtextsizes = {20: 12, 30: 10, 50: 8, 85: 6, np.inf: 5}
+_drotation = {20: 0, 40: 45, np.inf: 90}
+_dtextsortedkeys = list(_dtextsizes.keys())
+_dtextsortedkeys.sort()
+_drotationsortedkeys = list(_drotation.keys())
+_drotationsortedkeys.sort()
+
+
+def _remove_dups(L):
+    """
+    Remove duplicates AND preserve the original order of the elements.
+
+    The set class is not guaranteed to do this.
+    """
+    seen_before = set()
+    L2 = []
+    for i in L:
+        if i not in seen_before:
+            seen_before.add(i)
+            L2.append(i)
+    return L2
+
+
+def _get_tick_text_size(p):
+    for k in _dtextsortedkeys:
+        if p <= k:
+            return _dtextsizes[k]
+
+
+def _get_tick_rotation(p):
+    for k in _drotationsortedkeys:
+        if p <= k:
+            return _drotation[k]
+
+
+def _plot_dendrogram(icoords, dcoords, ivl, p, n, mh, orientation,
+                     no_labels, color_list, leaf_font_size=None,
+                     leaf_rotation=None, contraction_marks=None,
+                     ax=None, above_threshold_color='C0'):
+    # Import matplotlib here so that it's not imported unless dendrograms
+    # are plotted. Raise an informative error if importing fails.
+    try:
+        # if an axis is provided, don't use pylab at all
+        if ax is None:
+            import matplotlib.pylab
+        import matplotlib.patches
+        import matplotlib.collections
+    except ImportError as e:
+        raise ImportError("You must install the matplotlib library to plot "
+                          "the dendrogram. Use no_plot=True to calculate the "
+                          "dendrogram without plotting.") from e
+
+    if ax is None:
+        ax = matplotlib.pylab.gca()
+        # if we're using pylab, we want to trigger a draw at the end
+        trigger_redraw = True
+    else:
+        trigger_redraw = False
+
+    # Independent variable plot width
+    ivw = len(ivl) * 10
+    # Dependent variable plot height
+    dvw = mh + mh * 0.05
+
+    iv_ticks = np.arange(5, len(ivl) * 10 + 5, 10)
+    if orientation in ('top', 'bottom'):
+        if orientation == 'top':
+            ax.set_ylim([0, dvw])
+            ax.set_xlim([0, ivw])
+        else:
+            ax.set_ylim([dvw, 0])
+            ax.set_xlim([0, ivw])
+
+        xlines = icoords
+        ylines = dcoords
+        if no_labels:
+            ax.set_xticks([])
+            ax.set_xticklabels([])
+        else:
+            ax.set_xticks(iv_ticks)
+
+            if orientation == 'top':
+                ax.xaxis.set_ticks_position('bottom')
+            else:
+                ax.xaxis.set_ticks_position('top')
+
+            # Make the tick marks invisible because they cover up the links
+            for line in ax.get_xticklines():
+                line.set_visible(False)
+
+            leaf_rot = (float(_get_tick_rotation(len(ivl)))
+                        if (leaf_rotation is None) else leaf_rotation)
+            leaf_font = (float(_get_tick_text_size(len(ivl)))
+                         if (leaf_font_size is None) else leaf_font_size)
+            ax.set_xticklabels(ivl, rotation=leaf_rot, size=leaf_font)
+
+    elif orientation in ('left', 'right'):
+        if orientation == 'left':
+            ax.set_xlim([dvw, 0])
+            ax.set_ylim([0, ivw])
+        else:
+            ax.set_xlim([0, dvw])
+            ax.set_ylim([0, ivw])
+
+        xlines = dcoords
+        ylines = icoords
+        if no_labels:
+            ax.set_yticks([])
+            ax.set_yticklabels([])
+        else:
+            ax.set_yticks(iv_ticks)
+
+            if orientation == 'left':
+                ax.yaxis.set_ticks_position('right')
+            else:
+                ax.yaxis.set_ticks_position('left')
+
+            # Make the tick marks invisible because they cover up the links
+            for line in ax.get_yticklines():
+                line.set_visible(False)
+
+            leaf_font = (float(_get_tick_text_size(len(ivl)))
+                         if (leaf_font_size is None) else leaf_font_size)
+
+            if leaf_rotation is not None:
+                ax.set_yticklabels(ivl, rotation=leaf_rotation, size=leaf_font)
+            else:
+                ax.set_yticklabels(ivl, size=leaf_font)
+
+    # Let's use collections instead. This way there is a separate legend item
+    # for each tree grouping, rather than stupidly one for each line segment.
+    colors_used = _remove_dups(color_list)
+    color_to_lines = {}
+    for color in colors_used:
+        color_to_lines[color] = []
+    for (xline, yline, color) in zip(xlines, ylines, color_list):
+        color_to_lines[color].append(list(zip(xline, yline)))
+
+    colors_to_collections = {}
+    # Construct the collections.
+    for color in colors_used:
+        coll = matplotlib.collections.LineCollection(color_to_lines[color],
+                                                     colors=(color,))
+        colors_to_collections[color] = coll
+
+    # Add all the groupings below the color threshold.
+    for color in colors_used:
+        if color != above_threshold_color:
+            ax.add_collection(colors_to_collections[color])
+    # If there's a grouping of links above the color threshold, it goes last.
+    if above_threshold_color in colors_to_collections:
+        ax.add_collection(colors_to_collections[above_threshold_color])
+
+    if contraction_marks is not None:
+        Ellipse = matplotlib.patches.Ellipse
+        for (x, y) in contraction_marks:
+            if orientation in ('left', 'right'):
+                e = Ellipse((y, x), width=dvw / 100, height=1.0)
+            else:
+                e = Ellipse((x, y), width=1.0, height=dvw / 100)
+            ax.add_artist(e)
+            e.set_clip_box(ax.bbox)
+            e.set_alpha(0.5)
+            e.set_facecolor('k')
+
+    if trigger_redraw:
+        matplotlib.pylab.draw_if_interactive()
+
+
+# C0  is used for above threshold color
+_link_line_colors_default = ('C1', 'C2', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9')
+_link_line_colors = list(_link_line_colors_default)
+
+
+@xp_capabilities(out_of_scope=True)
+def set_link_color_palette(palette):
+    """
+    Set list of matplotlib color codes for use by dendrogram.
+
+    Note that this palette is global (i.e., setting it once changes the colors
+    for all subsequent calls to `dendrogram`) and that it affects only the
+    the colors below ``color_threshold``.
+
+    Note that `dendrogram` also accepts a custom coloring function through its
+    ``link_color_func`` keyword, which is more flexible and non-global.
+
+    Parameters
+    ----------
+    palette : list of str or None
+        A list of matplotlib color codes.  The order of the color codes is the
+        order in which the colors are cycled through when color thresholding in
+        the dendrogram.
+
+        If ``None``, resets the palette to its default (which are matplotlib
+        default colors C1 to C9).
+
+    Returns
+    -------
+    None
+
+    See Also
+    --------
+    dendrogram
+
+    Notes
+    -----
+    Ability to reset the palette with ``None`` added in SciPy 0.17.0.
+
+    Thread safety: using this function in a multi-threaded fashion may
+    result in `dendrogram` producing plots with unexpected colors.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster import hierarchy
+    >>> ytdist = np.array([662., 877., 255., 412., 996., 295., 468., 268.,
+    ...                    400., 754., 564., 138., 219., 869., 669.])
+    >>> Z = hierarchy.linkage(ytdist, 'single')
+    >>> dn = hierarchy.dendrogram(Z, no_plot=True)
+    >>> dn['color_list']
+    ['C1', 'C0', 'C0', 'C0', 'C0']
+    >>> hierarchy.set_link_color_palette(['c', 'm', 'y', 'k'])
+    >>> dn = hierarchy.dendrogram(Z, no_plot=True, above_threshold_color='b')
+    >>> dn['color_list']
+    ['c', 'b', 'b', 'b', 'b']
+    >>> dn = hierarchy.dendrogram(Z, no_plot=True, color_threshold=267,
+    ...                           above_threshold_color='k')
+    >>> dn['color_list']
+    ['c', 'm', 'm', 'k', 'k']
+
+    Now, reset the color palette to its default:
+
+    >>> hierarchy.set_link_color_palette(None)
+
+    """
+    if palette is None:
+        # reset to its default
+        palette = _link_line_colors_default
+    elif not isinstance(palette, list | tuple):
+        raise TypeError("palette must be a list or tuple")
+    _ptypes = [isinstance(p, str) for p in palette]
+
+    if False in _ptypes:
+        raise TypeError("all palette list elements must be color strings")
+
+    global _link_line_colors
+    _link_line_colors = palette
+
+
+@xp_capabilities(cpu_only=True, jax_jit=False, allow_dask_compute=True)
+def dendrogram(Z, p=30, truncate_mode=None, color_threshold=None,
+               get_leaves=True, orientation='top', labels=None,
+               count_sort=False, distance_sort=False, show_leaf_counts=True,
+               no_plot=False, no_labels=False, leaf_font_size=None,
+               leaf_rotation=None, leaf_label_func=None,
+               show_contracted=False, link_color_func=None, ax=None,
+               above_threshold_color='C0'):
+    """
+    Plot the hierarchical clustering as a dendrogram.
+
+    The dendrogram illustrates how each cluster is
+    composed by drawing a U-shaped link between a non-singleton
+    cluster and its children. The top of the U-link indicates a
+    cluster merge. The two legs of the U-link indicate which clusters
+    were merged. The length of the two legs of the U-link represents
+    the distance between the child clusters. It is also the
+    cophenetic distance between original observations in the two
+    children clusters.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The linkage matrix encoding the hierarchical clustering to
+        render as a dendrogram. See the ``linkage`` function for more
+        information on the format of ``Z``.
+    p : int, optional
+        The ``p`` parameter for ``truncate_mode``.
+    truncate_mode : str, optional
+        The dendrogram can be hard to read when the original
+        observation matrix from which the linkage is derived is
+        large. Truncation is used to condense the dendrogram. There
+        are several modes:
+
+        ``None``
+          No truncation is performed (default).
+          Note: ``'none'`` is an alias for ``None`` that's kept for
+          backward compatibility.
+
+        ``'lastp'``
+          The last ``p`` non-singleton clusters formed in the linkage are the
+          only non-leaf nodes in the linkage; they correspond to rows
+          ``Z[n-p-2:end]`` in ``Z``. All other non-singleton clusters are
+          contracted into leaf nodes.
+
+        ``'level'``
+          No more than ``p`` levels of the dendrogram tree are displayed.
+          A "level" includes all nodes with ``p`` merges from the final merge.
+
+          Note: ``'mtica'`` is an alias for ``'level'`` that's kept for
+          backward compatibility.
+
+    color_threshold : double, optional
+        For brevity, let :math:`t` be the ``color_threshold``.
+        Colors all the descendent links below a cluster node
+        :math:`k` the same color if :math:`k` is the first node below
+        the cut threshold :math:`t`. All links connecting nodes with
+        distances greater than or equal to the threshold are colored
+        with de default matplotlib color ``'C0'``. If :math:`t` is less
+        than or equal to zero, all nodes are colored ``'C0'``.
+        If ``color_threshold`` is None or 'default',
+        corresponding with MATLAB(TM) behavior, the threshold is set to
+        ``0.7*max(Z[:,2])``.
+
+    get_leaves : bool, optional
+        Includes a list ``R['leaves']=H`` in the result
+        dictionary. For each :math:`i`, ``H[i] == j``, cluster node
+        ``j`` appears in position ``i`` in the left-to-right traversal
+        of the leaves, where :math:`j < 2n-1` and :math:`i < n`.
+    orientation : str, optional
+        The direction to plot the dendrogram, which can be any
+        of the following strings:
+
+        ``'top'``
+          Plots the root at the top, and plot descendent links going downwards.
+          (default).
+
+        ``'bottom'``
+          Plots the root at the bottom, and plot descendent links going
+          upwards.
+
+        ``'left'``
+          Plots the root at the left, and plot descendent links going right.
+
+        ``'right'``
+          Plots the root at the right, and plot descendent links going left.
+
+    labels : ndarray, optional
+        By default, ``labels`` is None so the index of the original observation
+        is used to label the leaf nodes.  Otherwise, this is an :math:`n`-sized
+        sequence, with ``n == Z.shape[0] + 1``. The ``labels[i]`` value is the
+        text to put under the :math:`i` th leaf node only if it corresponds to
+        an original observation and not a non-singleton cluster.
+    count_sort : str or bool, optional
+        For each node n, the order (visually, from left-to-right) n's
+        two descendent links are plotted is determined by this
+        parameter, which can be any of the following values:
+
+        ``False``
+          Nothing is done.
+
+        ``'ascending'`` or ``True``
+          The child with the minimum number of original objects in its cluster
+          is plotted first.
+
+        ``'descending'``
+          The child with the maximum number of original objects in its cluster
+          is plotted first.
+
+        Note, ``distance_sort`` and ``count_sort`` cannot both be True.
+    distance_sort : str or bool, optional
+        For each node n, the order (visually, from left-to-right) n's
+        two descendent links are plotted is determined by this
+        parameter, which can be any of the following values:
+
+        ``False``
+          Nothing is done.
+
+        ``'ascending'`` or ``True``
+          The child with the minimum distance between its direct descendents is
+          plotted first.
+
+        ``'descending'``
+          The child with the maximum distance between its direct descendents is
+          plotted first.
+
+        Note ``distance_sort`` and ``count_sort`` cannot both be True.
+    show_leaf_counts : bool, optional
+         When True, leaf nodes representing :math:`k>1` original
+         observation are labeled with the number of observations they
+         contain in parentheses.
+    no_plot : bool, optional
+        When True, the final rendering is not performed. This is
+        useful if only the data structures computed for the rendering
+        are needed or if matplotlib is not available.
+    no_labels : bool, optional
+        When True, no labels appear next to the leaf nodes in the
+        rendering of the dendrogram.
+    leaf_rotation : double, optional
+        Specifies the angle (in degrees) to rotate the leaf
+        labels. When unspecified, the rotation is based on the number of
+        nodes in the dendrogram (default is 0).
+    leaf_font_size : int, optional
+        Specifies the font size (in points) of the leaf labels. When
+        unspecified, the size based on the number of nodes in the
+        dendrogram.
+    leaf_label_func : lambda or function, optional
+        When ``leaf_label_func`` is a callable function, for each
+        leaf with cluster index :math:`k < 2n-1`. The function
+        is expected to return a string with the label for the
+        leaf.
+
+        Indices :math:`k < n` correspond to original observations
+        while indices :math:`k \\geq n` correspond to non-singleton
+        clusters.
+
+        For example, to label singletons with their node id and
+        non-singletons with their id, count, and inconsistency
+        coefficient, simply do::
+
+            # First define the leaf label function.
+            def llf(id):
+                if id < n:
+                    return str(id)
+                else:
+                    return '[%d %d %1.2f]' % (id, count, R[n-id,3])
+
+            # The text for the leaf nodes is going to be big so force
+            # a rotation of 90 degrees.
+            dendrogram(Z, leaf_label_func=llf, leaf_rotation=90)
+
+            # leaf_label_func can also be used together with ``truncate_mode``,
+            # in which case you will get your leaves labeled after truncation:
+            dendrogram(Z, leaf_label_func=llf, leaf_rotation=90,
+                       truncate_mode='level', p=2)
+
+    show_contracted : bool, optional
+        When True the heights of non-singleton nodes contracted
+        into a leaf node are plotted as crosses along the link
+        connecting that leaf node.  This really is only useful when
+        truncation is used (see ``truncate_mode`` parameter).
+    link_color_func : callable, optional
+        If given, `link_color_function` is called with each non-singleton id
+        corresponding to each U-shaped link it will paint. The function is
+        expected to return the color to paint the link, encoded as a matplotlib
+        color string code. For example::
+
+            dendrogram(Z, link_color_func=lambda k: colors[k])
+
+        colors the direct links below each untruncated non-singleton node
+        ``k`` using ``colors[k]``.
+    ax : matplotlib Axes instance, optional
+        If None and `no_plot` is not True, the dendrogram will be plotted
+        on the current axes.  Otherwise if `no_plot` is not True the
+        dendrogram will be plotted on the given ``Axes`` instance. This can be
+        useful if the dendrogram is part of a more complex figure.
+    above_threshold_color : str, optional
+        This matplotlib color string sets the color of the links above the
+        color_threshold. The default is ``'C0'``.
+
+    Returns
+    -------
+    R : dict
+        A dictionary of data structures computed to render the
+        dendrogram. Its has the following keys:
+
+        ``'color_list'``
+          A list of color names. The k'th element represents the color of the
+          k'th link.
+
+        ``'icoord'`` and ``'dcoord'``
+          Each of them is a list of lists. Let ``icoord = [I1, I2, ..., Ip]``
+          where ``Ik = [xk1, xk2, xk3, xk4]`` and ``dcoord = [D1, D2, ..., Dp]``
+          where ``Dk = [yk1, yk2, yk3, yk4]``, then the k'th link painted is
+          ``(xk1, yk1)`` - ``(xk2, yk2)`` - ``(xk3, yk3)`` - ``(xk4, yk4)``.
+
+        ``'ivl'``
+          A list of labels corresponding to the leaf nodes.
+
+        ``'leaves'``
+          For each i, ``H[i] == j``, cluster node ``j`` appears in position
+          ``i`` in the left-to-right traversal of the leaves, where
+          :math:`j < 2n-1` and :math:`i < n`. If ``j`` is less than ``n``, the
+          ``i``-th leaf node corresponds to an original observation.
+          Otherwise, it corresponds to a non-singleton cluster.
+
+        ``'leaves_color_list'``
+          A list of color names. The k'th element represents the color of the
+          k'th leaf.
+
+    See Also
+    --------
+    linkage, set_link_color_palette
+
+    Notes
+    -----
+    It is expected that the distances in ``Z[:,2]`` be monotonic, otherwise
+    crossings appear in the dendrogram.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster import hierarchy
+    >>> import matplotlib.pyplot as plt
+
+    A very basic example:
+
+    >>> ytdist = np.array([662., 877., 255., 412., 996., 295., 468., 268.,
+    ...                    400., 754., 564., 138., 219., 869., 669.])
+    >>> Z = hierarchy.linkage(ytdist, 'single')
+    >>> plt.figure()
+    >>> dn = hierarchy.dendrogram(Z)
+
+    Now, plot in given axes, improve the color scheme and use both vertical and
+    horizontal orientations:
+
+    >>> hierarchy.set_link_color_palette(['m', 'c', 'y', 'k'])
+    >>> fig, axes = plt.subplots(1, 2, figsize=(8, 3))
+    >>> dn1 = hierarchy.dendrogram(Z, ax=axes[0], above_threshold_color='y',
+    ...                            orientation='top')
+    >>> dn2 = hierarchy.dendrogram(Z, ax=axes[1],
+    ...                            above_threshold_color='#bcbddc',
+    ...                            orientation='right')
+    >>> hierarchy.set_link_color_palette(None)  # reset to default after use
+    >>> plt.show()
+
+    """
+    # This feature was thought about but never implemented (still useful?):
+    #
+    #         ... = dendrogram(..., leaves_order=None)
+    #
+    #         Plots the leaves in the order specified by a vector of
+    #         original observation indices. If the vector contains duplicates
+    #         or results in a crossing, an exception will be thrown. Passing
+    #         None orders leaf nodes based on the order they appear in the
+    #         pre-order traversal.
+    xp = array_namespace(Z)
+    Z = _asarray(Z, order='C', xp=xp)
+
+    if orientation not in ["top", "left", "bottom", "right"]:
+        raise ValueError("orientation must be one of 'top', 'left', "
+                         "'bottom', or 'right'")
+
+    if labels is not None:
+        try:
+            len_labels = len(labels)
+        except (TypeError, AttributeError):
+            len_labels = labels.shape[0]
+        if Z.shape[0] + 1 != len_labels:
+            raise ValueError("Dimensions of Z and labels must be consistent.")
+
+    _is_valid_linkage(Z, throw=True, name='Z', materialize=True, xp=xp)
+    Zs = Z.shape
+    n = Zs[0] + 1
+    if isinstance(p, int | float):
+        p = int(p)
+    else:
+        raise TypeError('The second argument must be a number')
+
+    if truncate_mode not in ('lastp', 'mtica', 'level', 'none', None):
+        # 'mtica' is kept working for backwards compat.
+        raise ValueError('Invalid truncation mode.')
+
+    if truncate_mode == 'lastp':
+        if p > n or p == 0:
+            p = n
+
+    if truncate_mode == 'mtica':
+        # 'mtica' is an alias
+        truncate_mode = 'level'
+
+    if truncate_mode == 'level':
+        if p <= 0:
+            p = np.inf
+
+    if get_leaves:
+        lvs = []
+    else:
+        lvs = None
+
+    icoord_list = []
+    dcoord_list = []
+    color_list = []
+    current_color = [0]
+    currently_below_threshold = [False]
+    ivl = []  # list of leaves
+
+    if color_threshold is None or (isinstance(color_threshold, str) and
+                                   color_threshold == 'default'):
+        color_threshold = xp.max(Z[:, 2]) * 0.7
+
+    R = {'icoord': icoord_list, 'dcoord': dcoord_list, 'ivl': ivl,
+         'leaves': lvs, 'color_list': color_list}
+
+    # Empty list will be filled in _dendrogram_calculate_info
+    contraction_marks = [] if show_contracted else None
+
+    _dendrogram_calculate_info(
+        Z=Z, p=p,
+        truncate_mode=truncate_mode,
+        color_threshold=color_threshold,
+        get_leaves=get_leaves,
+        orientation=orientation,
+        labels=labels,
+        count_sort=count_sort,
+        distance_sort=distance_sort,
+        show_leaf_counts=show_leaf_counts,
+        i=2*n - 2,
+        iv=0.0,
+        ivl=ivl,
+        n=n,
+        icoord_list=icoord_list,
+        dcoord_list=dcoord_list,
+        lvs=lvs,
+        current_color=current_color,
+        color_list=color_list,
+        currently_below_threshold=currently_below_threshold,
+        leaf_label_func=leaf_label_func,
+        contraction_marks=contraction_marks,
+        link_color_func=link_color_func,
+        above_threshold_color=above_threshold_color)
+
+    if not no_plot:
+        mh = xp.max(Z[:, 2])
+        _plot_dendrogram(icoord_list, dcoord_list, ivl, p, n, mh, orientation,
+                         no_labels, color_list,
+                         leaf_font_size=leaf_font_size,
+                         leaf_rotation=leaf_rotation,
+                         contraction_marks=contraction_marks,
+                         ax=ax,
+                         above_threshold_color=above_threshold_color)
+
+    R["leaves_color_list"] = _get_leaves_color_list(R)
+
+    return R
+
+
+def _get_leaves_color_list(R):
+    leaves_color_list = [None] * len(R['leaves'])
+    for link_x, link_y, link_color in zip(R['icoord'],
+                                          R['dcoord'],
+                                          R['color_list']):
+        for (xi, yi) in zip(link_x, link_y):
+            if yi == 0.0 and (xi % 5 == 0 and xi % 2 == 1):
+                # if yi is 0.0 and xi is divisible by 5 and odd,
+                # the point is a leaf
+                # xi of leaves are      5, 15, 25, 35, ... (see `iv_ticks`)
+                # index of leaves are   0,  1,  2,  3, ... as below
+                leaf_index = (int(xi) - 5) // 10
+                # each leaf has a same color of its link.
+                leaves_color_list[leaf_index] = link_color
+    return leaves_color_list
+
+
+def _append_singleton_leaf_node(Z, p, n, level, lvs, ivl, leaf_label_func,
+                                i, labels):
+    # If the leaf id structure is not None and is a list then the caller
+    # to dendrogram has indicated that cluster id's corresponding to the
+    # leaf nodes should be recorded.
+
+    if lvs is not None:
+        lvs.append(int(i))
+
+    # If leaf node labels are to be displayed...
+    if ivl is not None:
+        # If a leaf_label_func has been provided, the label comes from the
+        # string returned from the leaf_label_func, which is a function
+        # passed to dendrogram.
+        if leaf_label_func:
+            ivl.append(leaf_label_func(int(i)))
+        else:
+            # Otherwise, if the dendrogram caller has passed a labels list
+            # for the leaf nodes, use it.
+            if labels is not None:
+                ivl.append(labels[int(i - n)])
+            else:
+                # Otherwise, use the id as the label for the leaf.x
+                ivl.append(str(int(i)))
+
+
+def _append_nonsingleton_leaf_node(Z, p, n, level, lvs, ivl, leaf_label_func,
+                                   i, labels, show_leaf_counts):
+    # If the leaf id structure is not None and is a list then the caller
+    # to dendrogram has indicated that cluster id's corresponding to the
+    # leaf nodes should be recorded.
+
+    if lvs is not None:
+        lvs.append(int(i))
+    if ivl is not None:
+        if leaf_label_func:
+            ivl.append(leaf_label_func(int(i)))
+        else:
+            if show_leaf_counts:
+                ivl.append("(" + str(np.asarray(Z[i - n, 3], dtype=np.int64)) + ")")
+            else:
+                ivl.append("")
+
+
+def _append_contraction_marks(Z, iv, i, n, contraction_marks, xp):
+    _append_contraction_marks_sub(Z, iv, int_floor(Z[i - n, 0], xp),
+                                  n, contraction_marks, xp)
+    _append_contraction_marks_sub(Z, iv, int_floor(Z[i - n, 1], xp),
+                                  n, contraction_marks, xp)
+
+
+def _append_contraction_marks_sub(Z, iv, i, n, contraction_marks, xp):
+    if i >= n:
+        contraction_marks.append((iv, Z[i - n, 2]))
+        _append_contraction_marks_sub(Z, iv, int_floor(Z[i - n, 0], xp),
+                                      n, contraction_marks, xp)
+        _append_contraction_marks_sub(Z, iv, int_floor(Z[i - n, 1], xp),
+                                      n, contraction_marks, xp)
+
+
+def _dendrogram_calculate_info(Z, p, truncate_mode,
+                               color_threshold=np.inf, get_leaves=True,
+                               orientation='top', labels=None,
+                               count_sort=False, distance_sort=False,
+                               show_leaf_counts=False, i=-1, iv=0.0,
+                               ivl=None, n=0, icoord_list=None, dcoord_list=None,
+                               lvs=None, mhr=False,
+                               current_color=None, color_list=None,
+                               currently_below_threshold=None,
+                               leaf_label_func=None, level=0,
+                               contraction_marks=None,
+                               link_color_func=None,
+                               above_threshold_color='C0'):
+    """
+    Calculate the endpoints of the links as well as the labels for the
+    the dendrogram rooted at the node with index i. iv is the independent
+    variable value to plot the left-most leaf node below the root node i
+    (if orientation='top', this would be the left-most x value where the
+    plotting of this root node i and its descendents should begin).
+
+    ivl is a list to store the labels of the leaf nodes. The leaf_label_func
+    is called whenever ivl != None, labels == None, and
+    leaf_label_func != None. When ivl != None and labels != None, the
+    labels list is used only for labeling the leaf nodes. When
+    ivl == None, no labels are generated for leaf nodes.
+
+    When get_leaves==True, a list of leaves is built as they are visited
+    in the dendrogram.
+
+    Returns a tuple with l being the independent variable coordinate that
+    corresponds to the midpoint of cluster to the left of cluster i if
+    i is non-singleton, otherwise the independent coordinate of the leaf
+    node if i is a leaf node.
+
+    Returns
+    -------
+    A tuple (left, w, h, md), where:
+        * left is the independent variable coordinate of the center of the
+          the U of the subtree
+
+        * w is the amount of space used for the subtree (in independent
+          variable units)
+
+        * h is the height of the subtree in dependent variable units
+
+        * md is the ``max(Z[*,2]``) for all nodes ``*`` below and including
+          the target node.
+
+    """
+    xp = array_namespace(Z)
+    if n == 0:
+        raise ValueError("Invalid singleton cluster count n.")
+
+    if i == -1:
+        raise ValueError("Invalid root cluster index i.")
+
+    if truncate_mode == 'lastp':
+        # If the node is a leaf node but corresponds to a non-singleton
+        # cluster, its label is either the empty string or the number of
+        # original observations belonging to cluster i.
+        if 2*n - p > i >= n:
+            d = Z[i - n, 2]
+            _append_nonsingleton_leaf_node(Z, p, n, level, lvs, ivl,
+                                           leaf_label_func, i, labels,
+                                           show_leaf_counts)
+            if contraction_marks is not None:
+                _append_contraction_marks(Z, iv + 5.0, i, n, contraction_marks, xp)
+            return (iv + 5.0, 10.0, 0.0, d)
+        elif i < n:
+            _append_singleton_leaf_node(Z, p, n, level, lvs, ivl,
+                                        leaf_label_func, i, labels)
+            return (iv + 5.0, 10.0, 0.0, 0.0)
+    elif truncate_mode == 'level':
+        if i > n and level > p:
+            d = Z[i - n, 2]
+            _append_nonsingleton_leaf_node(Z, p, n, level, lvs, ivl,
+                                           leaf_label_func, i, labels,
+                                           show_leaf_counts)
+            if contraction_marks is not None:
+                _append_contraction_marks(Z, iv + 5.0, i, n, contraction_marks, xp)
+            return (iv + 5.0, 10.0, 0.0, d)
+        elif i < n:
+            _append_singleton_leaf_node(Z, p, n, level, lvs, ivl,
+                                        leaf_label_func, i, labels)
+            return (iv + 5.0, 10.0, 0.0, 0.0)
+
+    # Otherwise, only truncate if we have a leaf node.
+    #
+    # Only place leaves if they correspond to original observations.
+    if i < n:
+        _append_singleton_leaf_node(Z, p, n, level, lvs, ivl,
+                                    leaf_label_func, i, labels)
+        return (iv + 5.0, 10.0, 0.0, 0.0)
+
+    # !!! Otherwise, we don't have a leaf node, so work on plotting a
+    # non-leaf node.
+    # Actual indices of a and b
+    aa = int_floor(Z[i - n, 0], xp)
+    ab = int_floor(Z[i - n, 1], xp)
+    if aa >= n:
+        # The number of singletons below cluster a
+        na = Z[aa - n, 3]
+        # The distance between a's two direct children.
+        da = Z[aa - n, 2]
+    else:
+        na = 1
+        da = 0.0
+    if ab >= n:
+        nb = Z[ab - n, 3]
+        db = Z[ab - n, 2]
+    else:
+        nb = 1
+        db = 0.0
+
+    if count_sort == 'ascending' or count_sort is True:
+        # If a has a count greater than b, it and its descendents should
+        # be drawn to the right. Otherwise, to the left.
+        if na > nb:
+            # The cluster index to draw to the left (ua) will be ab
+            # and the one to draw to the right (ub) will be aa
+            ua = ab
+            ub = aa
+        else:
+            ua = aa
+            ub = ab
+    elif count_sort == 'descending':
+        # If a has a count less than or equal to b, it and its
+        # descendents should be drawn to the left. Otherwise, to
+        # the right.
+        if na > nb:
+            ua = aa
+            ub = ab
+        else:
+            ua = ab
+            ub = aa
+    elif distance_sort == 'ascending' or distance_sort is True:
+        # If a has a distance greater than b, it and its descendents should
+        # be drawn to the right. Otherwise, to the left.
+        if da > db:
+            ua = ab
+            ub = aa
+        else:
+            ua = aa
+            ub = ab
+    elif distance_sort == 'descending':
+        # If a has a distance less than or equal to b, it and its
+        # descendents should be drawn to the left. Otherwise, to
+        # the right.
+        if da > db:
+            ua = aa
+            ub = ab
+        else:
+            ua = ab
+            ub = aa
+    else:
+        ua = aa
+        ub = ab
+
+    # Updated iv variable and the amount of space used.
+    (uiva, uwa, uah, uamd) = \
+        _dendrogram_calculate_info(
+            Z=Z, p=p,
+            truncate_mode=truncate_mode,
+            color_threshold=color_threshold,
+            get_leaves=get_leaves,
+            orientation=orientation,
+            labels=labels,
+            count_sort=count_sort,
+            distance_sort=distance_sort,
+            show_leaf_counts=show_leaf_counts,
+            i=ua, iv=iv, ivl=ivl, n=n,
+            icoord_list=icoord_list,
+            dcoord_list=dcoord_list, lvs=lvs,
+            current_color=current_color,
+            color_list=color_list,
+            currently_below_threshold=currently_below_threshold,
+            leaf_label_func=leaf_label_func,
+            level=level + 1, contraction_marks=contraction_marks,
+            link_color_func=link_color_func,
+            above_threshold_color=above_threshold_color)
+
+    h = Z[i - n, 2]
+    if h >= color_threshold or color_threshold <= 0:
+        c = above_threshold_color
+
+        if currently_below_threshold[0]:
+            current_color[0] = (current_color[0] + 1) % len(_link_line_colors)
+        currently_below_threshold[0] = False
+    else:
+        currently_below_threshold[0] = True
+        c = _link_line_colors[current_color[0]]
+
+    (uivb, uwb, ubh, ubmd) = \
+        _dendrogram_calculate_info(
+            Z=Z, p=p,
+            truncate_mode=truncate_mode,
+            color_threshold=color_threshold,
+            get_leaves=get_leaves,
+            orientation=orientation,
+            labels=labels,
+            count_sort=count_sort,
+            distance_sort=distance_sort,
+            show_leaf_counts=show_leaf_counts,
+            i=ub, iv=iv + uwa, ivl=ivl, n=n,
+            icoord_list=icoord_list,
+            dcoord_list=dcoord_list, lvs=lvs,
+            current_color=current_color,
+            color_list=color_list,
+            currently_below_threshold=currently_below_threshold,
+            leaf_label_func=leaf_label_func,
+            level=level + 1, contraction_marks=contraction_marks,
+            link_color_func=link_color_func,
+            above_threshold_color=above_threshold_color)
+
+    max_dist = max(uamd, ubmd, h)
+
+    icoord_list.append([uiva, uiva, uivb, uivb])
+    dcoord_list.append([uah, h, h, ubh])
+    if link_color_func is not None:
+        v = link_color_func(int(i))
+        if not isinstance(v, str):
+            raise TypeError("link_color_func must return a matplotlib "
+                            "color string!")
+        color_list.append(v)
+    else:
+        color_list.append(c)
+
+    return (((uiva + uivb) / 2), uwa + uwb, h, max_dist)
+
+
+@xp_capabilities()
+def is_isomorphic(T1, T2):
+    """
+    Determine if two different cluster assignments are equivalent.
+
+    Parameters
+    ----------
+    T1 : array_like
+        An assignment of singleton cluster ids to flat cluster ids.
+    T2 : array_like
+        An assignment of singleton cluster ids to flat cluster ids.
+
+    Returns
+    -------
+    b : bool
+        Whether the flat cluster assignments `T1` and `T2` are
+        equivalent.
+
+    See Also
+    --------
+    linkage : for a description of what a linkage matrix is.
+    fcluster : for the creation of flat cluster assignments.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import fcluster, is_isomorphic
+    >>> from scipy.cluster.hierarchy import single, complete
+    >>> from scipy.spatial.distance import pdist
+
+    Two flat cluster assignments can be isomorphic if they represent the same
+    cluster assignment, with different labels.
+
+    For example, we can use the `scipy.cluster.hierarchy.single` method
+    and flatten the output to four clusters:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = single(pdist(X))
+    >>> T = fcluster(Z, 1, criterion='distance')
+    >>> T
+    array([3, 3, 3, 4, 4, 4, 2, 2, 2, 1, 1, 1], dtype=int32)
+
+    We can then do the same using the
+    `scipy.cluster.hierarchy.complete`: method:
+
+    >>> Z = complete(pdist(X))
+    >>> T_ = fcluster(Z, 1.5, criterion='distance')
+    >>> T_
+    array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
+
+    As we can see, in both cases we obtain four clusters and all the data
+    points are distributed in the same way - the only thing that changes
+    are the flat cluster labels (3 => 1, 4 =>2, 2 =>3 and 4 =>1), so both
+    cluster assignments are isomorphic:
+
+    >>> is_isomorphic(T, T_)
+    True
+
+    """
+    xp = array_namespace(T1, T2)
+    T1 = _asarray(T1, xp=xp)
+    T2 = _asarray(T2, xp=xp)
+
+    if T1.ndim != 1:
+        raise ValueError('T1 must be one-dimensional.')
+    if T2.ndim != 1:
+        raise ValueError('T2 must be one-dimensional.')
+    if T1.shape != T2.shape:
+        raise ValueError('T1 and T2 must have the same number of elements.')
+
+    # For each pair of (i, j) indices, test that
+    # T1[i] == T1[j] <--> T2[i] == T2[j]
+    # In other words, if the same symbol appears multiple times in T1,
+    # then a potentially different symbol must also be repeated in the same
+    # positions in T2, and vice versa.
+
+    # O(n*log(n)) algorithm.
+    # It is also possible to write a O(n) algorithm on top of unique_all(),
+    # but in practice it's much slower even for large clusters.
+    idx = xp.argsort(T1)
+    T1 = xp.take(T1, idx)
+    T2 = xp.take(T2, idx)
+    changes1 = T1 != xp.roll(T1, -1)
+    changes2 = T2 != xp.roll(T2, -1)
+    return xp.all(changes1 == changes2)
+
+
+@lazy_cython
+def maxdists(Z):
+    """
+    Return the maximum distance between any non-singleton cluster.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The hierarchical clustering encoded as a matrix. See
+        ``linkage`` for more information.
+
+    Returns
+    -------
+    maxdists : ndarray
+        A ``(n-1)`` sized numpy array of doubles; ``MD[i]`` represents
+        the maximum distance between any cluster (including
+        singletons) below and including the node with index i. More
+        specifically, ``MD[i] = Z[Q(i)-n, 2].max()`` where ``Q(i)`` is the
+        set of all node indices below and including node i.
+
+    See Also
+    --------
+    linkage : for a description of what a linkage matrix is.
+    is_monotonic : for testing for monotonicity of a linkage matrix.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import median, maxdists
+    >>> from scipy.spatial.distance import pdist
+
+    Given a linkage matrix ``Z``, `scipy.cluster.hierarchy.maxdists`
+    computes for each new cluster generated (i.e., for each row of the linkage
+    matrix) what is the maximum distance between any two child clusters.
+
+    Due to the nature of hierarchical clustering, in many cases this is going
+    to be just the distance between the two child clusters that were merged
+    to form the current one - that is, Z[:,2].
+
+    However, for non-monotonic cluster assignments such as
+    `scipy.cluster.hierarchy.median` clustering this is not always the
+    case: There may be cluster formations were the distance between the two
+    clusters merged is smaller than the distance between their children.
+
+    We can see this in an example:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = median(pdist(X))
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.11803399,  3.        ],
+           [ 5.        , 13.        ,  1.11803399,  3.        ],
+           [ 8.        , 15.        ,  1.11803399,  3.        ],
+           [11.        , 14.        ,  1.11803399,  3.        ],
+           [18.        , 19.        ,  3.        ,  6.        ],
+           [16.        , 17.        ,  3.5       ,  6.        ],
+           [20.        , 21.        ,  3.25      , 12.        ]])
+    >>> maxdists(Z)
+    array([1.        , 1.        , 1.        , 1.        , 1.11803399,
+           1.11803399, 1.11803399, 1.11803399, 3.        , 3.5       ,
+           3.5       ])
+
+    Note that while the distance between the two clusters merged when creating the
+    last cluster is 3.25, there are two children (clusters 16 and 17) whose distance
+    is larger (3.5). Thus, `scipy.cluster.hierarchy.maxdists` returns 3.5 in
+    this case.
+
+    """
+    xp = array_namespace(Z)
+    Z = _asarray(Z, order='C', dtype=xp.float64, xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+
+    def cy_maxdists(Z, validate):
+        if validate:
+            _is_valid_linkage(Z, throw=True, name='Z', xp=np)
+        MD = np.zeros((Z.shape[0],))
+        _hierarchy.get_max_dist_for_each_cluster(Z, MD, Z.shape[0] + 1)
+        return MD
+
+    return xpx.lazy_apply(cy_maxdists, Z, validate=is_lazy_array(Z),
+                          shape=(Z.shape[0], ), dtype=xp.float64,
+                          as_numpy=True, xp=xp)
+
+
+@lazy_cython
+def maxinconsts(Z, R):
+    """
+    Return the maximum inconsistency coefficient for each
+    non-singleton cluster and its children.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The hierarchical clustering encoded as a matrix. See
+        `linkage` for more information.
+    R : ndarray
+        The inconsistency matrix.
+
+    Returns
+    -------
+    MI : ndarray
+        A monotonic ``(n-1)``-sized numpy array of doubles.
+
+    See Also
+    --------
+    linkage : for a description of what a linkage matrix is.
+    inconsistent : for the creation of a inconsistency matrix.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import median, inconsistent, maxinconsts
+    >>> from scipy.spatial.distance import pdist
+
+    Given a data set ``X``, we can apply a clustering method to obtain a
+    linkage matrix ``Z``. `scipy.cluster.hierarchy.inconsistent` can
+    be also used to obtain the inconsistency matrix ``R`` associated to
+    this clustering process:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = median(pdist(X))
+    >>> R = inconsistent(Z)
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.11803399,  3.        ],
+           [ 5.        , 13.        ,  1.11803399,  3.        ],
+           [ 8.        , 15.        ,  1.11803399,  3.        ],
+           [11.        , 14.        ,  1.11803399,  3.        ],
+           [18.        , 19.        ,  3.        ,  6.        ],
+           [16.        , 17.        ,  3.5       ,  6.        ],
+           [20.        , 21.        ,  3.25      , 12.        ]])
+    >>> R
+    array([[1.        , 0.        , 1.        , 0.        ],
+           [1.        , 0.        , 1.        , 0.        ],
+           [1.        , 0.        , 1.        , 0.        ],
+           [1.        , 0.        , 1.        , 0.        ],
+           [1.05901699, 0.08346263, 2.        , 0.70710678],
+           [1.05901699, 0.08346263, 2.        , 0.70710678],
+           [1.05901699, 0.08346263, 2.        , 0.70710678],
+           [1.05901699, 0.08346263, 2.        , 0.70710678],
+           [1.74535599, 1.08655358, 3.        , 1.15470054],
+           [1.91202266, 1.37522872, 3.        , 1.15470054],
+           [3.25      , 0.25      , 3.        , 0.        ]])
+
+    Here, `scipy.cluster.hierarchy.maxinconsts` can be used to compute
+    the maximum value of the inconsistency statistic (the last column of
+    ``R``) for each non-singleton cluster and its children:
+
+    >>> maxinconsts(Z, R)
+    array([0.        , 0.        , 0.        , 0.        , 0.70710678,
+           0.70710678, 0.70710678, 0.70710678, 1.15470054, 1.15470054,
+           1.15470054])
+
+    """
+    xp = array_namespace(Z, R)
+    Z = _asarray(Z, order='C', dtype=xp.float64, xp=xp)
+    R = _asarray(R, order='C', dtype=xp.float64, xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+    _is_valid_im(R, throw=True, name='R', xp=xp)
+
+    if Z.shape[0] != R.shape[0]:
+        raise ValueError("The inconsistency matrix and linkage matrix each "
+                         "have a different number of rows.")
+    
+    def cy_maxinconsts(Z, R, validate):
+        if validate:
+            _is_valid_linkage(Z, throw=True, name='Z', xp=np)
+            _is_valid_im(R, throw=True, name='R', xp=np)
+        n = Z.shape[0] + 1
+        MI = np.zeros((n - 1,))
+        _hierarchy.get_max_Rfield_for_each_cluster(Z, R, MI, n, 3)
+        return MI
+
+    return xpx.lazy_apply(cy_maxinconsts, Z, R, validate=is_lazy_array(Z),
+                          shape=(Z.shape[0], ), dtype=xp.float64,
+                          as_numpy=True, xp=xp)
+
+
+@lazy_cython
+def maxRstat(Z, R, i):
+    """
+    Return the maximum statistic for each non-singleton cluster and its
+    children.
+
+    Parameters
+    ----------
+    Z : array_like
+        The hierarchical clustering encoded as a matrix. See `linkage` for more
+        information.
+    R : array_like
+        The inconsistency matrix.
+    i : int
+        The column of `R` to use as the statistic.
+
+    Returns
+    -------
+    MR : ndarray
+        Calculates the maximum statistic for the i'th column of the
+        inconsistency matrix `R` for each non-singleton cluster
+        node. ``MR[j]`` is the maximum over ``R[Q(j)-n, i]``, where
+        ``Q(j)`` the set of all node ids corresponding to nodes below
+        and including ``j``.
+
+    See Also
+    --------
+    linkage : for a description of what a linkage matrix is.
+    inconsistent : for the creation of a inconsistency matrix.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import median, inconsistent, maxRstat
+    >>> from scipy.spatial.distance import pdist
+
+    Given a data set ``X``, we can apply a clustering method to obtain a
+    linkage matrix ``Z``. `scipy.cluster.hierarchy.inconsistent` can
+    be also used to obtain the inconsistency matrix ``R`` associated to
+    this clustering process:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = median(pdist(X))
+    >>> R = inconsistent(Z)
+    >>> R
+    array([[1.        , 0.        , 1.        , 0.        ],
+           [1.        , 0.        , 1.        , 0.        ],
+           [1.        , 0.        , 1.        , 0.        ],
+           [1.        , 0.        , 1.        , 0.        ],
+           [1.05901699, 0.08346263, 2.        , 0.70710678],
+           [1.05901699, 0.08346263, 2.        , 0.70710678],
+           [1.05901699, 0.08346263, 2.        , 0.70710678],
+           [1.05901699, 0.08346263, 2.        , 0.70710678],
+           [1.74535599, 1.08655358, 3.        , 1.15470054],
+           [1.91202266, 1.37522872, 3.        , 1.15470054],
+           [3.25      , 0.25      , 3.        , 0.        ]])
+
+    `scipy.cluster.hierarchy.maxRstat` can be used to compute
+    the maximum value of each column of ``R``, for each non-singleton
+    cluster and its children:
+
+    >>> maxRstat(Z, R, 0)
+    array([1.        , 1.        , 1.        , 1.        , 1.05901699,
+           1.05901699, 1.05901699, 1.05901699, 1.74535599, 1.91202266,
+           3.25      ])
+    >>> maxRstat(Z, R, 1)
+    array([0.        , 0.        , 0.        , 0.        , 0.08346263,
+           0.08346263, 0.08346263, 0.08346263, 1.08655358, 1.37522872,
+           1.37522872])
+    >>> maxRstat(Z, R, 3)
+    array([0.        , 0.        , 0.        , 0.        , 0.70710678,
+           0.70710678, 0.70710678, 0.70710678, 1.15470054, 1.15470054,
+           1.15470054])
+
+    """
+    xp = array_namespace(Z, R)
+    Z = _asarray(Z, order='C', dtype=xp.float64, xp=xp)
+    R = _asarray(R, order='C', dtype=xp.float64, xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+    _is_valid_im(R, throw=True, name='R', xp=xp)
+
+    if not isinstance(i, int):
+        raise TypeError('The third argument must be an integer.')
+
+    if i < 0 or i > 3:
+        raise ValueError('i must be an integer between 0 and 3 inclusive.')
+
+    if Z.shape[0] != R.shape[0]:
+        raise ValueError("The inconsistency matrix and linkage matrix each "
+                         "have a different number of rows.")
+
+    def cy_maxRstat(Z, R, i, validate):
+        if validate:
+            _is_valid_linkage(Z, throw=True, name='Z', xp=np)
+            _is_valid_im(R, throw=True, name='R', xp=np)
+        MR = np.zeros((Z.shape[0],))
+        n = Z.shape[0] + 1
+        _hierarchy.get_max_Rfield_for_each_cluster(Z, R, MR, n, i)
+        return MR
+
+    return xpx.lazy_apply(cy_maxRstat, Z, R, i=i, validate=is_lazy_array(Z),
+                          shape=(Z.shape[0], ), dtype=xp.float64,
+                          as_numpy=True, xp=xp)
+
+
+# Data-dependent output shape makes it impossible to use jax.jit
+@xp_capabilities(cpu_only=True, reason="Cython code", jax_jit=False,
+                 warnings=[("dask.array", "merges chunks")])
+def leaders(Z, T):
+    """
+    Return the root nodes in a hierarchical clustering.
+
+    Returns the root nodes in a hierarchical clustering corresponding
+    to a cut defined by a flat cluster assignment vector ``T``. See
+    the ``fcluster`` function for more information on the format of ``T``.
+
+    For each flat cluster :math:`j` of the :math:`k` flat clusters
+    represented in the n-sized flat cluster assignment vector ``T``,
+    this function finds the lowest cluster node :math:`i` in the linkage
+    tree Z, such that:
+
+      * leaf descendants belong only to flat cluster j
+        (i.e., ``T[p]==j`` for all :math:`p` in :math:`S(i)`, where
+        :math:`S(i)` is the set of leaf ids of descendant leaf nodes
+        with cluster node :math:`i`)
+
+      * there does not exist a leaf that is not a descendant with
+        :math:`i` that also belongs to cluster :math:`j`
+        (i.e., ``T[q]!=j`` for all :math:`q` not in :math:`S(i)`). If
+        this condition is violated, ``T`` is not a valid cluster
+        assignment vector, and an exception will be thrown.
+
+    Parameters
+    ----------
+    Z : ndarray
+        The hierarchical clustering encoded as a matrix. See
+        `linkage` for more information.
+    T : ndarray
+        The flat cluster assignment vector.
+
+    Returns
+    -------
+    L : ndarray
+        The leader linkage node id's stored as a k-element 1-D array,
+        where ``k`` is the number of flat clusters found in ``T``.
+
+        ``L[j]=i`` is the linkage cluster node id that is the
+        leader of flat cluster with id M[j]. If ``i < n``, ``i``
+        corresponds to an original observation, otherwise it
+        corresponds to a non-singleton cluster.
+    M : ndarray
+        The leader linkage node id's stored as a k-element 1-D array, where
+        ``k`` is the number of flat clusters found in ``T``. This allows the
+        set of flat cluster ids to be any arbitrary set of ``k`` integers.
+
+        For example: if ``L[3]=2`` and ``M[3]=8``, the flat cluster with
+        id 8's leader is linkage node 2.
+
+    See Also
+    --------
+    fcluster : for the creation of flat cluster assignments.
+
+    Examples
+    --------
+    >>> from scipy.cluster.hierarchy import ward, fcluster, leaders
+    >>> from scipy.spatial.distance import pdist
+
+    Given a linkage matrix ``Z`` - obtained after apply a clustering method
+    to a dataset ``X`` - and a flat cluster assignment array ``T``:
+
+    >>> X = [[0, 0], [0, 1], [1, 0],
+    ...      [0, 4], [0, 3], [1, 4],
+    ...      [4, 0], [3, 0], [4, 1],
+    ...      [4, 4], [3, 4], [4, 3]]
+
+    >>> Z = ward(pdist(X))
+    >>> Z
+    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
+           [ 3.        ,  4.        ,  1.        ,  2.        ],
+           [ 6.        ,  7.        ,  1.        ,  2.        ],
+           [ 9.        , 10.        ,  1.        ,  2.        ],
+           [ 2.        , 12.        ,  1.29099445,  3.        ],
+           [ 5.        , 13.        ,  1.29099445,  3.        ],
+           [ 8.        , 14.        ,  1.29099445,  3.        ],
+           [11.        , 15.        ,  1.29099445,  3.        ],
+           [16.        , 17.        ,  5.77350269,  6.        ],
+           [18.        , 19.        ,  5.77350269,  6.        ],
+           [20.        , 21.        ,  8.16496581, 12.        ]])
+
+    >>> T = fcluster(Z, 3, criterion='distance')
+    >>> T
+    array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
+
+    `scipy.cluster.hierarchy.leaders` returns the indices of the nodes
+    in the dendrogram that are the leaders of each flat cluster:
+
+    >>> L, M = leaders(Z, T)
+    >>> L
+    array([16, 17, 18, 19], dtype=int32)
+
+    (remember that indices 0-11 point to the 12 data points in ``X``,
+    whereas indices 12-22 point to the 11 rows of ``Z``)
+
+    `scipy.cluster.hierarchy.leaders` also returns the indices of
+    the flat clusters in ``T``:
+
+    >>> M
+    array([1, 2, 3, 4], dtype=int32)
+
+    Notes
+    -----
+    *Array API support (experimental):* This function returns arrays
+    with data-dependent shape. In JAX, at the moment of writing this makes it
+    impossible to execute it inside `@jax.jit`.
+    """
+    xp = array_namespace(Z, T)
+    Z = _asarray(Z, order='C', dtype=xp.float64, xp=xp)
+    T = _asarray(T, order='C', xp=xp)
+    _is_valid_linkage(Z, throw=True, name='Z', xp=xp)
+
+    if T.dtype != xp.int32:
+        raise TypeError('T must be a 1-D array of dtype int32.')
+
+    if T.shape[0] != Z.shape[0] + 1:
+        raise ValueError('Mismatch: len(T)!=Z.shape[0] + 1.')
+
+    n_obs = Z.shape[0] + 1
+
+    def cy_leaders(Z, T, validate):
+        if validate:
+            _is_valid_linkage(Z, throw=True, name='Z', xp=np)
+        n_clusters = int(xpx.nunique(T))
+        L = np.zeros(n_clusters, dtype=np.int32)
+        M = np.zeros(n_clusters, dtype=np.int32)
+        s = _hierarchy.leaders(Z, T, L, M, n_clusters, n_obs)
+        if s >= 0:
+            raise ValueError('T is not a valid assignment vector. Error found '
+                             f'when examining linkage node {s} (< 2n-1).')
+        return L, M
+
+    return xpx.lazy_apply(cy_leaders, Z, T, validate=is_lazy_array(Z),
+                          shape=((None,), (None, )), dtype=(xp.int32, xp.int32),
+                          as_numpy=True, xp=xp)
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@@ -0,0 +1,145 @@
+from numpy import array
+
+
+Q_X = array([[5.26563660e-01, 3.14160190e-01, 8.00656370e-02],
+             [7.50205180e-01, 4.60299830e-01, 8.98696460e-01],
+             [6.65461230e-01, 6.94011420e-01, 9.10465700e-01],
+             [9.64047590e-01, 1.43082200e-03, 7.39874220e-01],
+             [1.08159060e-01, 5.53028790e-01, 6.63804780e-02],
+             [9.31359130e-01, 8.25424910e-01, 9.52315440e-01],
+             [6.78086960e-01, 3.41903970e-01, 5.61481950e-01],
+             [9.82730940e-01, 7.04605210e-01, 8.70978630e-02],
+             [6.14691610e-01, 4.69989230e-02, 6.02406450e-01],
+             [5.80161260e-01, 9.17354970e-01, 5.88163850e-01],
+             [1.38246310e+00, 1.96358160e+00, 1.94437880e+00],
+             [2.10675860e+00, 1.67148730e+00, 1.34854480e+00],
+             [1.39880070e+00, 1.66142050e+00, 1.32224550e+00],
+             [1.71410460e+00, 1.49176380e+00, 1.45432170e+00],
+             [1.54102340e+00, 1.84374950e+00, 1.64658950e+00],
+             [2.08512480e+00, 1.84524350e+00, 2.17340850e+00],
+             [1.30748740e+00, 1.53801650e+00, 2.16007740e+00],
+             [1.41447700e+00, 1.99329070e+00, 1.99107420e+00],
+             [1.61943490e+00, 1.47703280e+00, 1.89788160e+00],
+             [1.59880600e+00, 1.54988980e+00, 1.57563350e+00],
+             [3.37247380e+00, 2.69635310e+00, 3.39981700e+00],
+             [3.13705120e+00, 3.36528090e+00, 3.06089070e+00],
+             [3.29413250e+00, 3.19619500e+00, 2.90700170e+00],
+             [2.65510510e+00, 3.06785900e+00, 2.97198540e+00],
+             [3.30941040e+00, 2.59283970e+00, 2.57714110e+00],
+             [2.59557220e+00, 3.33477370e+00, 3.08793190e+00],
+             [2.58206180e+00, 3.41615670e+00, 3.26441990e+00],
+             [2.71127000e+00, 2.77032450e+00, 2.63466500e+00],
+             [2.79617850e+00, 3.25473720e+00, 3.41801560e+00],
+             [2.64741750e+00, 2.54538040e+00, 3.25354110e+00]])
+
+ytdist = array([662., 877., 255., 412., 996., 295., 468., 268., 400., 754.,
+                564., 138., 219., 869., 669.])
+
+linkage_ytdist_single = array([[2., 5., 138., 2.],
+                               [3., 4., 219., 2.],
+                               [0., 7., 255., 3.],
+                               [1., 8., 268., 4.],
+                               [6., 9., 295., 6.]])
+
+linkage_ytdist_complete = array([[2., 5., 138., 2.],
+                                 [3., 4., 219., 2.],
+                                 [1., 6., 400., 3.],
+                                 [0., 7., 412., 3.],
+                                 [8., 9., 996., 6.]])
+
+linkage_ytdist_average = array([[2., 5., 138., 2.],
+                                [3., 4., 219., 2.],
+                                [0., 7., 333.5, 3.],
+                                [1., 6., 347.5, 3.],
+                                [8., 9., 680.77777778, 6.]])
+
+linkage_ytdist_weighted = array([[2., 5., 138., 2.],
+                                 [3., 4., 219., 2.],
+                                 [0., 7., 333.5, 3.],
+                                 [1., 6., 347.5, 3.],
+                                 [8., 9., 670.125, 6.]])
+
+# the optimal leaf ordering of linkage_ytdist_single
+linkage_ytdist_single_olo = array([[5., 2., 138., 2.],
+                                   [4., 3., 219., 2.],
+                                   [7., 0., 255., 3.],
+                                   [1., 8., 268., 4.],
+                                   [6., 9., 295., 6.]])
+
+X = array([[1.43054825, -7.5693489],
+           [6.95887839, 6.82293382],
+           [2.87137846, -9.68248579],
+           [7.87974764, -6.05485803],
+           [8.24018364, -6.09495602],
+           [7.39020262, 8.54004355]])
+ 
+linkage_X_centroid = array([[3., 4., 0.36265956, 2.],
+                            [1., 5., 1.77045373, 2.],
+                            [0., 2., 2.55760419, 2.],
+                            [6., 8., 6.43614494, 4.],
+                            [7., 9., 15.17363237, 6.]])
+
+linkage_X_median = array([[3., 4., 0.36265956, 2.],
+                          [1., 5., 1.77045373, 2.],
+                          [0., 2., 2.55760419, 2.],
+                          [6., 8., 6.43614494, 4.],
+                          [7., 9., 15.17363237, 6.]])
+
+linkage_X_ward = array([[3., 4., 0.36265956, 2.],
+                        [1., 5., 1.77045373, 2.],
+                        [0., 2., 2.55760419, 2.],
+                        [6., 8., 9.10208346, 4.],
+                        [7., 9., 24.7784379, 6.]])
+
+# the optimal leaf ordering of linkage_X_ward
+linkage_X_ward_olo = array([[4., 3., 0.36265956, 2.],
+                            [5., 1., 1.77045373, 2.],
+                            [2., 0., 2.55760419, 2.],
+                            [6., 8., 9.10208346, 4.],
+                            [7., 9., 24.7784379, 6.]])
+
+inconsistent_ytdist = {
+    1: array([[138., 0., 1., 0.],
+              [219., 0., 1., 0.],
+              [255., 0., 1., 0.],
+              [268., 0., 1., 0.],
+              [295., 0., 1., 0.]]),
+    2: array([[138., 0., 1., 0.],
+              [219., 0., 1., 0.],
+              [237., 25.45584412, 2., 0.70710678],
+              [261.5, 9.19238816, 2., 0.70710678],
+              [233.66666667, 83.9424406, 3., 0.7306594]]),
+    3: array([[138., 0., 1., 0.],
+              [219., 0., 1., 0.],
+              [237., 25.45584412, 2., 0.70710678],
+              [247.33333333, 25.38372182, 3., 0.81417007],
+              [239., 69.36377537, 4., 0.80733783]]),
+    4: array([[138., 0., 1., 0.],
+              [219., 0., 1., 0.],
+              [237., 25.45584412, 2., 0.70710678],
+              [247.33333333, 25.38372182, 3., 0.81417007],
+              [235., 60.73302232, 5., 0.98793042]])}
+
+fcluster_inconsistent = {
+    0.8: array([6, 2, 2, 4, 6, 2, 3, 7, 3, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1,
+                1, 1, 1, 1, 1, 1, 1, 1, 1]),
+    1.0: array([6, 2, 2, 4, 6, 2, 3, 7, 3, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1,
+                1, 1, 1, 1, 1, 1, 1, 1, 1]),
+    2.0: array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+                1, 1, 1, 1, 1, 1, 1, 1, 1])}
+
+fcluster_distance = {
+    0.6: array([4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 3,
+                1, 1, 1, 2, 1, 1, 1, 1, 1]),
+    1.0: array([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1,
+                1, 1, 1, 1, 1, 1, 1, 1, 1]),
+    2.0: array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+                1, 1, 1, 1, 1, 1, 1, 1, 1])}
+
+fcluster_maxclust = {
+    8.0: array([5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 4,
+                1, 1, 1, 3, 1, 1, 1, 1, 2]),
+    4.0: array([3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2,
+                1, 1, 1, 1, 1, 1, 1, 1, 1]),
+    1.0: array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+                1, 1, 1, 1, 1, 1, 1, 1, 1])}
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/tests/test_disjoint_set.py b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/tests/test_disjoint_set.py
new file mode 100644
index 0000000000000000000000000000000000000000..a73512d35eef168f625a1942a87d248e73a71aa2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/tests/test_disjoint_set.py
@@ -0,0 +1,202 @@
+import pytest
+from pytest import raises as assert_raises
+import numpy as np
+from scipy.cluster.hierarchy import DisjointSet
+import string
+
+
+def generate_random_token():
+    k = len(string.ascii_letters)
+    tokens = list(np.arange(k, dtype=int))
+    tokens += list(np.arange(k, dtype=float))
+    tokens += list(string.ascii_letters)
+    tokens += [None for i in range(k)]
+    tokens = np.array(tokens, dtype=object)
+    rng = np.random.RandomState(seed=0)
+
+    while 1:
+        size = rng.randint(1, 3)
+        element = rng.choice(tokens, size)
+        if size == 1:
+            yield element[0]
+        else:
+            yield tuple(element)
+
+
+def get_elements(n):
+    # dict is deterministic without difficulty of comparing numpy ints
+    elements = {}
+    for element in generate_random_token():
+        if element not in elements:
+            elements[element] = len(elements)
+            if len(elements) >= n:
+                break
+    return list(elements.keys())
+
+
+def test_init():
+    n = 10
+    elements = get_elements(n)
+    dis = DisjointSet(elements)
+    assert dis.n_subsets == n
+    assert list(dis) == elements
+
+
+def test_len():
+    n = 10
+    elements = get_elements(n)
+    dis = DisjointSet(elements)
+    assert len(dis) == n
+
+    dis.add("dummy")
+    assert len(dis) == n + 1
+
+
+@pytest.mark.parametrize("n", [10, 100])
+def test_contains(n):
+    elements = get_elements(n)
+    dis = DisjointSet(elements)
+    for x in elements:
+        assert x in dis
+
+    assert "dummy" not in dis
+
+
+@pytest.mark.parametrize("n", [10, 100])
+def test_add(n):
+    elements = get_elements(n)
+    dis1 = DisjointSet(elements)
+
+    dis2 = DisjointSet()
+    for i, x in enumerate(elements):
+        dis2.add(x)
+        assert len(dis2) == i + 1
+
+        # test idempotency by adding element again
+        dis2.add(x)
+        assert len(dis2) == i + 1
+
+    assert list(dis1) == list(dis2)
+
+
+def test_element_not_present():
+    elements = get_elements(n=10)
+    dis = DisjointSet(elements)
+
+    with assert_raises(KeyError):
+        dis["dummy"]
+
+    with assert_raises(KeyError):
+        dis.merge(elements[0], "dummy")
+
+    with assert_raises(KeyError):
+        dis.connected(elements[0], "dummy")
+
+
+@pytest.mark.parametrize("direction", ["forwards", "backwards"])
+@pytest.mark.parametrize("n", [10, 100])
+def test_linear_union_sequence(n, direction):
+    elements = get_elements(n)
+    dis = DisjointSet(elements)
+    assert elements == list(dis)
+
+    indices = list(range(n - 1))
+    if direction == "backwards":
+        indices = indices[::-1]
+
+    for it, i in enumerate(indices):
+        assert not dis.connected(elements[i], elements[i + 1])
+        assert dis.merge(elements[i], elements[i + 1])
+        assert dis.connected(elements[i], elements[i + 1])
+        assert dis.n_subsets == n - 1 - it
+
+    roots = [dis[i] for i in elements]
+    if direction == "forwards":
+        assert all(elements[0] == r for r in roots)
+    else:
+        assert all(elements[-2] == r for r in roots)
+    assert not dis.merge(elements[0], elements[-1])
+
+
+@pytest.mark.parametrize("n", [10, 100])
+def test_self_unions(n):
+    elements = get_elements(n)
+    dis = DisjointSet(elements)
+
+    for x in elements:
+        assert dis.connected(x, x)
+        assert not dis.merge(x, x)
+        assert dis.connected(x, x)
+    assert dis.n_subsets == len(elements)
+
+    assert elements == list(dis)
+    roots = [dis[x] for x in elements]
+    assert elements == roots
+
+
+@pytest.mark.parametrize("order", ["ab", "ba"])
+@pytest.mark.parametrize("n", [10, 100])
+def test_equal_size_ordering(n, order):
+    elements = get_elements(n)
+    dis = DisjointSet(elements)
+
+    rng = np.random.RandomState(seed=0)
+    indices = np.arange(n)
+    rng.shuffle(indices)
+
+    for i in range(0, len(indices), 2):
+        a, b = elements[indices[i]], elements[indices[i + 1]]
+        if order == "ab":
+            assert dis.merge(a, b)
+        else:
+            assert dis.merge(b, a)
+
+        expected = elements[min(indices[i], indices[i + 1])]
+        assert dis[a] == expected
+        assert dis[b] == expected
+
+
+@pytest.mark.parametrize("kmax", [5, 10])
+def test_binary_tree(kmax):
+    n = 2**kmax
+    elements = get_elements(n)
+    dis = DisjointSet(elements)
+    rng = np.random.RandomState(seed=0)
+
+    for k in 2**np.arange(kmax):
+        for i in range(0, n, 2 * k):
+            r1, r2 = rng.randint(0, k, size=2)
+            a, b = elements[i + r1], elements[i + k + r2]
+            assert not dis.connected(a, b)
+            assert dis.merge(a, b)
+            assert dis.connected(a, b)
+
+        assert elements == list(dis)
+        roots = [dis[i] for i in elements]
+        expected_indices = np.arange(n) - np.arange(n) % (2 * k)
+        expected = [elements[i] for i in expected_indices]
+        assert roots == expected
+
+
+@pytest.mark.parametrize("n", [10, 100])
+def test_subsets(n):
+    elements = get_elements(n)
+    dis = DisjointSet(elements)
+
+    rng = np.random.RandomState(seed=0)
+    for i, j in rng.randint(0, n, (n, 2)):
+        x = elements[i]
+        y = elements[j]
+
+        expected = {element for element in dis if {dis[element]} == {dis[x]}}
+        assert dis.subset_size(x) == len(dis.subset(x))
+        assert expected == dis.subset(x)
+
+        expected = {dis[element]: set() for element in dis}
+        for element in dis:
+            expected[dis[element]].add(element)
+        expected = list(expected.values())
+        assert expected == dis.subsets()
+
+        dis.merge(x, y)
+        assert dis.subset(x) == dis.subset(y)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/tests/test_hierarchy.py b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/tests/test_hierarchy.py
new file mode 100644
index 0000000000000000000000000000000000000000..e634bb0d9ee2c889236df3e1e4ecb7b6009c449b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/tests/test_hierarchy.py
@@ -0,0 +1,1237 @@
+#
+# Author: Damian Eads
+# Date: April 17, 2008
+#
+# Copyright (C) 2008 Damian Eads
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#
+# 1. Redistributions of source code must retain the above copyright
+#    notice, this list of conditions and the following disclaimer.
+#
+# 2. Redistributions in binary form must reproduce the above
+#    copyright notice, this list of conditions and the following
+#    disclaimer in the documentation and/or other materials provided
+#    with the distribution.
+#
+# 3. The name of the author may not be used to endorse or promote
+#    products derived from this software without specific prior
+#    written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
+# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
+# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
+# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
+# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal, assert_array_equal, assert_
+import pytest
+from pytest import raises as assert_raises
+
+from scipy.cluster.hierarchy import (
+    ClusterWarning, linkage, from_mlab_linkage, to_mlab_linkage,
+    num_obs_linkage, inconsistent, cophenet, fclusterdata, fcluster,
+    is_isomorphic, single, ward, leaders,
+    correspond, is_monotonic, maxdists, maxinconsts, maxRstat,
+    is_valid_linkage, is_valid_im, to_tree, leaves_list, dendrogram,
+    set_link_color_palette, cut_tree, optimal_leaf_ordering,
+    _order_cluster_tree, _hierarchy, _EUCLIDEAN_METHODS, _LINKAGE_METHODS)
+from scipy.cluster._hierarchy import Heap
+from scipy.spatial.distance import pdist
+from scipy._lib._array_api import (eager_warns, make_xp_test_case,
+                                   xp_assert_close, xp_assert_equal)
+import scipy._lib.array_api_extra as xpx
+
+from threading import Lock
+
+from . import hierarchy_test_data
+
+class eager:
+    # Bypass xpx.testing.lazy_xp_function when calling
+    # these functions from this namespace
+    is_valid_im = is_valid_im
+    is_valid_linkage = is_valid_linkage
+
+
+# Matplotlib is not a scipy dependency but is optionally used in dendrogram, so
+# check if it's available
+try:
+    import matplotlib
+    # and set the backend to be Agg (no gui)
+    matplotlib.use('Agg')
+    # before importing pyplot
+    import matplotlib.pyplot as plt
+    have_matplotlib = True
+except Exception:
+    have_matplotlib = False
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+
+@make_xp_test_case(linkage)
+class TestLinkage:
+
+    @skip_xp_backends("jax.numpy", reason="Can't raise inside jax.pure_callback")
+    def test_linkage_non_finite_elements_in_distance_matrix(self, xp):
+        # Tests linkage(Y) where Y contains a non-finite element (e.g. NaN or Inf).
+        # Exception expected.
+        y = xp.asarray([xp.nan] + [0.0]*5)
+        assert_raises(ValueError, linkage, y)
+
+    def test_linkage_empty_distance_matrix(self, xp):
+        # Tests linkage(Y) where Y is a 0x4 linkage matrix. Exception expected.
+        y = xp.zeros((0,))
+        assert_raises(ValueError, linkage, y)
+
+    def test_linkage_tdist(self, xp):
+        for method in ['single', 'complete', 'average', 'weighted']:
+            self.check_linkage_tdist(method, xp)
+
+    def check_linkage_tdist(self, method, xp):
+        # Tests linkage(Y, method) on the tdist data set.
+        Z = linkage(xp.asarray(hierarchy_test_data.ytdist), method)
+        expectedZ = getattr(hierarchy_test_data, 'linkage_ytdist_' + method)
+        xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-10)
+
+    def test_linkage_X(self, xp):
+        for method in ['centroid', 'median', 'ward']:
+            self.check_linkage_q(method, xp)
+
+    def check_linkage_q(self, method, xp):
+        # Tests linkage(Y, method) on the Q data set.
+        Z = linkage(xp.asarray(hierarchy_test_data.X), method)
+        expectedZ = getattr(hierarchy_test_data, 'linkage_X_' + method)
+        xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-06)
+
+        X = xp.asarray(hierarchy_test_data.X)
+        y = pdist(X, metric="euclidean")
+        Z = linkage(y, method)
+        xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-06)
+
+    def test_compare_with_trivial(self, xp):
+        rng = np.random.RandomState(0)
+        n = 20
+        X = rng.rand(n, 2)
+        d = pdist(X)
+
+        for method, code in _LINKAGE_METHODS.items():
+            Z_trivial = _hierarchy.linkage(d, n, code)
+            Z = linkage(xp.asarray(d), method)
+            xp_assert_close(Z, xp.asarray(Z_trivial), rtol=1e-14, atol=1e-15)
+
+    def test_optimal_leaf_ordering(self, xp):
+        Z = linkage(xp.asarray(hierarchy_test_data.ytdist), optimal_ordering=True)
+        expectedZ = getattr(hierarchy_test_data, 'linkage_ytdist_single_olo')
+        xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-10)
+
+    @pytest.mark.parametrize("method,expect", [
+        ('single',   [[0, 1, 1.41421356, 2],
+                      [2, 3, 1.41421356, 3]]),
+        ('complete', [[0, 1, 1.41421356, 2],
+                      [2, 3, 2.82842712, 3]]),
+        ('average',  [[0, 1, 1.41421356, 2],
+                      [2, 3, 2.12132034, 3]]),
+        ('weighted', [[0, 1, 1.41421356, 2],
+                      [2, 3, 2.12132034, 3]]),
+        ('centroid', [[0, 1, 1.41421356, 2],
+                      [2, 3, 2.12132034, 3]]),
+        ('median',   [[0, 1, 1.41421356, 2],
+                      [2, 3, 2.12132034, 3]]),
+        ('ward',     [[0, 1, 1.41421356, 2],
+                      [2, 3, 2.44948974, 3]]),
+    ])
+    def test_linkage_ties(self, method, expect, xp):
+        X = xp.asarray([[-1, -1], [0, 0], [1, 1]])
+        Z = linkage(X, method=method)
+        expect = xp.asarray(expect, dtype=xp.float64)
+        xp_assert_close(Z, expect, atol=1e-06)
+
+    def test_unsupported_uncondensed_distance_matrix_linkage_warning(self, xp):
+        X = xp.asarray([[0, 1], [1, 0]])
+        with eager_warns(ClusterWarning, xp=xp):
+            linkage(X)
+
+    @pytest.mark.parametrize("method", _EUCLIDEAN_METHODS)
+    def test_euclidean_linkage_value_error(self, method, xp):
+        X = xp.asarray([[1, 1], [1, 1]])
+        with pytest.raises(ValueError):
+            linkage(X, method=method, metric='cityblock')
+
+    def test_2x2_linkage(self, xp):
+        Z1 = linkage(xp.asarray([1]), method='single', metric='euclidean')
+        Z2 = linkage(xp.asarray([[0, 1], [0, 0]]), method='single', metric='euclidean')
+        xp_assert_close(Z1, Z2, rtol=1e-15)
+
+    @skip_xp_backends("jax.numpy", reason="Can't raise inside jax.pure_callback")
+    def test_centroid_neg_distance(self, xp):
+        # gh-21011
+        values = xp.asarray([0, 0, -1])
+        with pytest.raises(ValueError):
+            # This is just checking that this doesn't crash
+            linkage(values, method='centroid')
+
+
+@make_xp_test_case(inconsistent)
+class TestInconsistent:
+
+    def test_inconsistent_tdist(self, xp):
+        for depth in hierarchy_test_data.inconsistent_ytdist:
+            self.check_inconsistent_tdist(depth, xp)
+
+    def check_inconsistent_tdist(self, depth, xp):
+        Z = xp.asarray(hierarchy_test_data.linkage_ytdist_single)
+        xp_assert_close(inconsistent(Z, depth),
+                        xp.asarray(hierarchy_test_data.inconsistent_ytdist[depth]))
+
+
+@make_xp_test_case(cophenet)
+class TestCopheneticDistance:
+
+    def test_linkage_cophenet_tdist_Z(self, xp):
+        # Tests cophenet(Z) on tdist data set.
+        expectedM = xp.asarray([268, 295, 255, 255, 295, 295, 268, 268, 295, 295,
+                                295, 138, 219, 295, 295])
+        Z = xp.asarray(hierarchy_test_data.linkage_ytdist_single)
+        M = cophenet(Z)
+        xp_assert_close(M, xp.asarray(expectedM, dtype=xp.float64), atol=1e-10)
+
+    def test_linkage_cophenet_tdist_Z_Y(self, xp):
+        # Tests cophenet(Z, Y) on tdist data set.
+        Z = xp.asarray(hierarchy_test_data.linkage_ytdist_single)
+        (c, M) = cophenet(Z, xp.asarray(hierarchy_test_data.ytdist))
+        expectedM = xp.asarray([268, 295, 255, 255, 295, 295, 268, 268, 295, 295,
+                                295, 138, 219, 295, 295], dtype=xp.float64)
+        expectedc = xp.asarray(0.639931296433393415057366837573, dtype=xp.float64)[()]
+        xp_assert_close(c, expectedc, atol=1e-10)
+        xp_assert_close(M, expectedM, atol=1e-10)
+
+    @skip_xp_backends("jax.numpy", reason="Can't raise inside jax.pure_callback")
+    def test_gh_22183(self, xp):
+        # check for lack of segfault
+        # (out of bounds memory access)
+        # and correct interception of
+        # invalid linkage matrix
+        arr=[[0.0, 1.0, 1.0, 2.0],
+             [2.0, 12.0, 1.0, 3.0],
+             [3.0, 4.0, 1.0, 2.0],
+             [5.0, 14.0, 1.0, 3.0],
+             [6.0, 7.0, 1.0, 2.0],
+             [8.0, 16.0, 1.0, 3.0],
+             [9.0, 10.0, 1.0, 2.0],
+             [11.0, 18.0, 1.0, 3.0],
+             [13.0, 15.0, 2.0, 6.0],
+             [17.0, 20.0, 2.0, 32.0],
+             [19.0, 21.0, 2.0, 12.0]]
+        with pytest.raises(ValueError, match="excessive observations"):
+            cophenet(xp.asarray(arr))
+
+
+@make_xp_test_case(from_mlab_linkage, to_mlab_linkage)
+class TestMLabLinkageConversion:
+
+    def test_mlab_linkage_conversion_empty(self, xp):
+        # Tests from/to_mlab_linkage on empty linkage array.
+        X = xp.asarray([], dtype=xp.float64)
+        xp_assert_equal(from_mlab_linkage(X), X)
+        xp_assert_equal(to_mlab_linkage(X), X)
+
+    def test_mlab_linkage_conversion_single_row(self, xp):
+        # Tests from/to_mlab_linkage on linkage array with single row.
+        Z = xp.asarray([[0., 1., 3., 2.]])
+        Zm = xp.asarray([[1, 2, 3]])
+        xp_assert_close(from_mlab_linkage(Zm), xp.asarray(Z, dtype=xp.float64),
+                        rtol=1e-15)
+        xp_assert_close(to_mlab_linkage(Z), xp.asarray(Zm, dtype=xp.float64),
+                        rtol=1e-15)
+
+    def test_mlab_linkage_conversion_multiple_rows(self, xp):
+        # Tests from/to_mlab_linkage on linkage array with multiple rows.
+        Zm = xp.asarray([[3, 6, 138], [4, 5, 219],
+                         [1, 8, 255], [2, 9, 268], [7, 10, 295]])
+        Z = xp.asarray([[2., 5., 138., 2.],
+                        [3., 4., 219., 2.],
+                        [0., 7., 255., 3.],
+                        [1., 8., 268., 4.],
+                        [6., 9., 295., 6.]],
+                       dtype=xp.float64)
+        xp_assert_close(from_mlab_linkage(Zm), Z, rtol=1e-15)
+        xp_assert_close(to_mlab_linkage(Z), xp.asarray(Zm, dtype=xp.float64),
+                        rtol=1e-15)
+
+
+@make_xp_test_case(fclusterdata)
+class TestFclusterData:
+
+    @make_xp_test_case(is_isomorphic)
+    @pytest.mark.parametrize("criterion,t",
+        [("inconsistent", t) for t in hierarchy_test_data.fcluster_inconsistent]
+        + [("distance", t) for t in hierarchy_test_data.fcluster_distance]
+        + [("maxclust", t) for t in hierarchy_test_data.fcluster_maxclust]
+    )
+    def test_fclusterdata(self, t, criterion, xp):
+        # Tests fclusterdata(X, criterion=criterion, t=t) on a random 3-cluster data set
+        expectedT = xp.asarray(getattr(hierarchy_test_data, 'fcluster_' + criterion)[t])
+        X = xp.asarray(hierarchy_test_data.Q_X)
+        T = fclusterdata(X, criterion=criterion, t=t)
+        assert is_isomorphic(T, expectedT)
+
+
+@make_xp_test_case(fcluster)
+class TestFcluster:
+
+    @make_xp_test_case(single, is_isomorphic)
+    @pytest.mark.parametrize("criterion,t",
+        [("inconsistent", t) for t in hierarchy_test_data.fcluster_inconsistent]
+        + [("distance", t) for t in hierarchy_test_data.fcluster_distance]
+        + [("maxclust", t) for t in hierarchy_test_data.fcluster_maxclust]
+    )
+    def test_fcluster(self, t, criterion, xp):
+        # Tests fcluster(Z, criterion=criterion, t=t) on a random 3-cluster data set.
+        expectedT = xp.asarray(getattr(hierarchy_test_data, 'fcluster_' + criterion)[t])
+        Z = single(xp.asarray(hierarchy_test_data.Q_X))
+        T = fcluster(Z, criterion=criterion, t=t)
+        assert_(is_isomorphic(T, expectedT))
+
+    @make_xp_test_case(single, is_isomorphic, maxdists)
+    @pytest.mark.parametrize("t", hierarchy_test_data.fcluster_distance)
+    def test_fcluster_monocrit(self, t, xp):
+        expectedT = xp.asarray(hierarchy_test_data.fcluster_distance[t])
+        Z = single(xp.asarray(hierarchy_test_data.Q_X))
+        T = fcluster(Z, t, criterion='monocrit', monocrit=maxdists(Z))
+        assert_(is_isomorphic(T, expectedT))
+
+    @make_xp_test_case(single, is_isomorphic, maxdists)
+    @pytest.mark.parametrize("t", hierarchy_test_data.fcluster_maxclust)
+    def test_fcluster_maxclust_monocrit(self, t, xp):
+        expectedT = xp.asarray(hierarchy_test_data.fcluster_maxclust[t])
+        Z = single(xp.asarray(hierarchy_test_data.Q_X))
+        T = fcluster(Z, t, criterion='maxclust_monocrit', monocrit=maxdists(Z))
+        assert_(is_isomorphic(T, expectedT))
+
+    @make_xp_test_case(single)
+    def test_fcluster_maxclust_gh_12651(self, xp):
+        y = xp.asarray([[1], [4], [5]])
+        Z = single(y)
+        assert_array_equal(fcluster(Z, t=1, criterion="maxclust"),
+                           xp.asarray([1, 1, 1]))
+        assert_array_equal(fcluster(Z, t=2, criterion="maxclust"),
+                           xp.asarray([2, 1, 1]))
+        assert_array_equal(fcluster(Z, t=3, criterion="maxclust"),
+                           xp.asarray([1, 2, 3]))
+        assert_array_equal(fcluster(Z, t=5, criterion="maxclust"),
+                           xp.asarray([1, 2, 3]))
+
+
+@make_xp_test_case(leaders)
+class TestLeaders:
+
+    def test_leaders_single(self, xp):
+        # Tests leaders using a flat clustering generated by single linkage.
+        X = hierarchy_test_data.Q_X
+        Y = pdist(X)
+        Z = linkage(Y)
+        T = fcluster(Z, criterion='maxclust', t=3)
+        Z = xp.asarray(Z)
+        T = xp.asarray(T, dtype=xp.int32)
+        L = leaders(Z, T)
+        expect = xp.asarray([53, 55, 56, 2, 3, 1], dtype=xp.int32)
+        xp_assert_close(xp.concat(L), expect, rtol=1e-15)
+
+
+@make_xp_test_case(is_isomorphic)
+class TestIsIsomorphic:
+
+    def test_array_like(self):
+        assert is_isomorphic([1, 1, 1], [2, 2, 2])
+        assert is_isomorphic([], [])
+
+    def test_is_isomorphic_1(self, xp):
+        # Tests is_isomorphic on test case #1 (one flat cluster, different labellings)
+        a = xp.asarray([1, 1, 1])
+        b = xp.asarray([2, 2, 2])
+        assert is_isomorphic(a, b)
+        assert is_isomorphic(b, a)
+
+    def test_is_isomorphic_2(self, xp):
+        # Tests is_isomorphic on test case #2 (two flat clusters, different labelings)
+        a = xp.asarray([1, 7, 1])
+        b = xp.asarray([2, 3, 2])
+        assert is_isomorphic(a, b)
+        assert is_isomorphic(b, a)
+
+    def test_is_isomorphic_3(self, xp):
+        # Tests is_isomorphic on test case #3 (no flat clusters)
+        a = xp.asarray([])
+        b = xp.asarray([])
+        assert is_isomorphic(a, b)
+
+    def test_is_isomorphic_4A(self, xp):
+        # Tests is_isomorphic on test case #4A
+        # (3 flat clusters, different labelings, isomorphic)
+        a = xp.asarray([1, 2, 3])
+        b = xp.asarray([1, 3, 2])
+        assert is_isomorphic(a, b)
+        assert is_isomorphic(b, a)
+
+    def test_is_isomorphic_4B(self, xp):
+        # Tests is_isomorphic on test case #4B
+        # (3 flat clusters, different labelings, nonisomorphic)
+        a = xp.asarray([1, 2, 3, 3])
+        b = xp.asarray([1, 3, 2, 3])
+        assert not is_isomorphic(a, b)
+        assert not is_isomorphic(b, a)
+
+    def test_is_isomorphic_4C(self, xp):
+        # Tests is_isomorphic on test case #4C
+        # (3 flat clusters, different labelings, isomorphic)
+        a = xp.asarray([7, 2, 3])
+        b = xp.asarray([6, 3, 2])
+        assert is_isomorphic(a, b)
+        assert is_isomorphic(b, a)
+
+    @pytest.mark.parametrize("nclusters", [2, 3, 5])
+    def test_is_isomorphic_5(self, nclusters, xp):
+        # Tests is_isomorphic on test case #5 (1000 observations, 2/3/5 random
+        # clusters, random permutation of the labeling).
+        self.is_isomorphic_randperm(1000, nclusters, xp=xp)
+
+    @pytest.mark.parametrize("nclusters", [2, 3, 5])
+    def test_is_isomorphic_6(self, nclusters, xp):
+        # Tests is_isomorphic on test case #5A (1000 observations, 2/3/5 random
+        # clusters, random permutation of the labeling, slightly
+        # nonisomorphic.)
+        self.is_isomorphic_randperm(1000, nclusters, True, 5, xp=xp)
+
+    def test_is_isomorphic_7(self, xp):
+        # Regression test for gh-6271
+        a = xp.asarray([1, 2, 3])
+        b = xp.asarray([1, 1, 1])
+        assert not is_isomorphic(a, b)
+
+    def is_isomorphic_randperm(self, nobs, nclusters, noniso=False, nerrors=0, *, xp):
+        rng = np.random.default_rng()
+        for _ in range(3):
+            a = rng.integers(0, nclusters, size=nobs)
+            p = rng.permutation(nclusters)
+            b = p.take(a.astype(np.intp))
+            if noniso:
+                q = rng.permutation(nobs)
+                b[q[0:nerrors]] += 1
+                b[q[0:nerrors]] %= nclusters
+            a = xp.asarray(a)
+            b = xp.asarray(b)
+            assert is_isomorphic(a, b) == (not noniso)
+            assert is_isomorphic(b, a) == (not noniso)
+
+
+@make_xp_test_case(is_valid_linkage)
+class TestIsValidLinkage:
+
+    @pytest.mark.parametrize("nrow, ncol, valid", [(2, 5, False), (2, 3, False),
+                                                  (1, 4, True), (2, 4, True)])
+    def test_is_valid_linkage_various_size(self, nrow, ncol, valid, xp):
+        # Tests is_valid_linkage(Z) with linkage matrices of various sizes
+        Z = xp.asarray([[0, 1, 3.0, 2, 5],
+                        [3, 2, 4.0, 3, 3]], dtype=xp.float64)
+        Z = Z[:nrow, :ncol]
+        xp_assert_equal(is_valid_linkage(Z), valid, check_namespace=False)
+        if not valid:
+            assert_raises(ValueError, is_valid_linkage, Z, throw=True)
+
+    def test_is_valid_linkage_int_type(self, xp):
+        # Tests is_valid_linkage(Z) with integer type.
+        Z = xp.asarray([[0, 1, 3.0, 2],
+                        [3, 2, 4.0, 3]], dtype=xp.int64)
+        xp_assert_equal(is_valid_linkage(Z), False, check_namespace=False)
+        assert_raises(TypeError, is_valid_linkage, Z, throw=True)
+
+    def test_is_valid_linkage_empty(self, xp):
+        # Tests is_valid_linkage(Z) with empty linkage.
+        Z = xp.zeros((0, 4), dtype=xp.float64)
+        xp_assert_equal(is_valid_linkage(Z), False, check_namespace=False)
+        assert_raises(ValueError, is_valid_linkage, Z, throw=True)
+
+    def test_is_valid_linkage_4_and_up(self, xp):
+        # Tests is_valid_linkage(Z) on linkage on observation sets between
+        # sizes 4 and 15 (step size 3).
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = xp.asarray(linkage(y))
+            y = xp.asarray(y)
+            xp_assert_equal(is_valid_linkage(Z), True, check_namespace=False)
+
+    def test_is_valid_linkage_4_and_up_neg_index_left(self, xp):
+        # Tests is_valid_linkage(Z) on linkage on observation sets between
+        # sizes 4 and 15 (step size 3) with negative indices (left).
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = xp.asarray(linkage(y))
+            y = xp.asarray(y)
+            Z = xpx.at(Z)[i//2, 0].set(-2)
+            xp_assert_equal(is_valid_linkage(Z), False, check_namespace=False)
+            with pytest.raises(ValueError):
+                eager.is_valid_linkage(Z, throw=True)
+
+    def test_is_valid_linkage_4_and_up_neg_index_right(self, xp):
+        # Tests is_valid_linkage(Z) on linkage on observation sets between
+        # sizes 4 and 15 (step size 3) with negative indices (right).
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = xp.asarray(linkage(y))
+            y = xp.asarray(y)
+            Z = xpx.at(Z)[i//2, 1].set(-2)
+            xp_assert_equal(is_valid_linkage(Z), False, check_namespace=False)
+            with pytest.raises(ValueError):
+                eager.is_valid_linkage(Z, throw=True)
+
+    def test_is_valid_linkage_4_and_up_neg_dist(self, xp):
+        # Tests is_valid_linkage(Z) on linkage on observation sets between
+        # sizes 4 and 15 (step size 3) with negative distances.
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = xp.asarray(linkage(y))
+            y = xp.asarray(y)
+            Z = xpx.at(Z)[i//2, 2].set(-0.5)
+            xp_assert_equal(is_valid_linkage(Z), False, check_namespace=False)
+            with pytest.raises(ValueError):
+                eager.is_valid_linkage(Z, throw=True)
+
+    def test_is_valid_linkage_4_and_up_neg_counts(self, xp):
+        # Tests is_valid_linkage(Z) on linkage on observation sets between
+        # sizes 4 and 15 (step size 3) with negative counts.
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = xp.asarray(linkage(y))
+            y = xp.asarray(y)
+            Z = xpx.at(Z)[i//2, 3].set(-2)
+            xp_assert_equal(is_valid_linkage(Z), False, check_namespace=False)
+            with pytest.raises(ValueError):
+                eager.is_valid_linkage(Z, throw=True)
+
+
+@make_xp_test_case(is_valid_im)
+class TestIsValidInconsistent:
+
+    def test_is_valid_im_int_type(self, xp):
+        # Tests is_valid_im(R) with integer type.
+        R = xp.asarray([[0, 1, 3.0, 2],
+                        [3, 2, 4.0, 3]], dtype=xp.int64)
+        xp_assert_equal(is_valid_im(R), False, check_namespace=False)
+        assert_raises(TypeError, is_valid_im, R, throw=True)
+
+    @pytest.mark.parametrize("nrow, ncol, valid", [(2, 5, False), (2, 3, False),
+                                                  (1, 4, True), (2, 4, True)])
+    def test_is_valid_im_various_size(self, nrow, ncol, valid, xp):
+        # Tests is_valid_im(R) with linkage matrices of various sizes
+        R = xp.asarray([[0, 1, 3.0, 2, 5],
+                        [3, 2, 4.0, 3, 3]], dtype=xp.float64)
+        R = R[:nrow, :ncol]
+        xp_assert_equal(is_valid_im(R), valid, check_namespace=False)
+        if not valid:
+            assert_raises(ValueError, is_valid_im, R, throw=True)
+
+    def test_is_valid_im_empty(self, xp):
+        # Tests is_valid_im(R) with empty inconsistency matrix.
+        R = xp.zeros((0, 4), dtype=xp.float64)
+        xp_assert_equal(is_valid_im(R), False, check_namespace=False)
+        assert_raises(ValueError, is_valid_im, R, throw=True)
+
+    def test_is_valid_im_4_and_up(self, xp):
+        # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15
+        # (step size 3).
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = linkage(y)
+            R = inconsistent(Z)
+            R = xp.asarray(R)
+            xp_assert_equal(is_valid_im(R), True, check_namespace=False)
+
+    def test_is_valid_im_4_and_up_neg_index_left(self, xp):
+        # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15
+        # (step size 3) with negative link height means.
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = linkage(y)
+            R = inconsistent(Z)
+            R = xpx.at(R)[i//2 , 0].set(-2.0)
+            R = xp.asarray(R)
+            xp_assert_equal(is_valid_im(R), False, check_namespace=False)
+            with pytest.raises(ValueError):
+                eager.is_valid_im(R, throw=True)
+
+    def test_is_valid_im_4_and_up_neg_index_right(self, xp):
+        # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15
+        # (step size 3) with negative link height standard deviations.
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = linkage(y)
+            R = inconsistent(Z)
+            R = xpx.at(R)[i//2 , 1].set(-2.0)
+            R = xp.asarray(R)
+            xp_assert_equal(is_valid_im(R), False, check_namespace=False)
+            with pytest.raises(ValueError):
+                eager.is_valid_im(R, throw=True)
+
+    def test_is_valid_im_4_and_up_neg_dist(self, xp):
+        # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15
+        # (step size 3) with negative link counts.
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = linkage(y)
+            R = inconsistent(Z)
+            R = xpx.at(R)[i//2, 2].set(-0.5)
+            R = xp.asarray(R)
+            xp_assert_equal(is_valid_im(R), False, check_namespace=False)
+            with pytest.raises(ValueError):
+                eager.is_valid_im(R, throw=True)
+
+
+class TestNumObsLinkage:
+
+    def test_num_obs_linkage_empty(self, xp):
+        # Tests num_obs_linkage(Z) with empty linkage.
+        Z = xp.zeros((0, 4), dtype=xp.float64)
+        assert_raises(ValueError, num_obs_linkage, Z)
+
+    def test_num_obs_linkage_1x4(self, xp):
+        # Tests num_obs_linkage(Z) on linkage over 2 observations.
+        Z = xp.asarray([[0, 1, 3.0, 2]], dtype=xp.float64)
+        assert num_obs_linkage(Z) == 2
+
+    def test_num_obs_linkage_2x4(self, xp):
+        # Tests num_obs_linkage(Z) on linkage over 3 observations.
+        Z = xp.asarray([[0, 1, 3.0, 2],
+                        [3, 2, 4.0, 3]], dtype=xp.float64)
+        assert num_obs_linkage(Z) == 3
+
+    def test_num_obs_linkage_4_and_up(self, xp):
+        # Tests num_obs_linkage(Z) on linkage on observation sets between sizes
+        # 4 and 15 (step size 3).
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = xp.asarray(linkage(y))
+            assert num_obs_linkage(Z) == i
+
+    def test_num_obs_linkage_multi_matrix(self, xp):
+        # Tests num_obs_linkage with observation matrices of multiple sizes.
+        for n in range(2, 10):
+            X = np.random.rand(n, 4)
+            Y = pdist(X)
+            Z = xp.asarray(linkage(Y))
+            assert num_obs_linkage(Z) == n
+
+
+@make_xp_test_case(leaves_list, to_tree)
+class TestLeavesList:
+
+    def test_leaves_list_1x4(self, xp):
+        # Tests leaves_list(Z) on a 1x4 linkage.
+        Z = xp.asarray([[0, 1, 3.0, 2]], dtype=xp.float64)
+        to_tree(Z)
+        assert_allclose(leaves_list(Z), [0, 1], rtol=1e-15)
+
+    def test_leaves_list_2x4(self, xp):
+        # Tests leaves_list(Z) on a 2x4 linkage.
+        Z = xp.asarray([[0, 1, 3.0, 2],
+                        [3, 2, 4.0, 3]], dtype=xp.float64)
+        to_tree(Z)
+        assert_allclose(leaves_list(Z), [0, 1, 2], rtol=1e-15)
+
+    @pytest.mark.parametrize("method",
+        ['single', 'complete', 'average', 'weighted', 'centroid', 'median', 'ward'])
+    def test_leaves_list_Q(self, method, xp):
+        # Tests leaves_list(Z) on the Q data set
+        X = hierarchy_test_data.Q_X
+        Z = xp.asarray(linkage(X, method))
+        node = to_tree(Z)
+        assert_allclose(node.pre_order(), leaves_list(Z), rtol=1e-15)
+
+    def test_Q_subtree_pre_order(self, xp):
+        # Tests that pre_order() works when called on sub-trees.
+        X = hierarchy_test_data.Q_X
+        Z = xp.asarray(linkage(X, 'single'))
+        node = to_tree(Z)
+        assert_allclose(node.pre_order(),
+                        (node.get_left().pre_order() + node.get_right().pre_order()),
+                        rtol=1e-15)
+
+
+@make_xp_test_case(correspond)
+class TestCorrespond:
+
+    def test_correspond_empty(self, xp):
+        # Tests correspond(Z, y) with empty linkage and condensed distance matrix.
+        y = xp.zeros((0,), dtype=xp.float64)
+        Z = xp.zeros((0,4), dtype=xp.float64)
+        assert_raises(ValueError, correspond, Z, y)
+
+    def test_correspond_2_and_up(self, xp):
+        # Tests correspond(Z, y) on linkage and CDMs over observation sets of
+        # different sizes.
+        for i in range(2, 4):
+            y = np.random.rand(i*(i-1)//2)
+            Z = xp.asarray(linkage(y))
+            y = xp.asarray(y)
+            assert_(correspond(Z, y))
+        for i in range(4, 15, 3):
+            y = np.random.rand(i*(i-1)//2)
+            Z = xp.asarray(linkage(y))
+            y = xp.asarray(y)
+            assert_(correspond(Z, y))
+
+    def test_correspond_4_and_up(self, xp):
+        # Tests correspond(Z, y) on linkage and CDMs over observation sets of
+        # different sizes. Correspondence should be false.
+        for (i, j) in (list(zip(list(range(2, 4)), list(range(3, 5)))) +
+                       list(zip(list(range(3, 5)), list(range(2, 4))))):
+            y = np.random.rand(i*(i-1)//2)
+            y2 = np.random.rand(j*(j-1)//2)
+            Z = xp.asarray(linkage(y))
+            Z2 = xp.asarray(linkage(y2))
+            y = xp.asarray(y)
+            y2 = xp.asarray(y2)
+            assert not correspond(Z, y2)
+            assert not correspond(Z2, y)
+
+    def test_correspond_4_and_up_2(self, xp):
+        # Tests correspond(Z, y) on linkage and CDMs over observation sets of
+        # different sizes. Correspondence should be false.
+        for (i, j) in (list(zip(list(range(2, 7)), list(range(16, 21)))) +
+                       list(zip(list(range(2, 7)), list(range(16, 21))))):
+            y = np.random.rand(i*(i-1)//2)
+            y2 = np.random.rand(j*(j-1)//2)
+            Z = xp.asarray(linkage(y))
+            Z2 = xp.asarray(linkage(y2))
+            y = xp.asarray(y)
+            y2 = xp.asarray(y2)
+            assert not correspond(Z, y2)
+            assert not correspond(Z2, y)
+
+
+@make_xp_test_case(is_monotonic)
+class TestIsMonotonic:
+
+    def test_is_monotonic_empty(self, xp):
+        # Tests is_monotonic(Z) on an empty linkage.
+        Z = xp.zeros((0, 4), dtype=xp.float64)
+        assert_raises(ValueError, is_monotonic, Z)
+
+    def test_is_monotonic_1x4(self, xp):
+        # Tests is_monotonic(Z) on 1x4 linkage. Expecting True.
+        Z = xp.asarray([[0, 1, 0.3, 2]], dtype=xp.float64)
+        assert is_monotonic(Z)
+
+    def test_is_monotonic_2x4_T(self, xp):
+        # Tests is_monotonic(Z) on 2x4 linkage. Expecting True.
+        Z = xp.asarray([[0, 1, 0.3, 2],
+                        [2, 3, 0.4, 3]], dtype=xp.float64)
+        assert is_monotonic(Z)
+
+    def test_is_monotonic_2x4_F(self, xp):
+        # Tests is_monotonic(Z) on 2x4 linkage. Expecting False.
+        Z = xp.asarray([[0, 1, 0.4, 2],
+                        [2, 3, 0.3, 3]], dtype=xp.float64)
+        assert not is_monotonic(Z)
+
+    def test_is_monotonic_3x4_T(self, xp):
+        # Tests is_monotonic(Z) on 3x4 linkage. Expecting True.
+        Z = xp.asarray([[0, 1, 0.3, 2],
+                        [2, 3, 0.4, 2],
+                        [4, 5, 0.6, 4]], dtype=xp.float64)
+        assert is_monotonic(Z)
+
+    def test_is_monotonic_3x4_F1(self, xp):
+        # Tests is_monotonic(Z) on 3x4 linkage (case 1). Expecting False.
+        Z = xp.asarray([[0, 1, 0.3, 2],
+                        [2, 3, 0.2, 2],
+                        [4, 5, 0.6, 4]], dtype=xp.float64)
+        assert not is_monotonic(Z)
+
+    def test_is_monotonic_3x4_F2(self, xp):
+        # Tests is_monotonic(Z) on 3x4 linkage (case 2). Expecting False.
+        Z = xp.asarray([[0, 1, 0.8, 2],
+                        [2, 3, 0.4, 2],
+                        [4, 5, 0.6, 4]], dtype=xp.float64)
+        assert not is_monotonic(Z)
+
+    def test_is_monotonic_3x4_F3(self, xp):
+        # Tests is_monotonic(Z) on 3x4 linkage (case 3). Expecting False
+        Z = xp.asarray([[0, 1, 0.3, 2],
+                        [2, 3, 0.4, 2],
+                        [4, 5, 0.2, 4]], dtype=xp.float64)
+        assert not is_monotonic(Z)
+
+    def test_is_monotonic_tdist_linkage1(self, xp):
+        # Tests is_monotonic(Z) on clustering generated by single linkage on
+        # tdist data set. Expecting True.
+        Z = xp.asarray(linkage(hierarchy_test_data.ytdist, 'single'))
+        assert is_monotonic(Z)
+
+    def test_is_monotonic_tdist_linkage2(self, xp):
+        # Tests is_monotonic(Z) on clustering generated by single linkage on
+        # tdist data set. Perturbing. Expecting False.
+        Z = xp.asarray(linkage(hierarchy_test_data.ytdist, 'single'))
+        Z = xpx.at(Z)[2, 2].set(0.0)
+        assert not is_monotonic(Z)
+
+    def test_is_monotonic_Q_linkage(self, xp):
+        # Tests is_monotonic(Z) on clustering generated by single linkage on
+        # Q data set. Expecting True.
+        X = hierarchy_test_data.Q_X
+        Z = xp.asarray(linkage(X, 'single'))
+        assert is_monotonic(Z)
+
+
+@make_xp_test_case(maxdists)
+class TestMaxDists:
+
+    def test_maxdists_empty_linkage(self, xp):
+        # Tests maxdists(Z) on empty linkage. Expecting exception.
+        Z = xp.zeros((0, 4), dtype=xp.float64)
+        assert_raises(ValueError, maxdists, Z)
+
+    def test_maxdists_one_cluster_linkage(self, xp):
+        # Tests maxdists(Z) on linkage with one cluster.
+        Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64)
+        MD = maxdists(Z)
+        expectedMD = calculate_maximum_distances(Z, xp)
+        xp_assert_close(MD, expectedMD, atol=1e-15)
+
+    @pytest.mark.parametrize(
+        "method", ['single', 'complete', 'ward', 'centroid', 'median'])
+    def test_maxdists_Q_linkage(self, method, xp):
+        # Tests maxdists(Z) on the Q data set
+        X = hierarchy_test_data.Q_X
+        Z = xp.asarray(linkage(X, method))
+        MD = maxdists(Z)
+        expectedMD = calculate_maximum_distances(Z, xp)
+        xp_assert_close(MD, expectedMD, atol=1e-15)
+
+
+@make_xp_test_case(maxinconsts)
+class TestMaxInconsts:
+
+    def test_maxinconsts_empty_linkage(self, xp):
+        # Tests maxinconsts(Z, R) on empty linkage. Expecting exception.
+        Z = xp.zeros((0, 4), dtype=xp.float64)
+        R = xp.zeros((0, 4), dtype=xp.float64)
+        assert_raises(ValueError, maxinconsts, Z, R)
+
+    def test_maxinconsts_difrow_linkage(self, xp):
+        # Tests maxinconsts(Z, R) on linkage and inconsistency matrices with
+        # different numbers of clusters. Expecting exception.
+        Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64)
+        R = np.random.rand(2, 4)
+        R = xp.asarray(R)
+        assert_raises(ValueError, maxinconsts, Z, R)
+
+    def test_maxinconsts_one_cluster_linkage(self, xp):
+        # Tests maxinconsts(Z, R) on linkage with one cluster.
+        Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64)
+        R = xp.asarray([[0, 0, 0, 0.3]], dtype=xp.float64)
+        MD = maxinconsts(Z, R)
+        expectedMD = calculate_maximum_inconsistencies(Z, R, xp=xp)
+        xp_assert_close(MD, expectedMD, atol=1e-15)
+
+    @pytest.mark.parametrize(
+        "method", ['single', 'complete', 'ward', 'centroid', 'median'])
+    def test_maxinconsts_Q_linkage(self, method, xp):
+        # Tests maxinconsts(Z, R) on the Q data set
+        X = hierarchy_test_data.Q_X
+        Z = linkage(X, method)
+        R = xp.asarray(inconsistent(Z))
+        Z = xp.asarray(Z)
+        MD = maxinconsts(Z, R)
+        expectedMD = calculate_maximum_inconsistencies(Z, R, xp=xp)
+        xp_assert_close(MD, expectedMD, atol=1e-15)
+
+
+@make_xp_test_case(maxRstat)
+class TestMaxRStat:
+
+    def test_maxRstat_invalid_index(self, xp):
+        # Tests maxRstat(Z, R, i). Expecting exception.
+        Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64)
+        R = xp.asarray([[0, 0, 0, 0.3]], dtype=xp.float64)
+        with pytest.raises(TypeError):
+            maxRstat(Z, R, 3.3)
+        with pytest.raises(ValueError):
+            maxRstat(Z, R, -1)
+        with pytest.raises(ValueError):
+            maxRstat(Z, R, 4)
+
+    @pytest.mark.parametrize("i", range(4))
+    def test_maxRstat_empty_linkage(self, i, xp):
+        # Tests maxRstat(Z, R, i) on empty linkage. Expecting exception.
+        Z = xp.zeros((0, 4), dtype=xp.float64)
+        R = xp.zeros((0, 4), dtype=xp.float64)
+        assert_raises(ValueError, maxRstat, Z, R, i)
+
+    @pytest.mark.parametrize("i", range(4))
+    def test_maxRstat_difrow_linkage(self, i, xp):
+        # Tests maxRstat(Z, R, i) on linkage and inconsistency matrices with
+        # different numbers of clusters. Expecting exception.
+        Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64)
+        R = np.random.rand(2, 4)
+        R = xp.asarray(R)
+        assert_raises(ValueError, maxRstat, Z, R, i)
+
+    def test_maxRstat_one_cluster_linkage(self, xp):
+        # Tests maxRstat(Z, R, i) on linkage with one cluster.
+        Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64)
+        R = xp.asarray([[0, 0, 0, 0.3]], dtype=xp.float64)
+        MD = maxRstat(Z, R, 1)
+        expectedMD = calculate_maximum_inconsistencies(Z, R, 1, xp)
+        xp_assert_close(MD, expectedMD, atol=1e-15)
+
+    @pytest.mark.parametrize(
+        "method", ['single', 'complete', 'ward', 'centroid', 'median'])
+    def test_maxRstat_Q_linkage(self, method, xp):
+        # Tests maxRstat(Z, R, 1) on the Q data set
+        X = hierarchy_test_data.Q_X
+        Z = linkage(X, method)
+        R = xp.asarray(inconsistent(Z))
+        Z = xp.asarray(Z)
+        MD = maxRstat(Z, R, 1)
+        expectedMD = calculate_maximum_inconsistencies(Z, R, 1, xp)
+        xp_assert_close(MD, expectedMD, atol=1e-15)
+
+
+@make_xp_test_case(dendrogram)
+class TestDendrogram:
+
+    def test_dendrogram_single_linkage_tdist(self, xp):
+        # Tests dendrogram calculation on single linkage of the tdist data set.
+        Z = xp.asarray(linkage(hierarchy_test_data.ytdist, 'single'))
+        R = dendrogram(Z, no_plot=True)
+        leaves = R["leaves"]
+        assert_equal(leaves, [2, 5, 1, 0, 3, 4])
+
+    def test_valid_orientation(self, xp):
+        Z = xp.asarray(linkage(hierarchy_test_data.ytdist, 'single'))
+        assert_raises(ValueError, dendrogram, Z, orientation="foo")
+
+    def test_labels_as_array_or_list(self, xp):
+        # test for gh-12418
+        Z = xp.asarray(linkage(hierarchy_test_data.ytdist, 'single'))
+        labels = [1, 3, 2, 6, 4, 5]
+        result1 = dendrogram(Z, labels=xp.asarray(labels), no_plot=True)
+        result2 = dendrogram(Z, labels=labels, no_plot=True)
+        assert result1 == result2
+
+    @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib")
+    def test_valid_label_size(self, xp):
+        link = xp.asarray([
+            [0, 1, 1.0, 4],
+            [2, 3, 1.0, 5],
+            [4, 5, 2.0, 6],
+        ])
+        plt.figure()
+        with pytest.raises(ValueError) as exc_info:
+            dendrogram(link, labels=list(range(100)))
+        assert "Dimensions of Z and labels must be consistent."\
+               in str(exc_info.value)
+
+        with pytest.raises(
+                ValueError,
+                match="Dimensions of Z and labels must be consistent."):
+            dendrogram(link, labels=[])
+
+        plt.close()
+
+    @skip_xp_backends('torch',
+         reason='MPL 3.9.2 & torch DeprecationWarning from __array_wrap__'
+                ' and NumPy 2.0'
+    )
+    @skip_xp_backends('dask.array',
+         reason='dask.array has bad interaction with matplotlib'
+    )
+    @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib")
+    @pytest.mark.parametrize("orientation", ['top', 'bottom', 'left', 'right'])
+    def test_dendrogram_plot(self, orientation, xp):
+        # Tests dendrogram plotting.
+        Z = xp.asarray(linkage(hierarchy_test_data.ytdist, 'single'))
+        expected = {'color_list': ['C1', 'C0', 'C0', 'C0', 'C0'],
+                    'dcoord': [[0.0, 138.0, 138.0, 0.0],
+                               [0.0, 219.0, 219.0, 0.0],
+                               [0.0, 255.0, 255.0, 219.0],
+                               [0.0, 268.0, 268.0, 255.0],
+                               [138.0, 295.0, 295.0, 268.0]],
+                    'icoord': [[5.0, 5.0, 15.0, 15.0],
+                               [45.0, 45.0, 55.0, 55.0],
+                               [35.0, 35.0, 50.0, 50.0],
+                               [25.0, 25.0, 42.5, 42.5],
+                               [10.0, 10.0, 33.75, 33.75]],
+                    'ivl': ['2', '5', '1', '0', '3', '4'],
+                    'leaves': [2, 5, 1, 0, 3, 4],
+                    'leaves_color_list': ['C1', 'C1', 'C0', 'C0', 'C0', 'C0'],
+                    }
+
+        fig = plt.figure()
+        ax = fig.add_subplot(221)
+
+        # test that dendrogram accepts ax keyword
+        R1 = dendrogram(Z, ax=ax, orientation=orientation)
+        R1['dcoord'] = np.asarray(R1['dcoord'])
+        assert_equal(R1, expected)
+
+        # test that dendrogram accepts and handle the leaf_font_size and
+        # leaf_rotation keywords
+        dendrogram(Z, ax=ax, orientation=orientation,
+                   leaf_font_size=20, leaf_rotation=90)
+        testlabel = (
+            ax.get_xticklabels()[0]
+            if orientation in ['top', 'bottom']
+            else ax.get_yticklabels()[0]
+        )
+        assert_equal(testlabel.get_rotation(), 90)
+        assert_equal(testlabel.get_size(), 20)
+        dendrogram(Z, ax=ax, orientation=orientation,
+                   leaf_rotation=90)
+        testlabel = (
+            ax.get_xticklabels()[0]
+            if orientation in ['top', 'bottom']
+            else ax.get_yticklabels()[0]
+        )
+        assert_equal(testlabel.get_rotation(), 90)
+        dendrogram(Z, ax=ax, orientation=orientation,
+                   leaf_font_size=20)
+        testlabel = (
+            ax.get_xticklabels()[0]
+            if orientation in ['top', 'bottom']
+            else ax.get_yticklabels()[0]
+        )
+        assert_equal(testlabel.get_size(), 20)
+        plt.close()
+
+        # test plotting to gca (will import pylab)
+        R2 = dendrogram(Z, orientation=orientation)
+        plt.close()
+        R2['dcoord'] = np.asarray(R2['dcoord'])
+        assert_equal(R2, expected)
+
+    @skip_xp_backends('torch',
+          reason='MPL 3.9.2 & torch DeprecationWarning from __array_wrap__'
+                 ' and NumPy 2.0'
+     )
+    @skip_xp_backends('dask.array',
+         reason='dask.array has bad interaction with matplotlib'
+    )
+    @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib")
+    def test_dendrogram_truncate_mode(self, xp):
+        Z = xp.asarray(linkage(hierarchy_test_data.ytdist, 'single'))
+
+        R = dendrogram(Z, 2, 'lastp', show_contracted=True)
+        plt.close()
+        R['dcoord'] = np.asarray(R['dcoord'])
+        assert_equal(R, {'color_list': ['C0'],
+                         'dcoord': [[0.0, 295.0, 295.0, 0.0]],
+                         'icoord': [[5.0, 5.0, 15.0, 15.0]],
+                         'ivl': ['(2)', '(4)'],
+                         'leaves': [6, 9],
+                         'leaves_color_list': ['C0', 'C0'],
+                         })
+
+        R = dendrogram(Z, 2, 'mtica', show_contracted=True)
+        plt.close()
+        R['dcoord'] = np.asarray(R['dcoord'])
+        assert_equal(R, {'color_list': ['C1', 'C0', 'C0', 'C0'],
+                         'dcoord': [[0.0, 138.0, 138.0, 0.0],
+                                    [0.0, 255.0, 255.0, 0.0],
+                                    [0.0, 268.0, 268.0, 255.0],
+                                    [138.0, 295.0, 295.0, 268.0]],
+                         'icoord': [[5.0, 5.0, 15.0, 15.0],
+                                    [35.0, 35.0, 45.0, 45.0],
+                                    [25.0, 25.0, 40.0, 40.0],
+                                    [10.0, 10.0, 32.5, 32.5]],
+                         'ivl': ['2', '5', '1', '0', '(2)'],
+                         'leaves': [2, 5, 1, 0, 7],
+                         'leaves_color_list': ['C1', 'C1', 'C0', 'C0', 'C0'],
+                         })
+
+    @pytest.fixture
+    def dendrogram_lock(self):
+        return Lock()
+
+    def test_dendrogram_colors(self, xp, dendrogram_lock):
+        # Tests dendrogram plots with alternate colors
+        Z = xp.asarray(linkage(hierarchy_test_data.ytdist, 'single'))
+
+        with dendrogram_lock:
+            # Global color palette might be changed concurrently
+            set_link_color_palette(['c', 'm', 'y', 'k'])
+            R = dendrogram(Z, no_plot=True,
+                           above_threshold_color='g', color_threshold=250)
+            set_link_color_palette(['g', 'r', 'c', 'm', 'y', 'k'])
+
+            color_list = R['color_list']
+            assert_equal(color_list, ['c', 'm', 'g', 'g', 'g'])
+
+            # reset color palette (global list)
+            set_link_color_palette(None)
+
+    def test_dendrogram_leaf_colors_zero_dist(self, xp):
+        # tests that the colors of leafs are correct for tree
+        # with two identical points
+        X = np.asarray([[1, 0, 0],
+                        [0, 0, 1],
+                        [0, 2, 0],
+                        [0, 0, 1],
+                        [0, 1, 0],
+                        [0, 1, 0]])
+        Z = xp.asarray(linkage(X, "single"))
+        d = dendrogram(Z, no_plot=True)
+        exp_colors = ['C0', 'C1', 'C1', 'C0', 'C2', 'C2']
+        colors = d["leaves_color_list"]
+        assert_equal(colors, exp_colors)
+
+    def test_dendrogram_leaf_colors(self, xp):
+        # tests that the colors are correct for a tree
+        # with two near points ((0, 0, 1.1) and (0, 0, 1))
+        X = np.asarray([[1, 0, 0],
+                        [0, 0, 1.1],
+                        [0, 2, 0],
+                        [0, 0, 1],
+                        [0, 1, 0],
+                        [0, 1, 0]])
+        Z = xp.asarray(linkage(X, "single"))
+        d = dendrogram(Z, no_plot=True)
+        exp_colors = ['C0', 'C1', 'C1', 'C0', 'C2', 'C2']
+        colors = d["leaves_color_list"]
+        assert_equal(colors, exp_colors)
+
+
+def calculate_maximum_distances(Z, xp):
+    # Used for testing correctness of maxdists.
+    n = Z.shape[0] + 1
+    B = xp.zeros((n-1,), dtype=Z.dtype)
+    for i in range(0, n - 1):
+        q = xp.zeros((3,))
+        left = Z[i, 0]
+        right = Z[i, 1]
+        if left >= n:
+            b_left = B[xp.asarray(left, dtype=xp.int64) - n]
+            q = xpx.at(q, 0).set(b_left)
+        if right >= n:
+            b_right = B[xp.asarray(right, dtype=xp.int64) - n]
+            q = xpx.at(q, 1).set(b_right)
+        q = xpx.at(q, 2).set(Z[i, 2])
+        B = xpx.at(B, i).set(xp.max(q))
+    return B
+
+
+def calculate_maximum_inconsistencies(Z, R, k=3, xp=np):
+    # Used for testing correctness of maxinconsts.
+    n = Z.shape[0] + 1
+    dtype = xp.result_type(Z, R)
+    B = xp.zeros((n-1,), dtype=dtype)
+    for i in range(0, n - 1):
+        q = xp.zeros((3,))
+        left = Z[i, 0]
+        right = Z[i, 1]
+        if left >= n:
+            b_left = B[xp.asarray(left, dtype=xp.int64) - n]
+            q = xpx.at(q, 0).set(b_left)
+        if right >= n:
+            b_right = B[xp.asarray(right, dtype=xp.int64) - n]
+            q = xpx.at(q, 1).set(b_right)
+        q = xpx.at(q, 2).set(R[i, k])
+        B = xpx.at(B, i).set(xp.max(q))
+    return B
+
+
+@make_xp_test_case(to_tree)
+def test_node_compare(xp):
+    np.random.seed(23)
+    nobs = 50
+    X = np.random.randn(nobs, 4)
+    Z = xp.asarray(ward(X))
+    tree = to_tree(Z)
+    assert_(tree > tree.get_left())
+    assert_(tree.get_right() > tree.get_left())
+    assert_(tree.get_right() == tree.get_right())
+    assert_(tree.get_right() != tree.get_left())
+
+
+@make_xp_test_case(cut_tree)
+def test_cut_tree(xp):
+    np.random.seed(23)
+    nobs = 50
+    X = np.random.randn(nobs, 4)
+    Z = xp.asarray(ward(X))
+    cutree = cut_tree(Z)
+
+    # cutree.dtype varies between int32 and int64 over platforms
+    xp_assert_close(cutree[:, 0], xp.arange(nobs), rtol=1e-15, check_dtype=False)
+    xp_assert_close(cutree[:, -1], xp.zeros(nobs), rtol=1e-15, check_dtype=False)
+    assert_equal(np.asarray(cutree).max(0), np.arange(nobs - 1, -1, -1))
+
+    xp_assert_close(cutree[:, [-5]], cut_tree(Z, n_clusters=5), rtol=1e-15)
+    xp_assert_close(cutree[:, [-5, -10]], cut_tree(Z, n_clusters=[5, 10]), rtol=1e-15)
+    xp_assert_close(cutree[:, [-10, -5]], cut_tree(Z, n_clusters=[10, 5]), rtol=1e-15)
+
+    nodes = _order_cluster_tree(Z)
+    heights = xp.asarray([node.dist for node in nodes])
+
+    xp_assert_close(cutree[:, np.searchsorted(heights, [5])],
+                    cut_tree(Z, height=5), rtol=1e-15)
+    xp_assert_close(cutree[:, np.searchsorted(heights, [5, 10])],
+                    cut_tree(Z, height=[5, 10]), rtol=1e-15)
+    xp_assert_close(cutree[:, np.searchsorted(heights, [10, 5])],
+                    cut_tree(Z, height=[10, 5]), rtol=1e-15)
+
+
+@make_xp_test_case(optimal_leaf_ordering)
+def test_optimal_leaf_ordering(xp):
+    # test with the distance vector y
+    Z = optimal_leaf_ordering(xp.asarray(linkage(hierarchy_test_data.ytdist)),
+                              xp.asarray(hierarchy_test_data.ytdist))
+    expectedZ = hierarchy_test_data.linkage_ytdist_single_olo
+    xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-10)
+
+    # test with the observation matrix X
+    Z = optimal_leaf_ordering(xp.asarray(linkage(hierarchy_test_data.X, 'ward')),
+                              xp.asarray(hierarchy_test_data.X))
+    expectedZ = hierarchy_test_data.linkage_X_ward_olo
+    xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-06)
+
+
+@skip_xp_backends(np_only=True, reason='`Heap` only supports NumPy backend')
+def test_Heap(xp):
+    values = xp.asarray([2, -1, 0, -1.5, 3])
+    heap = Heap(values)
+
+    pair = heap.get_min()
+    assert_equal(pair['key'], 3)
+    assert_equal(pair['value'], -1.5)
+
+    heap.remove_min()
+    pair = heap.get_min()
+    assert_equal(pair['key'], 1)
+    assert_equal(pair['value'], -1)
+
+    heap.change_value(1, 2.5)
+    pair = heap.get_min()
+    assert_equal(pair['key'], 2)
+    assert_equal(pair['value'], 0)
+
+    heap.remove_min()
+    heap.remove_min()
+
+    heap.change_value(1, 10)
+    pair = heap.get_min()
+    assert_equal(pair['key'], 4)
+    assert_equal(pair['value'], 3)
+
+    heap.remove_min()
+    pair = heap.get_min()
+    assert_equal(pair['key'], 1)
+    assert_equal(pair['value'], 10)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/tests/test_vq.py b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/tests/test_vq.py
new file mode 100644
index 0000000000000000000000000000000000000000..cd285d96ed0badb8aa42d7c68ae04998b717c4a3
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/tests/test_vq.py
@@ -0,0 +1,437 @@
+import math
+import sys
+import warnings
+from copy import deepcopy
+from threading import Lock
+
+import numpy as np
+from numpy.testing import assert_array_equal
+import pytest
+from pytest import raises as assert_raises
+
+from scipy.cluster.vq import (kmeans, kmeans2, py_vq, vq, whiten,
+                              ClusterError, _krandinit)
+from scipy.cluster import _vq
+from scipy.sparse._sputils import matrix
+
+from scipy._lib import array_api_extra as xpx
+from scipy._lib._array_api import (
+    SCIPY_ARRAY_API, eager_warns, is_lazy_array, make_xp_test_case,
+    xp_copy, xp_assert_close, xp_assert_equal
+)
+
+xfail_xp_backends = pytest.mark.xfail_xp_backends
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+TESTDATA_2D = np.array([
+    -2.2, 1.17, -1.63, 1.69, -2.04, 4.38, -3.09, 0.95, -1.7, 4.79, -1.68, 0.68,
+    -2.26, 3.34, -2.29, 2.55, -1.72, -0.72, -1.99, 2.34, -2.75, 3.43, -2.45,
+    2.41, -4.26, 3.65, -1.57, 1.87, -1.96, 4.03, -3.01, 3.86, -2.53, 1.28,
+    -4.0, 3.95, -1.62, 1.25, -3.42, 3.17, -1.17, 0.12, -3.03, -0.27, -2.07,
+    -0.55, -1.17, 1.34, -2.82, 3.08, -2.44, 0.24, -1.71, 2.48, -5.23, 4.29,
+    -2.08, 3.69, -1.89, 3.62, -2.09, 0.26, -0.92, 1.07, -2.25, 0.88, -2.25,
+    2.02, -4.31, 3.86, -2.03, 3.42, -2.76, 0.3, -2.48, -0.29, -3.42, 3.21,
+    -2.3, 1.73, -2.84, 0.69, -1.81, 2.48, -5.24, 4.52, -2.8, 1.31, -1.67,
+    -2.34, -1.18, 2.17, -2.17, 2.82, -1.85, 2.25, -2.45, 1.86, -6.79, 3.94,
+    -2.33, 1.89, -1.55, 2.08, -1.36, 0.93, -2.51, 2.74, -2.39, 3.92, -3.33,
+    2.99, -2.06, -0.9, -2.83, 3.35, -2.59, 3.05, -2.36, 1.85, -1.69, 1.8,
+    -1.39, 0.66, -2.06, 0.38, -1.47, 0.44, -4.68, 3.77, -5.58, 3.44, -2.29,
+    2.24, -1.04, -0.38, -1.85, 4.23, -2.88, 0.73, -2.59, 1.39, -1.34, 1.75,
+    -1.95, 1.3, -2.45, 3.09, -1.99, 3.41, -5.55, 5.21, -1.73, 2.52, -2.17,
+    0.85, -2.06, 0.49, -2.54, 2.07, -2.03, 1.3, -3.23, 3.09, -1.55, 1.44,
+    -0.81, 1.1, -2.99, 2.92, -1.59, 2.18, -2.45, -0.73, -3.12, -1.3, -2.83,
+    0.2, -2.77, 3.24, -1.98, 1.6, -4.59, 3.39, -4.85, 3.75, -2.25, 1.71, -3.28,
+    3.38, -1.74, 0.88, -2.41, 1.92, -2.24, 1.19, -2.48, 1.06, -1.68, -0.62,
+    -1.3, 0.39, -1.78, 2.35, -3.54, 2.44, -1.32, 0.66, -2.38, 2.76, -2.35,
+    3.95, -1.86, 4.32, -2.01, -1.23, -1.79, 2.76, -2.13, -0.13, -5.25, 3.84,
+    -2.24, 1.59, -4.85, 2.96, -2.41, 0.01, -0.43, 0.13, -3.92, 2.91, -1.75,
+    -0.53, -1.69, 1.69, -1.09, 0.15, -2.11, 2.17, -1.53, 1.22, -2.1, -0.86,
+    -2.56, 2.28, -3.02, 3.33, -1.12, 3.86, -2.18, -1.19, -3.03, 0.79, -0.83,
+    0.97, -3.19, 1.45, -1.34, 1.28, -2.52, 4.22, -4.53, 3.22, -1.97, 1.75,
+    -2.36, 3.19, -0.83, 1.53, -1.59, 1.86, -2.17, 2.3, -1.63, 2.71, -2.03,
+    3.75, -2.57, -0.6, -1.47, 1.33, -1.95, 0.7, -1.65, 1.27, -1.42, 1.09, -3.0,
+    3.87, -2.51, 3.06, -2.6, 0.74, -1.08, -0.03, -2.44, 1.31, -2.65, 2.99,
+    -1.84, 1.65, -4.76, 3.75, -2.07, 3.98, -2.4, 2.67, -2.21, 1.49, -1.21,
+    1.22, -5.29, 2.38, -2.85, 2.28, -5.6, 3.78, -2.7, 0.8, -1.81, 3.5, -3.75,
+    4.17, -1.29, 2.99, -5.92, 3.43, -1.83, 1.23, -1.24, -1.04, -2.56, 2.37,
+    -3.26, 0.39, -4.63, 2.51, -4.52, 3.04, -1.7, 0.36, -1.41, 0.04, -2.1, 1.0,
+    -1.87, 3.78, -4.32, 3.59, -2.24, 1.38, -1.99, -0.22, -1.87, 1.95, -0.84,
+    2.17, -5.38, 3.56, -1.27, 2.9, -1.79, 3.31, -5.47, 3.85, -1.44, 3.69,
+    -2.02, 0.37, -1.29, 0.33, -2.34, 2.56, -1.74, -1.27, -1.97, 1.22, -2.51,
+    -0.16, -1.64, -0.96, -2.99, 1.4, -1.53, 3.31, -2.24, 0.45, -2.46, 1.71,
+    -2.88, 1.56, -1.63, 1.46, -1.41, 0.68, -1.96, 2.76, -1.61,
+    2.11]).reshape((200, 2))
+
+
+# Global data
+X = np.array([[3.0, 3], [4, 3], [4, 2],
+              [9, 2], [5, 1], [6, 2], [9, 4],
+              [5, 2], [5, 4], [7, 4], [6, 5]])
+
+CODET1 = np.array([[3.0000, 3.0000],
+                   [6.2000, 4.0000],
+                   [5.8000, 1.8000]])
+
+CODET2 = np.array([[11.0/3, 8.0/3],
+                   [6.7500, 4.2500],
+                   [6.2500, 1.7500]])
+
+LABEL1 = np.array([0, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1])
+
+
+@make_xp_test_case(whiten)
+class TestWhiten:
+
+    def test_whiten(self, xp):
+        desired = xp.asarray([[5.08738849, 2.97091878],
+                            [3.19909255, 0.69660580],
+                            [4.51041982, 0.02640918],
+                            [4.38567074, 0.95120889],
+                            [2.32191480, 1.63195503]])
+
+        obs = xp.asarray([[0.98744510, 0.82766775],
+                          [0.62093317, 0.19406729],
+                          [0.87545741, 0.00735733],
+                          [0.85124403, 0.26499712],
+                          [0.45067590, 0.45464607]])
+        xp_assert_close(whiten(obs), desired, rtol=1e-5)
+
+    def test_whiten_zero_std(self, xp):
+        desired = xp.asarray([[0., 1.0, 2.86666544],
+                              [0., 1.0, 1.32460034],
+                              [0., 1.0, 3.74382172]])
+
+        obs = xp.asarray([[0., 1., 0.74109533],
+                          [0., 1., 0.34243798],
+                          [0., 1., 0.96785929]])
+
+        with eager_warns(RuntimeWarning, match="Some columns have standard...", xp=xp):
+            actual = whiten(obs)
+        xp_assert_close(actual, desired, rtol=1e-5)
+
+    @pytest.mark.filterwarnings("ignore:invalid value encountered:RuntimeWarning:dask")
+    @pytest.mark.parametrize("bad_value", [math.nan, math.inf, -math.inf])
+    def test_whiten_not_finite(self, bad_value, xp):
+        obs = xp.asarray([[0.98744510, bad_value],
+                          [0.62093317, 0.19406729],
+                          [0.87545741, 0.00735733],
+                          [0.85124403, 0.26499712],
+                          [0.45067590, 0.45464607]])
+
+        if is_lazy_array(obs):
+            desired = xp.asarray([[5.08738849, math.nan],
+                                  [3.19909255, math.nan],
+                                  [4.51041982, math.nan],
+                                  [4.38567074, math.nan],
+                                  [2.32191480, math.nan]])
+            xp_assert_close(whiten(obs), desired, rtol=1e-5)
+        else:
+            assert_raises(ValueError, whiten, obs)
+
+    @pytest.mark.skipif(SCIPY_ARRAY_API,
+                        reason='`np.matrix` unsupported in array API mode')
+    def test_whiten_not_finite_matrix(self):
+        for bad_value in np.nan, np.inf, -np.inf:
+            obs = matrix([[0.98744510, bad_value],
+                          [0.62093317, 0.19406729],
+                          [0.87545741, 0.00735733],
+                          [0.85124403, 0.26499712],
+                          [0.45067590, 0.45464607]])
+            assert_raises(ValueError, whiten, obs)
+
+
+@make_xp_test_case(vq)
+class TestVq:
+
+    def test_py_vq(self, xp):
+        initc = np.concatenate([[X[0]], [X[1]], [X[2]]])
+        # label1.dtype varies between int32 and int64 over platforms
+        label1 = py_vq(xp.asarray(X), xp.asarray(initc))[0]
+        xp_assert_equal(label1, xp.asarray(LABEL1, dtype=xp.int64),
+                        check_dtype=False)
+
+    @pytest.mark.skipif(SCIPY_ARRAY_API,
+                        reason='`np.matrix` unsupported in array API mode')
+    def test_py_vq_matrix(self):
+        initc = np.concatenate([[X[0]], [X[1]], [X[2]]])
+        # label1.dtype varies between int32 and int64 over platforms
+        label1 = py_vq(matrix(X), matrix(initc))[0]
+        assert_array_equal(label1, LABEL1)
+
+    def test_vq(self, xp):
+        initc = np.concatenate([[X[0]], [X[1]], [X[2]]])
+        label1, _ = _vq.vq(X, initc)
+        assert_array_equal(label1, LABEL1)
+        _, _ = vq(xp.asarray(X), xp.asarray(initc))
+
+    @pytest.mark.skipif(SCIPY_ARRAY_API,
+                        reason='`np.matrix` unsupported in array API mode')
+    def test_vq_matrix(self):
+        initc = np.concatenate([[X[0]], [X[1]], [X[2]]])
+        label1, _ = _vq.vq(matrix(X), matrix(initc))
+        assert_array_equal(label1, LABEL1)
+        _, _ = vq(matrix(X), matrix(initc))
+
+    def test_vq_1d(self, xp):
+        # Test special rank 1 vq algo, python implementation.
+        data = X[:, 0]
+        initc = data[:3]
+        a, b = _vq.vq(data, initc)
+        data = xp.asarray(data)
+        initc = xp.asarray(initc)
+        ta, tb = py_vq(data[:, np.newaxis], initc[:, np.newaxis])
+        # ta.dtype varies between int32 and int64 over platforms
+        xp_assert_equal(ta, xp.asarray(a, dtype=xp.int64), check_dtype=False)
+        xp_assert_equal(tb, xp.asarray(b))
+
+    def test__vq_sametype(self):
+        a = np.asarray([1.0, 2.0])
+        b = a.astype(np.float32)
+        assert_raises(TypeError, _vq.vq, a, b)
+
+    def test__vq_invalid_type(self):
+        a = np.asarray([1, 2], dtype=int)
+        assert_raises(TypeError, _vq.vq, a, a)
+
+    def test_vq_large_nfeat(self, xp):
+        X = np.random.rand(20, 20)
+        code_book = np.random.rand(3, 20)
+
+        codes0, dis0 = _vq.vq(X, code_book)
+        codes1, dis1 = py_vq(
+            xp.asarray(X), xp.asarray(code_book)
+        )
+        xp_assert_close(dis1, xp.asarray(dis0), rtol=1e-5)
+        # codes1.dtype varies between int32 and int64 over platforms
+        xp_assert_equal(codes1, xp.asarray(codes0, dtype=xp.int64), check_dtype=False)
+
+        X = X.astype(np.float32)
+        code_book = code_book.astype(np.float32)
+
+        codes0, dis0 = _vq.vq(X, code_book)
+        codes1, dis1 = py_vq(
+            xp.asarray(X), xp.asarray(code_book)
+        )
+        xp_assert_close(dis1, xp.asarray(dis0, dtype=xp.float64), rtol=1e-5)
+        # codes1.dtype varies between int32 and int64 over platforms
+        xp_assert_equal(codes1, xp.asarray(codes0, dtype=xp.int64), check_dtype=False)
+
+    def test_vq_large_features(self, xp):
+        X = np.random.rand(10, 5) * 1000000
+        code_book = np.random.rand(2, 5) * 1000000
+
+        codes0, dis0 = _vq.vq(X, code_book)
+        codes1, dis1 = py_vq(
+            xp.asarray(X), xp.asarray(code_book)
+        )
+        xp_assert_close(dis1, xp.asarray(dis0), rtol=1e-5)
+        # codes1.dtype varies between int32 and int64 over platforms
+        xp_assert_equal(codes1, xp.asarray(codes0, dtype=xp.int64), check_dtype=False)
+
+
+# Whole class skipped on GPU for now;
+# once pdist/cdist are hooked up for CuPy, more tests will work
+@make_xp_test_case(kmeans, kmeans2)
+class TestKMeans:
+
+    def test_large_features(self, xp):
+        # Generate a data set with large values, and run kmeans on it to
+        # (regression for 1077).
+        d = 300
+        n = 100
+
+        m1 = np.random.randn(d)
+        m2 = np.random.randn(d)
+        x = 10000 * np.random.randn(n, d) - 20000 * m1
+        y = 10000 * np.random.randn(n, d) + 20000 * m2
+
+        data = np.empty((x.shape[0] + y.shape[0], d), np.float64)
+        data[:x.shape[0]] = x
+        data[x.shape[0]:] = y
+
+        # use `seed` to ensure backwards compatibility after SPEC7
+        kmeans(xp.asarray(data), 2, seed=1)
+
+    def test_kmeans_simple(self, xp):
+        rng = np.random.default_rng(54321)
+        initc = np.concatenate([[X[0]], [X[1]], [X[2]]])
+        code1 = kmeans(xp.asarray(X), xp.asarray(initc), iter=1, rng=rng)[0]
+        xp_assert_close(code1, xp.asarray(CODET2))
+
+    @pytest.mark.skipif(SCIPY_ARRAY_API,
+                        reason='`np.matrix` unsupported in array API mode')
+    def test_kmeans_simple_matrix(self):
+        rng = np.random.default_rng(54321)
+        initc = np.concatenate([[X[0]], [X[1]], [X[2]]])
+        code1 = kmeans(matrix(X), matrix(initc), iter=1, rng=rng)[0]
+        xp_assert_close(code1, CODET2)
+
+    def test_kmeans_lost_cluster(self, xp):
+        # This will cause kmeans to have a cluster with no points.
+        data = xp.asarray(TESTDATA_2D)
+        initk = xp.asarray([[-1.8127404, -0.67128041],
+                            [2.04621601, 0.07401111],
+                            [-2.31149087, -0.05160469]])
+
+        kmeans(data, initk)
+        with warnings.catch_warnings():
+            warnings.filterwarnings(
+                "ignore",
+                ("One of the clusters is empty. Re-run kmeans with a different "
+                 "initialization"),
+                UserWarning,
+            )
+            kmeans2(data, initk, missing='warn')
+
+        assert_raises(ClusterError, kmeans2, data, initk, missing='raise')
+
+    def test_kmeans2_simple(self, xp):
+        rng = np.random.default_rng(12345678)
+        initc = xp.asarray(np.concatenate([[X[0]], [X[1]], [X[2]]]))
+        arrays = [xp.asarray] if SCIPY_ARRAY_API else [np.asarray, matrix]
+        for tp in arrays:
+            code1 = kmeans2(tp(X), tp(initc), iter=1, rng=rng)[0]
+            code2 = kmeans2(tp(X), tp(initc), iter=2, rng=rng)[0]
+
+            xp_assert_close(code1, xp.asarray(CODET1))
+            xp_assert_close(code2, xp.asarray(CODET2))
+
+    @pytest.mark.skipif(SCIPY_ARRAY_API,
+                        reason='`np.matrix` unsupported in array API mode')
+    def test_kmeans2_simple_matrix(self):
+        rng = np.random.default_rng(12345678)
+        initc = np.concatenate([[X[0]], [X[1]], [X[2]]])
+        code1 = kmeans2(matrix(X), matrix(initc), iter=1, rng=rng)[0]
+        code2 = kmeans2(matrix(X), matrix(initc), iter=2, rng=rng)[0]
+
+        xp_assert_close(code1, CODET1)
+        xp_assert_close(code2, CODET2)
+
+    def test_kmeans2_rank1(self, xp):
+        data = xp.asarray(TESTDATA_2D)
+        data1 = data[:, 0]
+
+        initc = data1[:3]
+        code = xp_copy(initc, xp=xp)
+
+        # use `seed` to ensure backwards compatibility after SPEC7
+        kmeans2(data1, code, iter=1, seed=1)[0]
+        kmeans2(data1, code, iter=2)[0]
+
+    def test_kmeans2_rank1_2(self, xp):
+        data = xp.asarray(TESTDATA_2D)
+        data1 = data[:, 0]
+        kmeans2(data1, 2, iter=1)
+
+    def test_kmeans2_high_dim(self, xp):
+        # test kmeans2 when the number of dimensions exceeds the number
+        # of input points
+        data = xp.asarray(TESTDATA_2D)
+        data = xp.reshape(data, (20, 20))[:10, :]
+        kmeans2(data, 2)
+
+    def test_kmeans2_init(self, xp):
+        rng = np.random.default_rng(12345678)
+        data = xp.asarray(TESTDATA_2D)
+        k = 3
+
+        kmeans2(data, k, minit='points', rng=rng)
+        kmeans2(data[:, 1], k, minit='points', rng=rng)  # special case (1-D)
+
+        kmeans2(data, k, minit='++', rng=rng)
+        kmeans2(data[:, 1], k, minit='++', rng=rng)  # special case (1-D)
+
+        # minit='random' can give warnings, filter those
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "One of the clusters is empty. Re-run.")
+            kmeans2(data, k, minit='random', rng=rng)
+            kmeans2(data[:, 1], k, minit='random', rng=rng)  # special case (1-D)
+
+    @pytest.fixture
+    def krand_lock(self):
+        return Lock()
+
+    @xfail_xp_backends('dask.array', reason="Wrong answer")
+    @pytest.mark.skipif(sys.platform == 'win32',
+                        reason='Fails with MemoryError in Wine.')
+    def test_krandinit(self, xp, krand_lock):
+        data = xp.asarray(TESTDATA_2D)
+        datas = [xp.reshape(data, (200, 2)),
+                 xp.reshape(data, (20, 20))[:10, :]]
+        k = int(1e6)
+        with krand_lock:
+            for data in datas:
+                rng = np.random.default_rng(1234)
+                init = _krandinit(data, k, rng, xp)
+                orig_cov = xpx.cov(data.T, xp=xp)
+                init_cov = xpx.cov(init.T, xp=xp)
+                xp_assert_close(orig_cov, init_cov, atol=1.1e-2)
+
+    def test_kmeans2_empty(self, xp):
+        # Regression test for gh-1032.
+        assert_raises(ValueError, kmeans2, xp.asarray([]), 2)
+
+    def test_kmeans_0k(self, xp):
+        # Regression test for gh-1073: fail when k arg is 0.
+        assert_raises(ValueError, kmeans, xp.asarray(X), 0)
+        assert_raises(ValueError, kmeans2, xp.asarray(X), 0)
+        assert_raises(ValueError, kmeans2, xp.asarray(X), xp.asarray([]))
+
+    def test_kmeans_large_thres(self, xp):
+        # Regression test for gh-1774
+        x = xp.asarray([1, 2, 3, 4, 10], dtype=xp.float64)
+        res = kmeans(x, 1, thresh=1e16)
+        xp_assert_close(res[0], xp.asarray([4.], dtype=xp.float64))
+        xp_assert_close(res[1], xp.asarray(2.3999999999999999, dtype=xp.float64)[()])
+
+    def test_kmeans2_kpp_low_dim(self, xp):
+        # Regression test for gh-11462
+        rng = np.random.default_rng(2358792345678234568)
+        prev_res = xp.asarray([[-1.95266667, 0.898],
+                               [-3.153375, 3.3945]], dtype=xp.float64)
+        res, _ = kmeans2(xp.asarray(TESTDATA_2D), 2, minit='++', rng=rng)
+        xp_assert_close(res, prev_res)
+
+    def test_kmeans2_kpp_high_dim(self, xp):
+        # Regression test for gh-11462
+        rng = np.random.default_rng(23587923456834568)
+        n_dim = 100
+        size = 10
+        centers = np.vstack([5 * np.ones(n_dim),
+                             -5 * np.ones(n_dim)])
+
+        data = np.vstack([
+            rng.multivariate_normal(centers[0], np.eye(n_dim), size=size),
+            rng.multivariate_normal(centers[1], np.eye(n_dim), size=size)
+        ])
+
+        data = xp.asarray(data)
+        res, _ = kmeans2(data, 2, minit='++', rng=rng)
+        xp_assert_equal(xp.sign(res), xp.sign(xp.asarray(centers)))
+
+    def test_kmeans_diff_convergence(self, xp):
+        # Regression test for gh-8727
+        obs = xp.asarray([-3, -1, 0, 1, 1, 8], dtype=xp.float64)
+        res = kmeans(obs, xp.asarray([-3., 0.99]))
+        xp_assert_close(res[0], xp.asarray([-0.4,  8.], dtype=xp.float64))
+        xp_assert_close(res[1], xp.asarray(1.0666666666666667, dtype=xp.float64)[()])
+
+    def test_kmeans_and_kmeans2_random_seed(self, xp):
+
+        seed_list = [
+            1234, np.random.RandomState(1234), np.random.default_rng(1234)
+        ]
+
+        for seed in seed_list:
+            seed1 = deepcopy(seed)
+            seed2 = deepcopy(seed)
+            data = xp.asarray(TESTDATA_2D)
+            # test for kmeans
+            res1, _ = kmeans(data, 2, seed=seed1)
+            res2, _ = kmeans(data, 2, seed=seed2)
+            xp_assert_close(res1, res2)  # should be same results
+            # test for kmeans2
+            for minit in ["random", "points", "++"]:
+                res1, _ = kmeans2(data, 2, minit=minit, seed=seed1)
+                res2, _ = kmeans2(data, 2, minit=minit, seed=seed2)
+                xp_assert_close(res1, res2)  # should be same results
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/vq.py b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/vq.py
new file mode 100644
index 0000000000000000000000000000000000000000..65debbbde3ab3913be052cf56e3ffbae98dbe378
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/cluster/vq.py
@@ -0,0 +1,832 @@
+"""
+K-means clustering and vector quantization (:mod:`scipy.cluster.vq`)
+====================================================================
+
+Provides routines for k-means clustering, generating code books
+from k-means models and quantizing vectors by comparing them with
+centroids in a code book.
+
+.. autosummary::
+   :toctree: generated/
+
+   whiten -- Normalize a group of observations so each feature has unit variance
+   vq -- Calculate code book membership of a set of observation vectors
+   kmeans -- Perform k-means on a set of observation vectors forming k clusters
+   kmeans2 -- A different implementation of k-means with more methods
+           -- for initializing centroids
+
+Background information
+----------------------
+The k-means algorithm takes as input the number of clusters to
+generate, k, and a set of observation vectors to cluster. It
+returns a set of centroids, one for each of the k clusters. An
+observation vector is classified with the cluster number or
+centroid index of the centroid closest to it.
+
+A vector v belongs to cluster i if it is closer to centroid i than
+any other centroid. If v belongs to i, we say centroid i is the
+dominating centroid of v. The k-means algorithm tries to
+minimize distortion, which is defined as the sum of the squared distances
+between each observation vector and its dominating centroid.
+The minimization is achieved by iteratively reclassifying
+the observations into clusters and recalculating the centroids until
+a configuration is reached in which the centroids are stable. One can
+also define a maximum number of iterations.
+
+Since vector quantization is a natural application for k-means,
+information theory terminology is often used. The centroid index
+or cluster index is also referred to as a "code" and the table
+mapping codes to centroids and, vice versa, is often referred to as a
+"code book". The result of k-means, a set of centroids, can be
+used to quantize vectors. Quantization aims to find an encoding of
+vectors that reduces the expected distortion.
+
+All routines expect obs to be an M by N array, where the rows are
+the observation vectors. The codebook is a k by N array, where the
+ith row is the centroid of code word i. The observation vectors
+and centroids have the same feature dimension.
+
+As an example, suppose we wish to compress a 24-bit color image
+(each pixel is represented by one byte for red, one for blue, and
+one for green) before sending it over the web. By using a smaller
+8-bit encoding, we can reduce the amount of data by two
+thirds. Ideally, the colors for each of the 256 possible 8-bit
+encoding values should be chosen to minimize distortion of the
+color. Running k-means with k=256 generates a code book of 256
+codes, which fills up all possible 8-bit sequences. Instead of
+sending a 3-byte value for each pixel, the 8-bit centroid index
+(or code word) of the dominating centroid is transmitted. The code
+book is also sent over the wire so each 8-bit code can be
+translated back to a 24-bit pixel value representation. If the
+image of interest was of an ocean, we would expect many 24-bit
+blues to be represented by 8-bit codes. If it was an image of a
+human face, more flesh-tone colors would be represented in the
+code book.
+
+"""
+import warnings
+import numpy as np
+from collections import deque
+from scipy._lib._array_api import (_asarray, array_namespace, is_lazy_array,
+                                   xp_capabilities, xp_copy, xp_size)
+from scipy._lib._util import (check_random_state, rng_integers,
+                              _transition_to_rng)
+from scipy._lib import array_api_extra as xpx
+from scipy.spatial.distance import cdist
+
+from . import _vq
+
+__docformat__ = 'restructuredtext'
+
+__all__ = ['whiten', 'vq', 'kmeans', 'kmeans2']
+
+
+class ClusterError(Exception):
+    pass
+
+
+@xp_capabilities()
+def whiten(obs, check_finite=None):
+    """
+    Normalize a group of observations on a per feature basis.
+
+    Before running k-means, it is beneficial to rescale each feature
+    dimension of the observation set by its standard deviation (i.e. "whiten"
+    it - as in "white noise" where each frequency has equal power).
+    Each feature is divided by its standard deviation across all observations
+    to give it unit variance.
+
+    Parameters
+    ----------
+    obs : ndarray
+        Each row of the array is an observation.  The
+        columns are the features seen during each observation::
+
+            #        f0  f1  f2
+            obs = [[ 1., 1., 1.],  #o0
+                   [ 2., 2., 2.],  #o1
+                   [ 3., 3., 3.],  #o2
+                   [ 4., 4., 4.]]  #o3
+
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True for eager backends and False for lazy ones.
+
+    Returns
+    -------
+    result : ndarray
+        Contains the values in `obs` scaled by the standard deviation
+        of each column.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster.vq import whiten
+    >>> features  = np.array([[1.9, 2.3, 1.7],
+    ...                       [1.5, 2.5, 2.2],
+    ...                       [0.8, 0.6, 1.7,]])
+    >>> whiten(features)
+    array([[ 4.17944278,  2.69811351,  7.21248917],
+           [ 3.29956009,  2.93273208,  9.33380951],
+           [ 1.75976538,  0.7038557 ,  7.21248917]])
+
+    """
+    xp = array_namespace(obs)
+    if check_finite is None:
+        check_finite = not is_lazy_array(obs)
+    obs = _asarray(obs, check_finite=check_finite, xp=xp)
+    std_dev = xp.std(obs, axis=0)
+    zero_std_mask = std_dev == 0
+    std_dev = xpx.at(std_dev, zero_std_mask).set(1.0)
+    if check_finite and xp.any(zero_std_mask):
+        warnings.warn("Some columns have standard deviation zero. "
+                      "The values of these columns will not change.",
+                      RuntimeWarning, stacklevel=2)
+    return obs / std_dev
+
+
+@xp_capabilities(cpu_only=True, reason="uses spatial.distance.cdist",
+                 jax_jit=False, allow_dask_compute=True)
+def vq(obs, code_book, check_finite=True):
+    """
+    Assign codes from a code book to observations.
+
+    Assigns a code from a code book to each observation. Each
+    observation vector in the 'M' by 'N' `obs` array is compared with the
+    centroids in the code book and assigned the code of the closest
+    centroid.
+
+    The features in `obs` should have unit variance, which can be
+    achieved by passing them through the whiten function. The code
+    book can be created with the k-means algorithm or a different
+    encoding algorithm.
+
+    Parameters
+    ----------
+    obs : ndarray
+        Each row of the 'M' x 'N' array is an observation. The columns are
+        the "features" seen during each observation. The features must be
+        whitened first using the whiten function or something equivalent.
+    code_book : ndarray
+        The code book is usually generated using the k-means algorithm.
+        Each row of the array holds a different code, and the columns are
+        the features of the code::
+
+            #              f0  f1  f2  f3
+            code_book = [[ 1., 2., 3., 4.],  #c0
+                         [ 1., 2., 3., 4.],  #c1
+                         [ 1., 2., 3., 4.]]  #c2
+
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+
+    Returns
+    -------
+    code : ndarray
+        A length M array holding the code book index for each observation.
+    dist : ndarray
+        The distortion (distance) between the observation and its nearest
+        code.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster.vq import vq
+    >>> code_book = np.array([[1., 1., 1.],
+    ...                       [2., 2., 2.]])
+    >>> features  = np.array([[1.9, 2.3, 1.7],
+    ...                       [1.5, 2.5, 2.2],
+    ...                       [0.8, 0.6, 1.7]])
+    >>> vq(features, code_book)
+    (array([1, 1, 0], dtype=int32), array([0.43588989, 0.73484692, 0.83066239]))
+
+    """
+    xp = array_namespace(obs, code_book)
+    obs = _asarray(obs, xp=xp, check_finite=check_finite)
+    code_book = _asarray(code_book, xp=xp, check_finite=check_finite)
+    ct = xp.result_type(obs, code_book)
+
+    if xp.isdtype(ct, kind='real floating'):
+        c_obs = xp.astype(obs, ct, copy=False)
+        c_code_book = xp.astype(code_book, ct, copy=False)
+        c_obs = np.asarray(c_obs)
+        c_code_book = np.asarray(c_code_book)
+        result = _vq.vq(c_obs, c_code_book)
+        return xp.asarray(result[0]), xp.asarray(result[1])
+    return py_vq(obs, code_book, check_finite=False)
+
+
+def py_vq(obs, code_book, check_finite=True):
+    """ Python version of vq algorithm.
+
+    The algorithm computes the Euclidean distance between each
+    observation and every frame in the code_book.
+
+    Parameters
+    ----------
+    obs : ndarray
+        Expects a rank 2 array. Each row is one observation.
+    code_book : ndarray
+        Code book to use. Same format than obs. Should have same number of
+        features (e.g., columns) than obs.
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+
+    Returns
+    -------
+    code : ndarray
+        code[i] gives the label of the ith obversation; its code is
+        code_book[code[i]].
+    mind_dist : ndarray
+        min_dist[i] gives the distance between the ith observation and its
+        corresponding code.
+
+    Notes
+    -----
+    This function is slower than the C version but works for
+    all input types. If the inputs have the wrong types for the
+    C versions of the function, this one is called as a last resort.
+
+    It is about 20 times slower than the C version.
+
+    """
+    xp = array_namespace(obs, code_book)
+    obs = _asarray(obs, xp=xp, check_finite=check_finite)
+    code_book = _asarray(code_book, xp=xp, check_finite=check_finite)
+
+    if obs.ndim != code_book.ndim:
+        raise ValueError("Observation and code_book should have the same rank")
+
+    if obs.ndim == 1:
+        obs = obs[:, xp.newaxis]
+        code_book = code_book[:, xp.newaxis]
+
+    # Once `cdist` has array API support, this `xp.asarray` call can be removed
+    dist = xp.asarray(cdist(obs, code_book))
+    code = xp.argmin(dist, axis=1)
+    min_dist = xp.min(dist, axis=1)
+    return code, min_dist
+
+
+def _kmeans(obs, guess, thresh=1e-5, xp=None):
+    """ "raw" version of k-means.
+
+    Returns
+    -------
+    code_book
+        The lowest distortion codebook found.
+    avg_dist
+        The average distance a observation is from a code in the book.
+        Lower means the code_book matches the data better.
+
+    See Also
+    --------
+    kmeans : wrapper around k-means
+
+    Examples
+    --------
+    Note: not whitened in this example.
+
+    >>> import numpy as np
+    >>> from scipy.cluster.vq import _kmeans
+    >>> features  = np.array([[ 1.9,2.3],
+    ...                       [ 1.5,2.5],
+    ...                       [ 0.8,0.6],
+    ...                       [ 0.4,1.8],
+    ...                       [ 1.0,1.0]])
+    >>> book = np.array((features[0],features[2]))
+    >>> _kmeans(features,book)
+    (array([[ 1.7       ,  2.4       ],
+           [ 0.73333333,  1.13333333]]), 0.40563916697728591)
+
+    """
+    xp = np if xp is None else xp
+    code_book = guess
+    diff = xp.inf
+    prev_avg_dists = deque([diff], maxlen=2)
+
+    np_obs = np.asarray(obs)
+    while diff > thresh:
+        # compute membership and distances between obs and code_book
+        obs_code, distort = vq(obs, code_book, check_finite=False)
+        prev_avg_dists.append(xp.mean(distort, axis=-1))
+        # recalc code_book as centroids of associated obs
+        obs_code = np.asarray(obs_code)
+        code_book, has_members = _vq.update_cluster_means(np_obs, obs_code,
+                                                          code_book.shape[0])
+        code_book = code_book[has_members]
+        code_book = xp.asarray(code_book)
+        diff = xp.abs(prev_avg_dists[0] - prev_avg_dists[1])
+
+    return code_book, prev_avg_dists[1]
+
+
+@xp_capabilities(cpu_only=True, jax_jit=False, allow_dask_compute=True)
+@_transition_to_rng("seed")
+def kmeans(obs, k_or_guess, iter=20, thresh=1e-5, check_finite=True,
+           *, rng=None):
+    """
+    Performs k-means on a set of observation vectors forming k clusters.
+
+    The k-means algorithm adjusts the classification of the observations
+    into clusters and updates the cluster centroids until the position of
+    the centroids is stable over successive iterations. In this
+    implementation of the algorithm, the stability of the centroids is
+    determined by comparing the absolute value of the change in the average
+    Euclidean distance between the observations and their corresponding
+    centroids against a threshold. This yields
+    a code book mapping centroids to codes and vice versa.
+
+    Parameters
+    ----------
+    obs : ndarray
+       Each row of the M by N array is an observation vector. The
+       columns are the features seen during each observation.
+       The features must be whitened first with the `whiten` function.
+
+    k_or_guess : int or ndarray
+       The number of centroids to generate. A code is assigned to
+       each centroid, which is also the row index of the centroid
+       in the code_book matrix generated.
+
+       The initial k centroids are chosen by randomly selecting
+       observations from the observation matrix. Alternatively,
+       passing a k by N array specifies the initial k centroids.
+
+    iter : int, optional
+       The number of times to run k-means, returning the codebook
+       with the lowest distortion. This argument is ignored if
+       initial centroids are specified with an array for the
+       ``k_or_guess`` parameter. This parameter does not represent the
+       number of iterations of the k-means algorithm.
+
+    thresh : float, optional
+       Terminates the k-means algorithm if the change in
+       distortion since the last k-means iteration is less than
+       or equal to threshold.
+
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    codebook : ndarray
+       A k by N array of k centroids. The ith centroid
+       codebook[i] is represented with the code i. The centroids
+       and codes generated represent the lowest distortion seen,
+       not necessarily the globally minimal distortion.
+       Note that the number of centroids is not necessarily the same as the
+       ``k_or_guess`` parameter, because centroids assigned to no observations
+       are removed during iterations.
+
+    distortion : float
+       The mean (non-squared) Euclidean distance between the observations
+       passed and the centroids generated. Note the difference to the standard
+       definition of distortion in the context of the k-means algorithm, which
+       is the sum of the squared distances.
+
+    See Also
+    --------
+    kmeans2 : a different implementation of k-means clustering
+       with more methods for generating initial centroids but without
+       using a distortion change threshold as a stopping criterion.
+
+    whiten : must be called prior to passing an observation matrix
+       to kmeans.
+
+    Notes
+    -----
+    For more functionalities or optimal performance, you can use
+    `sklearn.cluster.KMeans `_.
+    `This `_
+    is a benchmark result of several implementations.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.cluster.vq import vq, kmeans, whiten
+    >>> import matplotlib.pyplot as plt
+    >>> features  = np.array([[ 1.9,2.3],
+    ...                       [ 1.5,2.5],
+    ...                       [ 0.8,0.6],
+    ...                       [ 0.4,1.8],
+    ...                       [ 0.1,0.1],
+    ...                       [ 0.2,1.8],
+    ...                       [ 2.0,0.5],
+    ...                       [ 0.3,1.5],
+    ...                       [ 1.0,1.0]])
+    >>> whitened = whiten(features)
+    >>> book = np.array((whitened[0],whitened[2]))
+    >>> kmeans(whitened,book)
+    (array([[ 2.3110306 ,  2.86287398],    # random
+           [ 0.93218041,  1.24398691]]), 0.85684700941625547)
+
+    >>> codes = 3
+    >>> kmeans(whitened,codes)
+    (array([[ 2.3110306 ,  2.86287398],    # random
+           [ 1.32544402,  0.65607529],
+           [ 0.40782893,  2.02786907]]), 0.5196582527686241)
+
+    >>> # Create 50 datapoints in two clusters a and b
+    >>> pts = 50
+    >>> rng = np.random.default_rng()
+    >>> a = rng.multivariate_normal([0, 0], [[4, 1], [1, 4]], size=pts)
+    >>> b = rng.multivariate_normal([30, 10],
+    ...                             [[10, 2], [2, 1]],
+    ...                             size=pts)
+    >>> features = np.concatenate((a, b))
+    >>> # Whiten data
+    >>> whitened = whiten(features)
+    >>> # Find 2 clusters in the data
+    >>> codebook, distortion = kmeans(whitened, 2)
+    >>> # Plot whitened data and cluster centers in red
+    >>> plt.scatter(whitened[:, 0], whitened[:, 1])
+    >>> plt.scatter(codebook[:, 0], codebook[:, 1], c='r')
+    >>> plt.show()
+
+    """
+    if isinstance(k_or_guess, int):
+        xp = array_namespace(obs)
+    else:
+        xp = array_namespace(obs, k_or_guess)
+    obs = _asarray(obs, xp=xp, check_finite=check_finite)
+    guess = _asarray(k_or_guess, xp=xp, check_finite=check_finite)
+    if iter < 1:
+        raise ValueError(f"iter must be at least 1, got {iter}")
+
+    # Determine whether a count (scalar) or an initial guess (array) was passed.
+    if xp_size(guess) != 1:
+        if xp_size(guess) < 1:
+            raise ValueError(f"Asked for 0 clusters. Initial book was {guess}")
+        return _kmeans(obs, guess, thresh=thresh, xp=xp)
+
+    # k_or_guess is a scalar, now verify that it's an integer
+    k = int(guess)
+    if k != guess:
+        raise ValueError("If k_or_guess is a scalar, it must be an integer.")
+    if k < 1:
+        raise ValueError(f"Asked for {k} clusters.")
+
+    rng = check_random_state(rng)
+
+    # initialize best distance value to a large value
+    best_dist = xp.inf
+    for i in range(iter):
+        # the initial code book is randomly selected from observations
+        guess = _kpoints(obs, k, rng, xp)
+        book, dist = _kmeans(obs, guess, thresh=thresh, xp=xp)
+        if dist < best_dist:
+            best_book = book
+            best_dist = dist
+    return best_book, best_dist
+
+
+def _kpoints(data, k, rng, xp):
+    """Pick k points at random in data (one row = one observation).
+
+    Parameters
+    ----------
+    data : ndarray
+        Expect a rank 1 or 2 array. Rank 1 are assumed to describe one
+        dimensional data, rank 2 multidimensional data, in which case one
+        row is one observation.
+    k : int
+        Number of samples to generate.
+    rng : `numpy.random.Generator` or `numpy.random.RandomState`
+        Random number generator.
+
+    Returns
+    -------
+    x : ndarray
+        A 'k' by 'N' containing the initial centroids
+
+    """
+    idx = rng.choice(data.shape[0], size=int(k), replace=False)
+    # convert to array with default integer dtype (avoids numpy#25607)
+    idx = xp.asarray(idx, dtype=xp.asarray([1]).dtype)
+    return xp.take(data, idx, axis=0)
+
+
+def _krandinit(data, k, rng, xp):
+    """Returns k samples of a random variable whose parameters depend on data.
+
+    More precisely, it returns k observations sampled from a Gaussian random
+    variable whose mean and covariances are the ones estimated from the data.
+
+    Parameters
+    ----------
+    data : ndarray
+        Expect a rank 1 or 2 array. Rank 1 is assumed to describe 1-D
+        data, rank 2 multidimensional data, in which case one
+        row is one observation.
+    k : int
+        Number of samples to generate.
+    rng : `numpy.random.Generator` or `numpy.random.RandomState`
+        Random number generator.
+
+    Returns
+    -------
+    x : ndarray
+        A 'k' by 'N' containing the initial centroids
+
+    """
+    mu = xp.mean(data, axis=0)
+    k = np.asarray(k)
+
+    if data.ndim == 1:
+        _cov = xpx.cov(data, xp=xp)
+        x = rng.standard_normal(size=k)
+        x = xp.asarray(x)
+        x *= xp.sqrt(_cov)
+    elif data.shape[1] > data.shape[0]:
+        # initialize when the covariance matrix is rank deficient
+        _, s, vh = xp.linalg.svd(data - mu, full_matrices=False)
+        x = rng.standard_normal(size=(k, xp_size(s)))
+        x = xp.asarray(x)
+        sVh = s[:, None] * vh / xp.sqrt(data.shape[0] - xp.asarray(1.))
+        x = x @ sVh
+    else:
+        _cov = xpx.atleast_nd(xpx.cov(data.T, xp=xp), ndim=2, xp=xp)
+
+        # k rows, d cols (one row = one obs)
+        # Generate k sample of a random variable ~ Gaussian(mu, cov)
+        x = rng.standard_normal(size=(k, xp_size(mu)))
+        x = xp.asarray(x)
+        x = x @ xp.linalg.cholesky(_cov).T
+
+    x += mu
+    return x
+
+
+def _kpp(data, k, rng, xp):
+    """ Picks k points in the data based on the kmeans++ method.
+
+    Parameters
+    ----------
+    data : ndarray
+        Expect a rank 1 or 2 array. Rank 1 is assumed to describe 1-D
+        data, rank 2 multidimensional data, in which case one
+        row is one observation.
+    k : int
+        Number of samples to generate.
+    rng : `numpy.random.Generator` or `numpy.random.RandomState`
+        Random number generator.
+
+    Returns
+    -------
+    init : ndarray
+        A 'k' by 'N' containing the initial centroids.
+
+    References
+    ----------
+    .. [1] D. Arthur and S. Vassilvitskii, "k-means++: the advantages of
+       careful seeding", Proceedings of the Eighteenth Annual ACM-SIAM Symposium
+       on Discrete Algorithms, 2007.
+    """
+
+    ndim = len(data.shape)
+    if ndim == 1:
+        data = data[:, None]
+
+    dims = data.shape[1]
+
+    init = xp.empty((int(k), dims))
+
+    for i in range(k):
+        if i == 0:
+            data_idx = rng_integers(rng, data.shape[0])
+        else:
+            D2 = cdist(init[:i,:], data, metric='sqeuclidean').min(axis=0)
+            probs = D2/D2.sum()
+            cumprobs = probs.cumsum()
+            r = rng.uniform()
+            cumprobs = np.asarray(cumprobs)
+            data_idx = int(np.searchsorted(cumprobs, r))
+
+        init = xpx.at(init)[i, :].set(data[data_idx, :])
+
+    if ndim == 1:
+        init = init[:, 0]
+    return init
+
+
+_valid_init_meth = {'random': _krandinit, 'points': _kpoints, '++': _kpp}
+
+
+def _missing_warn():
+    """Print a warning when called."""
+    warnings.warn("One of the clusters is empty. "
+                  "Re-run kmeans with a different initialization.",
+                  stacklevel=3)
+
+
+def _missing_raise():
+    """Raise a ClusterError when called."""
+    raise ClusterError("One of the clusters is empty. "
+                       "Re-run kmeans with a different initialization.")
+
+
+_valid_miss_meth = {'warn': _missing_warn, 'raise': _missing_raise}
+
+
+@xp_capabilities(cpu_only=True, jax_jit=False, allow_dask_compute=True)
+@_transition_to_rng("seed")
+def kmeans2(data, k, iter=10, thresh=1e-5, minit='random',
+            missing='warn', check_finite=True, *, rng=None):
+    """
+    Classify a set of observations into k clusters using the k-means algorithm.
+
+    The algorithm attempts to minimize the Euclidean distance between
+    observations and centroids. Several initialization methods are
+    included.
+
+    Parameters
+    ----------
+    data : ndarray
+        A 'M' by 'N' array of 'M' observations in 'N' dimensions or a length
+        'M' array of 'M' 1-D observations.
+    k : int or ndarray
+        The number of clusters to form as well as the number of
+        centroids to generate. If `minit` initialization string is
+        'matrix', or if a ndarray is given instead, it is
+        interpreted as initial cluster to use instead.
+    iter : int, optional
+        Number of iterations of the k-means algorithm to run. Note
+        that this differs in meaning from the iters parameter to
+        the kmeans function.
+    thresh : float, optional
+        (not used yet)
+    minit : str, optional
+        Method for initialization. Available methods are 'random',
+        'points', '++' and 'matrix':
+
+        'random': generate k centroids from a Gaussian with mean and
+        variance estimated from the data.
+
+        'points': choose k observations (rows) at random from data for
+        the initial centroids.
+
+        '++': choose k observations accordingly to the kmeans++ method
+        (careful seeding)
+
+        'matrix': interpret the k parameter as a k by M (or length k
+        array for 1-D data) array of initial centroids.
+    missing : str, optional
+        Method to deal with empty clusters. Available methods are
+        'warn' and 'raise':
+
+        'warn': give a warning and continue.
+
+        'raise': raise an ClusterError and terminate the algorithm.
+    check_finite : bool, optional
+        Whether to check that the input matrices contain only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+        Default: True
+    rng : `numpy.random.Generator`, optional
+        Pseudorandom number generator state. When `rng` is None, a new
+        `numpy.random.Generator` is created using entropy from the
+        operating system. Types other than `numpy.random.Generator` are
+        passed to `numpy.random.default_rng` to instantiate a ``Generator``.
+
+    Returns
+    -------
+    centroid : ndarray
+        A 'k' by 'N' array of centroids found at the last iteration of
+        k-means.
+    label : ndarray
+        label[i] is the code or index of the centroid the
+        ith observation is closest to.
+
+    See Also
+    --------
+    kmeans
+
+    References
+    ----------
+    .. [1] D. Arthur and S. Vassilvitskii, "k-means++: the advantages of
+       careful seeding", Proceedings of the Eighteenth Annual ACM-SIAM Symposium
+       on Discrete Algorithms, 2007.
+
+    Examples
+    --------
+    >>> from scipy.cluster.vq import kmeans2
+    >>> import matplotlib.pyplot as plt
+    >>> import numpy as np
+
+    Create z, an array with shape (100, 2) containing a mixture of samples
+    from three multivariate normal distributions.
+
+    >>> rng = np.random.default_rng()
+    >>> a = rng.multivariate_normal([0, 6], [[2, 1], [1, 1.5]], size=45)
+    >>> b = rng.multivariate_normal([2, 0], [[1, -1], [-1, 3]], size=30)
+    >>> c = rng.multivariate_normal([6, 4], [[5, 0], [0, 1.2]], size=25)
+    >>> z = np.concatenate((a, b, c))
+    >>> rng.shuffle(z)
+
+    Compute three clusters.
+
+    >>> centroid, label = kmeans2(z, 3, minit='points')
+    >>> centroid
+    array([[ 2.22274463, -0.61666946],  # may vary
+           [ 0.54069047,  5.86541444],
+           [ 6.73846769,  4.01991898]])
+
+    How many points are in each cluster?
+
+    >>> counts = np.bincount(label)
+    >>> counts
+    array([29, 51, 20])  # may vary
+
+    Plot the clusters.
+
+    >>> w0 = z[label == 0]
+    >>> w1 = z[label == 1]
+    >>> w2 = z[label == 2]
+    >>> plt.plot(w0[:, 0], w0[:, 1], 'o', alpha=0.5, label='cluster 0')
+    >>> plt.plot(w1[:, 0], w1[:, 1], 'd', alpha=0.5, label='cluster 1')
+    >>> plt.plot(w2[:, 0], w2[:, 1], 's', alpha=0.5, label='cluster 2')
+    >>> plt.plot(centroid[:, 0], centroid[:, 1], 'k*', label='centroids')
+    >>> plt.axis('equal')
+    >>> plt.legend(shadow=True)
+    >>> plt.show()
+
+    """
+    if int(iter) < 1:
+        raise ValueError(f"Invalid iter ({iter}), must be a positive integer.")
+    try:
+        miss_meth = _valid_miss_meth[missing]
+    except KeyError as e:
+        raise ValueError(f"Unknown missing method {missing!r}") from e
+
+    if isinstance(k, int):
+        xp = array_namespace(data)
+    else:
+        xp = array_namespace(data, k)
+    data = _asarray(data, xp=xp, check_finite=check_finite)
+    code_book = xp_copy(k, xp=xp)
+    if data.ndim == 1:
+        d = 1
+    elif data.ndim == 2:
+        d = data.shape[1]
+    else:
+        raise ValueError("Input of rank > 2 is not supported.")
+
+    if xp_size(data) < 1 or xp_size(code_book) < 1:
+        raise ValueError("Empty input is not supported.")
+
+    # If k is not a single value, it should be compatible with data's shape
+    if minit == 'matrix' or xp_size(code_book) > 1:
+        if data.ndim != code_book.ndim:
+            raise ValueError("k array doesn't match data rank")
+        nc = code_book.shape[0]
+        if data.ndim > 1 and code_book.shape[1] != d:
+            raise ValueError("k array doesn't match data dimension")
+    else:
+        nc = int(code_book)
+
+        if nc < 1:
+            raise ValueError(
+                f"Cannot ask kmeans2 for {nc} clusters (k was {code_book})"
+            )
+        elif nc != code_book:
+            warnings.warn("k was not an integer, was converted.", stacklevel=2)
+
+        try:
+            init_meth = _valid_init_meth[minit]
+        except KeyError as e:
+            raise ValueError(f"Unknown init method {minit!r}") from e
+        else:
+            rng = check_random_state(rng)
+            code_book = init_meth(data, code_book, rng, xp)
+
+    data = np.asarray(data)
+    code_book = np.asarray(code_book)
+    for _ in range(iter):
+        # Compute the nearest neighbor for each obs using the current code book
+        label = vq(data, code_book, check_finite=check_finite)[0]
+        # Update the code book by computing centroids
+        new_code_book, has_members = _vq.update_cluster_means(data, label, nc)
+        if not has_members.all():
+            miss_meth()
+            # Set the empty clusters to their previous positions
+            new_code_book[~has_members] = code_book[~has_members]
+        code_book = new_code_book
+
+    return xp.asarray(code_book), xp.asarray(label)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/conftest.py b/.venv_haddock/lib/python3.12/site-packages/scipy/conftest.py
new file mode 100644
index 0000000000000000000000000000000000000000..63676695bf6388f931acfc4374d770c0cac0e902
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/conftest.py
@@ -0,0 +1,708 @@
+# Pytest customization
+import json
+import multiprocessing
+import os
+import sys
+import warnings
+import tempfile
+from contextlib import contextmanager
+from typing import Literal
+
+import numpy as np
+import pytest
+try:
+    import hypothesis
+    hypothesis_available = True
+except ImportError:
+    hypothesis_available = False
+
+from scipy._lib._fpumode import get_fpu_mode
+from scipy._lib._array_api import (
+    SCIPY_ARRAY_API, SCIPY_DEVICE, array_namespace, default_xp,
+    is_cupy, is_dask, is_jax, is_torch,
+)
+from scipy._lib._testutils import FPUModeChangeWarning
+from scipy._lib.array_api_extra.testing import patch_lazy_xp_functions
+from scipy._lib import _pep440
+
+try:
+    from scipy_doctest.conftest import dt_config
+    HAVE_SCPDT = True
+except ModuleNotFoundError:
+    HAVE_SCPDT = False
+
+try:
+    import pytest_run_parallel  # noqa:F401
+    PARALLEL_RUN_AVAILABLE = True
+except Exception:
+    PARALLEL_RUN_AVAILABLE = False
+
+
+def pytest_configure(config):
+    """
+    Add pytest markers to avoid PytestUnknownMarkWarning
+
+    This needs to contain all markers that are SciPy-specific, as well as
+    dummy fallbacks for markers defined in optional test packages.
+
+    Note that we need both the registration here *and* in `pytest.ini`.
+    """
+    config.addinivalue_line("markers",
+        "slow: Tests that are very slow.")
+    config.addinivalue_line("markers",
+        "xslow: mark test as extremely slow (not run unless explicitly requested)")
+    config.addinivalue_line("markers",
+        "xfail_on_32bit: mark test as failing on 32-bit platforms")
+    config.addinivalue_line("markers",
+        "array_api_backends: test iterates on all array API backends")
+    config.addinivalue_line("markers",
+        ("skip_xp_backends(backends, reason=None, np_only=False, cpu_only=False, " +
+         "eager_only=False, exceptions=None): mark the desired skip configuration " +
+         "for the `skip_xp_backends` fixture"))
+    config.addinivalue_line("markers",
+        ("xfail_xp_backends(backends, reason=None, np_only=False, cpu_only=False, " +
+         "eager_only=False, exceptions=None): mark the desired xfail configuration " +
+         "for the `xfail_xp_backends` fixture"))
+
+    try:
+        import pytest_timeout  # noqa:F401
+    except Exception:
+        config.addinivalue_line(
+            "markers", 'timeout: mark a test for a non-default timeout')
+    try:
+        # This is a more reliable test of whether pytest_fail_slow is installed
+        # When I uninstalled it, `import pytest_fail_slow` didn't fail!
+        from pytest_fail_slow import parse_duration  # type: ignore[import-not-found] # noqa:F401,E501
+    except Exception:
+        config.addinivalue_line(
+            "markers", 'fail_slow: mark a test for a non-default timeout failure')
+
+    if not PARALLEL_RUN_AVAILABLE:
+        config.addinivalue_line(
+            'markers',
+            'parallel_threads_limit(n): run the given test function in parallel '
+            'using `n` threads.')
+        config.addinivalue_line(
+            "markers",
+            "thread_unsafe: mark the test function as single-threaded",
+        )
+        config.addinivalue_line(
+            "markers",
+            "iterations(n): run the given test function `n` times in each thread",
+        )
+
+    if os.name == 'posix' and sys.version_info < (3, 14):
+        # On POSIX, Python 3.13 and older uses the 'fork' context by
+        # default. Calling fork() from multiple threads leads to
+        # deadlocks. This has been changed in 3.14 to 'forkserver'.
+        multiprocessing.set_start_method('forkserver', force=True)
+
+
+def pytest_runtest_setup(item):
+    mark = item.get_closest_marker("xslow")
+    if mark is not None:
+        try:
+            v = int(os.environ.get('SCIPY_XSLOW', '0'))
+        except ValueError:
+            v = False
+        if not v:
+            pytest.skip("very slow test; "
+                        "set environment variable SCIPY_XSLOW=1 to run it")
+    mark = item.get_closest_marker("xfail_on_32bit")
+    if mark is not None and np.intp(0).itemsize < 8:
+        pytest.xfail(f'Fails on our 32-bit test platform(s): {mark.args[0]}')
+
+    # Older versions of threadpoolctl have an issue that may lead to this
+    # warning being emitted, see gh-14441
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", pytest.PytestUnraisableExceptionWarning)
+
+        try:
+            from threadpoolctl import threadpool_limits
+
+            HAS_THREADPOOLCTL = True
+        except Exception:  # observed in gh-14441: (ImportError, AttributeError)
+            # Optional dependency only. All exceptions are caught, for robustness
+            HAS_THREADPOOLCTL = False
+
+        if HAS_THREADPOOLCTL:
+            # Set the number of openmp threads based on the number of workers
+            # xdist is using to prevent oversubscription. Simplified version of what
+            # sklearn does (it can rely on threadpoolctl and its builtin OpenMP helper
+            # functions)
+            try:
+                xdist_worker_count = int(os.environ['PYTEST_XDIST_WORKER_COUNT'])
+            except KeyError:
+                # raises when pytest-xdist is not installed
+                return
+
+            if not os.getenv('OMP_NUM_THREADS'):
+                max_openmp_threads = os.cpu_count() // 2  # use nr of physical cores
+                threads_per_worker = max(max_openmp_threads // xdist_worker_count, 1)
+                try:
+                    threadpool_limits(threads_per_worker, user_api='blas')
+                except Exception:
+                    # May raise AttributeError for older versions of OpenBLAS.
+                    # Catch any error for robustness.
+                    return
+
+
+@pytest.fixture(scope="function", autouse=True)
+def check_fpu_mode(request):
+    """
+    Check FPU mode was not changed during the test.
+    """
+    old_mode = get_fpu_mode()
+    yield
+    new_mode = get_fpu_mode()
+
+    if old_mode != new_mode:
+        warnings.warn(f"FPU mode changed from {old_mode:#x} to {new_mode:#x} during "
+                      "the test",
+                      category=FPUModeChangeWarning, stacklevel=0)
+
+
+if not PARALLEL_RUN_AVAILABLE:
+    @pytest.fixture
+    def num_parallel_threads():
+        return 1
+
+
+# Array API backend handling
+xp_known_backends = {'numpy', 'array_api_strict', 'torch', 'cupy', 'jax.numpy',
+                     'dask.array'}
+xp_available_backends = [
+    pytest.param(np, id='numpy', marks=pytest.mark.array_api_backends)
+]
+xp_skip_cpu_only_backends = set()
+xp_skip_eager_only_backends = set()
+
+if SCIPY_ARRAY_API:
+    # fill the dict of backends with available libraries
+    try:
+        import array_api_strict
+        xp_available_backends.append(
+            pytest.param(array_api_strict, id='array_api_strict',
+                         marks=pytest.mark.array_api_backends))
+        if _pep440.parse(array_api_strict.__version__) < _pep440.Version('2.3'):
+            raise ImportError("array-api-strict must be >= version 2.3")
+        array_api_strict.set_array_api_strict_flags(
+            api_version='2024.12'
+        )
+    except ImportError:
+        pass
+
+    try:
+        import torch  # type: ignore[import-not-found]
+        xp_available_backends.append(
+            pytest.param(torch, id='torch',
+            marks=pytest.mark.array_api_backends))
+        torch.set_default_device(SCIPY_DEVICE)
+        if SCIPY_DEVICE != "cpu":
+            xp_skip_cpu_only_backends.add('torch')
+
+        # default to float64 unless explicitly requested
+        default = os.getenv('SCIPY_DEFAULT_DTYPE', default='float64')
+        if default == 'float64':
+            torch.set_default_dtype(torch.float64)
+        elif default != "float32":
+            raise ValueError(
+                "SCIPY_DEFAULT_DTYPE env var, if set, can only be either 'float64' "
+               f"or 'float32'. Got '{default}' instead."
+            )
+    except ImportError:
+        pass
+
+    try:
+        import cupy  # type: ignore[import-not-found]
+        # Note: cupy disregards SCIPY_DEVICE and always runs on cuda.
+        # It will fail to import if you don't have CUDA hardware and drivers.
+        xp_available_backends.append(
+            pytest.param(cupy, id='cupy',
+            marks=pytest.mark.array_api_backends))
+        xp_skip_cpu_only_backends.add('cupy')
+
+        # this is annoying in CuPy 13.x
+        warnings.filterwarnings(
+            'ignore', 'cupyx.jit.rawkernel is experimental', category=FutureWarning
+        )
+        from cupyx.scipy import signal
+        del signal
+    except ImportError:
+        pass
+
+    try:
+        import jax.numpy  # type: ignore[import-not-found]
+        
+        xp_available_backends.append(
+            pytest.param(jax.numpy, id='jax.numpy',
+            marks=[pytest.mark.array_api_backends,
+                   # Uses xpx.testing.patch_lazy_xp_functions to monkey-patch module
+                   pytest.mark.thread_unsafe]))
+
+        jax.config.update("jax_enable_x64", True)
+        jax.config.update("jax_default_device", jax.devices(SCIPY_DEVICE)[0])
+        if SCIPY_DEVICE != "cpu":
+            xp_skip_cpu_only_backends.add('jax.numpy')
+        # JAX can be eager or lazy (when wrapped in jax.jit). However it is
+        # recommended by upstream devs to assume it's always lazy.
+        xp_skip_eager_only_backends.add('jax.numpy')
+    except ImportError:
+        pass
+
+    try:
+        import dask.array as da
+
+        xp_available_backends.append(
+            pytest.param(da, id='dask.array',
+            marks=[pytest.mark.array_api_backends,
+                   # Uses xpx.testing.patch_lazy_xp_functions to monkey-patch module
+                   pytest.mark.thread_unsafe]))
+
+        # Dask can wrap around cupy. However, this is untested in scipy
+        # (and will almost surely not work as delegation will misbehave).
+
+        # Dask, strictly speaking, can be eager, in the sense that
+        # __array__, __bool__ etc. are implemented and do not raise.
+        # However, calling them triggers an extra computation of the whole graph
+        # until that point, which is highly destructive for performance.
+        xp_skip_eager_only_backends.add('dask.array')
+    except ImportError:
+        pass
+
+    xp_available_backend_ids = {p.id for p in xp_available_backends}
+    assert not xp_available_backend_ids - xp_known_backends
+
+    # by default, use all available backends
+    if (
+        isinstance(SCIPY_ARRAY_API, str)
+        and SCIPY_ARRAY_API.lower() not in ("1", "true", "all")
+    ):
+        SCIPY_ARRAY_API_ = set(json.loads(SCIPY_ARRAY_API))
+        if SCIPY_ARRAY_API_ != {'all'}:
+            if SCIPY_ARRAY_API_ - xp_available_backend_ids:
+                msg = ("'--array-api-backend' must be in "
+                       f"{xp_available_backend_ids}; got {SCIPY_ARRAY_API_}")
+                raise ValueError(msg)
+            # Only select a subset of backends
+            xp_available_backends = [
+                param for param in xp_available_backends
+                if param.id in SCIPY_ARRAY_API_
+            ]
+
+
+@pytest.fixture(params=xp_available_backends)
+def xp(request):
+    """Run the test that uses this fixture on each available array API library.
+
+    You can select all and only the tests that use the `xp` fixture by
+    passing `-m array_api_backends` to pytest.
+
+    You can select where individual tests run through the `@skip_xp_backends`,
+    `@xfail_xp_backends`, and `@skip_xp_invalid_arg` pytest markers.
+
+    Please read: https://docs.scipy.org/doc/scipy/dev/api-dev/array_api.html#adding-tests
+    """
+    # Read all @pytest.marks.skip_xp_backends markers that decorate to the test,
+    # if any, and raise pytest.skip() if the current xp is in the list.
+    skip_or_xfail_xp_backends(request, "skip")
+    # Read all @pytest.marks.xfail_xp_backends markers that decorate the test,
+    # if any, and raise pytest.xfail() if the current xp is in the list.
+    skip_or_xfail_xp_backends(request, "xfail")
+
+    xp = request.param
+    # Potentially wrap namespace with array_api_compat
+    xp = array_namespace(xp.empty(0))
+
+    if SCIPY_ARRAY_API:
+        # If xp==jax.numpy, wrap tested functions in jax.jit
+        # If xp==dask.array, wrap tested functions to test that graph is not computed
+        with patch_lazy_xp_functions(request=request, xp=request.param):
+            # Throughout all calls to assert_almost_equal, assert_array_almost_equal,
+            # and xp_assert_* functions, test that the array namespace is xp in both
+            # the expected and actual arrays. This is to detect the case where both
+            # arrays are erroneously just plain numpy while xp is something else.
+            with default_xp(xp):
+                yield xp
+    else:
+        yield xp
+
+
+skip_xp_invalid_arg = pytest.mark.skipif(SCIPY_ARRAY_API,
+    reason = ('Test involves masked arrays, object arrays, or other types '
+              'that are not valid input when `SCIPY_ARRAY_API` is used.'))
+
+
+def _backends_kwargs_from_request(request, skip_or_xfail):
+    """A helper for {skip,xfail}_xp_backends.
+
+    Return dict of {backend to skip/xfail: top reason to skip/xfail it}
+    """
+    markers = list(request.node.iter_markers(f'{skip_or_xfail}_xp_backends'))
+    reasons = {backend: [] for backend in xp_known_backends}
+
+    for marker in markers:
+        invalid_kwargs = set(marker.kwargs) - {
+            "cpu_only", "np_only", "eager_only", "reason", "exceptions"}
+        if invalid_kwargs:
+            raise TypeError(f"Invalid kwargs: {invalid_kwargs}")
+
+        exceptions = set(marker.kwargs.get('exceptions', []))
+        invalid_exceptions = exceptions - xp_known_backends
+        if (invalid_exceptions := list(exceptions - xp_known_backends)):
+            raise ValueError(f"Unknown backend(s): {invalid_exceptions}; "
+                             f"must be a subset of {list(xp_known_backends)}")
+
+        if marker.kwargs.get('np_only', False):
+            reason = marker.kwargs.get("reason") or "do not run with non-NumPy backends"
+            for backend, backend_reasons in reasons.items():
+                if backend != 'numpy' and backend not in exceptions:
+                    backend_reasons.append(reason)
+
+        elif marker.kwargs.get('cpu_only', False):
+            reason = marker.kwargs.get("reason") or (
+                "no array-agnostic implementation or delegation available "
+                "for this backend and device")
+            for backend in xp_skip_cpu_only_backends - exceptions:
+                reasons[backend].append(reason)
+
+        elif marker.kwargs.get('eager_only', False):
+            reason = marker.kwargs.get("reason") or (
+                "eager checks not executed on lazy backends")
+            for backend in xp_skip_eager_only_backends - exceptions:
+                reasons[backend].append(reason)
+
+        # add backends, if any
+        if len(marker.args) == 1:
+            backend = marker.args[0]
+            if backend not in xp_known_backends:
+                raise ValueError(f"Unknown backend: {backend}; "
+                                 f"must be one of {list(xp_known_backends)}")
+            reason = marker.kwargs.get("reason") or (
+                f"do not run with array API backend: {backend}")
+            # reason overrides the ones from cpu_only, np_only, and eager_only.
+            # This is regardless of order of appearence of the markers.
+            reasons[backend].insert(0, reason)
+
+            for kwarg in ("cpu_only", "np_only", "eager_only", "exceptions"):
+                if kwarg in marker.kwargs:
+                    raise ValueError(f"{kwarg} is mutually exclusive with {backend}")
+
+        elif len(marker.args) > 1:
+            raise ValueError(
+                f"Please specify only one backend per marker: {marker.args}"
+            )
+
+    return {backend: backend_reasons[0]
+            for backend, backend_reasons in reasons.items()
+            if backend_reasons}
+
+
+def skip_or_xfail_xp_backends(request: pytest.FixtureRequest,
+                              skip_or_xfail: Literal['skip', 'xfail']) -> None:
+    """
+    Helper of the `xp` fixture.
+    Skip or xfail based on the ``skip_xp_backends`` or ``xfail_xp_backends`` markers.
+
+    See the "Support for the array API standard" docs page for usage examples.
+
+    Usage
+    -----
+    ::
+        skip_xp_backends = pytest.mark.skip_xp_backends
+        xfail_xp_backends = pytest.mark.xfail_xp_backends
+        ...
+
+        @skip_xp_backends(backend, *, reason=None)
+        @skip_xp_backends(*, cpu_only=True, exceptions=(), reason=None)
+        @skip_xp_backends(*, eager_only=True, exceptions=(), reason=None)
+        @skip_xp_backends(*, np_only=True, exceptions=(), reason=None)
+
+        @xfail_xp_backends(backend, *, reason=None)
+        @xfail_xp_backends(*, cpu_only=True, exceptions=(), reason=None)
+        @xfail_xp_backends(*, eager_only=True, exceptions=(), reason=None)
+        @xfail_xp_backends(*, np_only=True, exceptions=(), reason=None)
+
+    Parameters
+    ----------
+    backend : str, optional
+        Backend to skip/xfail, e.g. ``"torch"``.
+        Mutually exclusive with ``cpu_only``, ``eager_only``, and ``np_only``.
+    cpu_only : bool, optional
+        When ``True``, the test is skipped/xfailed on non-CPU devices,
+        minus exceptions. Mutually exclusive with ``backend``.
+    eager_only : bool, optional
+        When ``True``, the test is skipped/xfailed for lazy backends, e.g. those
+        with major caveats when invoking ``__array__``, ``__bool__``, ``__float__``,
+        or ``__complex__``, minus exceptions. Mutually exclusive with ``backend``.
+    np_only : bool, optional
+        When ``True``, the test is skipped/xfailed for all backends other
+        than the default NumPy backend and the exceptions.
+        Mutually exclusive with ``backend``. Implies ``cpu_only`` and ``eager_only``.
+    reason : str, optional
+        A reason for the skip/xfail. If omitted, a default reason is used.
+    exceptions : list[str], optional
+        A list of exceptions for use with ``cpu_only``, ``eager_only``, or ``np_only``.
+        This should be provided when delegation is implemented for some,
+        but not all, non-CPU/non-NumPy backends.
+    """
+    if f"{skip_or_xfail}_xp_backends" not in request.keywords:
+        return
+
+    skip_xfail_reasons = _backends_kwargs_from_request(
+        request, skip_or_xfail=skip_or_xfail
+    )
+    xp = request.param
+    if xp.__name__ in skip_xfail_reasons:
+        reason = skip_xfail_reasons[xp.__name__]
+        assert reason  # Default reason applied above
+        skip_or_xfail = getattr(pytest, skip_or_xfail)
+        skip_or_xfail(reason=reason)
+
+
+@pytest.fixture
+def devices(xp):
+    """Fixture that returns a list of all devices for the backend, plus None.
+    Used to test input->output device propagation.
+
+    Usage
+    -----
+    from scipy._lib._array_api import xp_device
+
+    def test_device(xp, devices):
+        for d in devices:
+            x = xp.asarray(..., device=d)
+            y = f(x)
+            assert xp_device(y) == xp_device(x)
+    """
+    if is_cupy(xp):
+        # CuPy does not support devices other than the current one
+        # data-apis/array-api-compat#293
+        pytest.xfail(reason="data-apis/array-api-compat#293")
+    if is_dask(xp):
+        # Skip dummy DASK_DEVICE from array-api-compat, which does not propagate
+        return ["cpu", None]
+    if is_jax(xp):
+        # The .device attribute is not accessible inside jax.jit; the consequence
+        # (downstream of array-api-compat hacks) is that a non-default device in
+        # input is not guaranteed to propagate to the output even if the scipy code
+        # states `device=xp_device(arg)`` in all array creation functions.
+        # While this issue is specific to jax.jit, it would be unnecessarily
+        # verbose to skip the test for each jit-capable function and run it for
+        # those that only support eager mode.
+        pytest.xfail(reason="jax-ml/jax#26000")
+    if is_torch(xp):
+        devices = xp.__array_namespace_info__().devices()
+        # open an issue about this - cannot branch based on `any`/`all`?
+        return (device for device in devices if device.type != 'meta')
+
+    return xp.__array_namespace_info__().devices() + [None]
+
+
+if hypothesis_available:
+    # Following the approach of NumPy's conftest.py...
+    # Use a known and persistent tmpdir for hypothesis' caches, which
+    # can be automatically cleared by the OS or user.
+    hypothesis.configuration.set_hypothesis_home_dir(
+        os.path.join(tempfile.gettempdir(), ".hypothesis")
+    )
+
+    # We register two custom profiles for SciPy - for details see
+    # https://hypothesis.readthedocs.io/en/latest/settings.html
+    # The first is designed for our own CI runs; the latter also
+    # forces determinism and is designed for use via scipy.test()
+    hypothesis.settings.register_profile(
+        name="nondeterministic", deadline=None, print_blob=True,
+    )
+    hypothesis.settings.register_profile(
+        name="deterministic",
+        deadline=None, print_blob=True, database=None, derandomize=True,
+        suppress_health_check=list(hypothesis.HealthCheck),
+    )
+
+    # Profile is currently set by environment variable `SCIPY_HYPOTHESIS_PROFILE`
+    # In the future, it would be good to work the choice into `.spin/cmds.py`.
+    SCIPY_HYPOTHESIS_PROFILE = os.environ.get("SCIPY_HYPOTHESIS_PROFILE",
+                                              "deterministic")
+    hypothesis.settings.load_profile(SCIPY_HYPOTHESIS_PROFILE)
+
+
+############################################################################
+# doctesting stuff
+
+if HAVE_SCPDT:
+
+    # FIXME: populate the dict once
+    @contextmanager
+    def warnings_errors_and_rng(test=None):
+        """Temporarily turn (almost) all warnings to errors.
+
+        Filter out known warnings which we allow.
+        """
+        known_warnings = dict()
+
+        # these functions are known to emit "divide by zero" RuntimeWarnings
+        divide_by_zero = [
+            'scipy.linalg.norm', 'scipy.ndimage.center_of_mass',
+        ]
+        for name in divide_by_zero:
+            known_warnings[name] = dict(category=RuntimeWarning,
+                                        message='divide by zero')
+
+        # Deprecated stuff
+        deprecated = []
+        for name in deprecated:
+            known_warnings[name] = dict(category=DeprecationWarning)
+
+        from scipy import integrate
+        # the functions are known to emit IntegrationWarnings
+        integration_w = ['scipy.special.ellip_normal',
+                         'scipy.special.ellip_harm_2',
+        ]
+        for name in integration_w:
+            known_warnings[name] = dict(category=integrate.IntegrationWarning,
+                                        message='The occurrence of roundoff')
+
+        # scipy.stats deliberately emits UserWarnings sometimes
+        user_w = ['scipy.stats.anderson_ksamp', 'scipy.stats.kurtosistest',
+                  'scipy.stats.normaltest', 'scipy.sparse.linalg.norm']
+        for name in user_w:
+            known_warnings[name] = dict(category=UserWarning)
+
+        # additional one-off warnings to filter
+        dct = {
+            'scipy.sparse.linalg.norm':
+                dict(category=UserWarning, message="Exited at iteration"),
+            # tutorials
+            'linalg.rst':
+                dict(message='the matrix subclass is not',
+                     category=PendingDeprecationWarning),
+            'stats.rst':
+                dict(message='The maximum number of subdivisions',
+                     category=integrate.IntegrationWarning),
+        }
+        known_warnings.update(dct)
+
+        # these legitimately emit warnings in examples
+        legit = set('scipy.signal.normalize')
+
+        # Now, the meat of the matter: filter warnings,
+        # also control the random seed for each doctest.
+
+        # XXX: this matches the refguide-check behavior, but is a tad strange:
+        # makes sure that the seed the old-fashioned np.random* methods is
+        # *NOT* reproducible but the new-style `default_rng()` *IS* repoducible.
+        # Should these two be either both repro or both not repro?
+
+        from scipy._lib._util import _fixed_default_rng
+        import numpy as np
+        with _fixed_default_rng():
+            np.random.seed(None)
+            with warnings.catch_warnings():
+                if test and test.name in known_warnings:
+                    warnings.filterwarnings('ignore', **known_warnings[test.name])
+                    yield
+                elif test and test.name in legit:
+                    yield
+                else:
+                    warnings.simplefilter('error', Warning)
+                    warnings.filterwarnings('ignore', ".*odr.*", DeprecationWarning)
+                    yield
+
+    dt_config.user_context_mgr = warnings_errors_and_rng
+    dt_config.skiplist = set([
+        'scipy.linalg.LinAlgError',     # comes from numpy
+        'scipy.fftpack.fftshift',       # fftpack stuff is also from numpy
+        'scipy.fftpack.ifftshift',
+        'scipy.fftpack.fftfreq',
+        'scipy.special.sinc',           # sinc is from numpy
+        'scipy.optimize.show_options',  # does not have much to doctest
+        'scipy.signal.normalize',       # manipulates warnings (XXX temp skip)
+        'scipy.sparse.linalg.norm',     # XXX temp skip
+        # these below test things which inherit from np.ndarray
+        # cross-ref https://github.com/numpy/numpy/issues/28019
+        'scipy.io.matlab.MatlabObject.strides',
+        'scipy.io.matlab.MatlabObject.dtype',
+        'scipy.io.matlab.MatlabOpaque.dtype',
+        'scipy.io.matlab.MatlabOpaque.strides',
+        'scipy.io.matlab.MatlabFunction.strides',
+        'scipy.io.matlab.MatlabFunction.dtype'
+    ])
+
+    # these are affected by NumPy 2.0 scalar repr: rely on string comparison
+    if np.__version__ < "2":
+        dt_config.skiplist.update(set([
+            'scipy.io.hb_read',
+            'scipy.io.hb_write',
+            'scipy.sparse.csgraph.connected_components',
+            'scipy.sparse.csgraph.depth_first_order',
+            'scipy.sparse.csgraph.shortest_path',
+            'scipy.sparse.csgraph.floyd_warshall',
+            'scipy.sparse.csgraph.dijkstra',
+            'scipy.sparse.csgraph.bellman_ford',
+            'scipy.sparse.csgraph.johnson',
+            'scipy.sparse.csgraph.yen',
+            'scipy.sparse.csgraph.breadth_first_order',
+            'scipy.sparse.csgraph.reverse_cuthill_mckee',
+            'scipy.sparse.csgraph.structural_rank',
+            'scipy.sparse.csgraph.construct_dist_matrix',
+            'scipy.sparse.csgraph.reconstruct_path',
+            'scipy.ndimage.value_indices',
+            'scipy.stats.mstats.describe',
+    ]))
+
+    # help pytest collection a bit: these names are either private
+    # (distributions), or just do not need doctesting.
+    dt_config.pytest_extra_ignore = [
+        "scipy.stats.distributions",
+        "scipy.optimize.cython_optimize",
+        "scipy.test",
+        "scipy.show_config",
+        # equivalent to "pytest --ignore=path/to/file"
+        "scipy/special/_precompute",
+        "scipy/interpolate/_interpnd_info.py",
+        "scipy/interpolate/_rbfinterp_pythran.py",
+        "scipy/_build_utils/tempita.py",
+        "scipy/_lib/array_api_compat",
+        "scipy/_lib/highs",
+        "scipy/_lib/unuran",
+        "scipy/_lib/_gcutils.py",
+        "scipy/_lib/doccer.py",
+        "scipy/_lib/_uarray",
+        "scipy/linalg/_cython_signature_generator.py",
+        "scipy/linalg/_generate_pyx.py",
+        "scipy/linalg/_linalg_pythran.py",
+        "scipy/linalg/_matfuncs_sqrtm_triu.py",
+        "scipy/ndimage/utils/generate_label_testvectors.py",
+        "scipy/optimize/_group_columns.py",
+        "scipy/optimize/_max_len_seq_inner.py",
+        "scipy/signal/_max_len_seq_inner.py",
+        "scipy/sparse/_generate_sparsetools.py",
+        "scipy/special/_generate_pyx.py",
+        "scipy/stats/_stats_pythran.py",
+    ]
+
+    dt_config.pytest_extra_xfail = {
+        # name: reason
+        "ND_regular_grid.rst": "ReST parser limitation",
+        "extrapolation_examples.rst": "ReST parser limitation",
+        "sampling_pinv.rst": "__cinit__ unexpected argument",
+        "sampling_srou.rst": "nan in scalar_power",
+        "probability_distributions.rst": "integration warning",
+    }
+
+    # tutorials
+    dt_config.pseudocode = set(['integrate.nquad(func,'])
+    dt_config.local_resources = {
+        'io.rst': [
+            "octave_a.mat",
+            "octave_cells.mat",
+            "octave_struct.mat"
+        ]
+    }
+
+    dt_config.strict_check = True
+
+    # ignore Matplotlib's `ax.text`:
+    dt_config.stopwords.add('.text(')
+############################################################################
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@@ -0,0 +1,358 @@
+r"""
+==================================
+Constants (:mod:`scipy.constants`)
+==================================
+
+.. currentmodule:: scipy.constants
+
+Physical and mathematical constants and units.
+
+
+Mathematical constants
+======================
+
+================  =================================================================
+``pi``            Pi
+``golden``        Golden ratio
+``golden_ratio``  Golden ratio
+================  =================================================================
+
+
+Physical constants
+==================
+The following physical constants are available as attributes of `scipy.constants`.
+All units are `SI `_.
+
+===========================  ================================================================  ===============
+Attribute                    Quantity                                                          Units
+===========================  ================================================================  ===============
+``c``                        speed of light in vacuum                                          m s^-1
+``speed_of_light``           speed of light in vacuum                                          m s^-1
+``mu_0``                     the magnetic constant :math:`\mu_0`                               N A^-2
+``epsilon_0``                the electric constant (vacuum permittivity), :math:`\epsilon_0`   F m^-1
+``h``                        the Planck constant :math:`h`                                     J Hz^-1
+``Planck``                   the Planck constant :math:`h`                                     J Hz^-1
+``hbar``                     the reduced Planck constant, :math:`\hbar = h/(2\pi)`             J s
+``G``                        Newtonian constant of gravitation                                 m^3 kg^-1 s^-2
+``gravitational_constant``   Newtonian constant of gravitation                                 m^3 kg^-1 s^-2
+``g``                        standard acceleration of gravity                                  m s^-2
+``e``                        elementary charge                                                 C
+``elementary_charge``        elementary charge                                                 C
+``R``                        molar gas constant                                                J mol^-1 K^-1
+``gas_constant``             molar gas constant                                                J mol^-1 K^-1
+``alpha``                    fine-structure constant                                           (unitless)
+``fine_structure``           fine-structure constant                                           (unitless)
+``N_A``                      Avogadro constant                                                 mol^-1
+``Avogadro``                 Avogadro constant                                                 mol^-1
+``k``                        Boltzmann constant                                                J K^-1
+``Boltzmann``                Boltzmann constant                                                J K^-1
+``sigma``                    Stefan-Boltzmann constant :math:`\sigma`                          W m^-2 K^-4
+``Stefan_Boltzmann``         Stefan-Boltzmann constant :math:`\sigma`                          W m^-2 K^-4
+``Wien``                     Wien wavelength displacement law constant                         m K
+``Rydberg``                  Rydberg constant                                                  m^-1
+``m_e``                      electron mass                                                     kg
+``electron_mass``            electron mass                                                     kg
+``m_p``                      proton mass                                                       kg
+``proton_mass``              proton mass                                                       kg
+``m_n``                      neutron mass                                                      kg
+``neutron_mass``             neutron mass                                                      kg
+===========================  ================================================================  ===============
+
+
+Constants database
+------------------
+
+In addition to the above variables, :mod:`scipy.constants` also contains the
+2022 CODATA recommended values [CODATA2022]_ database containing more physical
+constants.
+
+.. autosummary::
+   :toctree: generated/
+
+   value      -- Value in physical_constants indexed by key
+   unit       -- Unit in physical_constants indexed by key
+   precision  -- Relative precision in physical_constants indexed by key
+   find       -- Return list of physical_constant keys with a given string
+   ConstantWarning -- Constant sought not in newest CODATA data set
+
+.. data:: physical_constants
+
+   Dictionary of physical constants, of the format
+   ``physical_constants[name] = (value, unit, uncertainty)``.
+   The CODATA database uses ellipses to indicate that a value is defined
+   (exactly) in terms of others but cannot be represented exactly with the
+   allocated number of digits. In these cases, SciPy calculates the derived
+   value and reports it to the full precision of a Python ``float``. Although 
+   ``physical_constants`` lists the uncertainty as ``0.0`` to indicate that
+   the CODATA value is exact, the value in ``physical_constants`` is still
+   subject to the truncation error inherent in double-precision representation.
+
+Available constants:
+
+======================================================================  ====
+%(constant_names)s
+======================================================================  ====
+
+
+Units
+=====
+
+SI prefixes
+-----------
+
+============  =================================================================
+``quetta``    :math:`10^{30}`
+``ronna``     :math:`10^{27}`
+``yotta``     :math:`10^{24}`
+``zetta``     :math:`10^{21}`
+``exa``       :math:`10^{18}`
+``peta``      :math:`10^{15}`
+``tera``      :math:`10^{12}`
+``giga``      :math:`10^{9}`
+``mega``      :math:`10^{6}`
+``kilo``      :math:`10^{3}`
+``hecto``     :math:`10^{2}`
+``deka``      :math:`10^{1}`
+``deci``      :math:`10^{-1}`
+``centi``     :math:`10^{-2}`
+``milli``     :math:`10^{-3}`
+``micro``     :math:`10^{-6}`
+``nano``      :math:`10^{-9}`
+``pico``      :math:`10^{-12}`
+``femto``     :math:`10^{-15}`
+``atto``      :math:`10^{-18}`
+``zepto``     :math:`10^{-21}`
+``yocto``     :math:`10^{-24}`
+``ronto``     :math:`10^{-27}`
+``quecto``    :math:`10^{-30}`
+============  =================================================================
+
+Binary prefixes
+---------------
+
+============  =================================================================
+``kibi``      :math:`2^{10}`
+``mebi``      :math:`2^{20}`
+``gibi``      :math:`2^{30}`
+``tebi``      :math:`2^{40}`
+``pebi``      :math:`2^{50}`
+``exbi``      :math:`2^{60}`
+``zebi``      :math:`2^{70}`
+``yobi``      :math:`2^{80}`
+============  =================================================================
+
+Mass
+----
+
+=================  ============================================================
+``gram``           :math:`10^{-3}` kg
+``metric_ton``     :math:`10^{3}` kg
+``grain``          one grain in kg
+``lb``             one pound (avoirdupous) in kg
+``pound``          one pound (avoirdupous) in kg
+``blob``           one inch version of a slug in kg (added in 1.0.0)
+``slinch``         one inch version of a slug in kg (added in 1.0.0)
+``slug``           one slug in kg (added in 1.0.0)
+``oz``             one ounce in kg
+``ounce``          one ounce in kg
+``stone``          one stone in kg
+``grain``          one grain in kg
+``long_ton``       one long ton in kg
+``short_ton``      one short ton in kg
+``troy_ounce``     one Troy ounce in kg
+``troy_pound``     one Troy pound in kg
+``carat``          one carat in kg
+``m_u``            atomic mass constant (in kg)
+``u``              atomic mass constant (in kg)
+``atomic_mass``    atomic mass constant (in kg)
+=================  ============================================================
+
+Angle
+-----
+
+=================  ============================================================
+``degree``         degree in radians
+``arcmin``         arc minute in radians
+``arcminute``      arc minute in radians
+``arcsec``         arc second in radians
+``arcsecond``      arc second in radians
+=================  ============================================================
+
+
+Time
+----
+
+=================  ============================================================
+``minute``         one minute in seconds
+``hour``           one hour in seconds
+``day``            one day in seconds
+``week``           one week in seconds
+``year``           one year (365 days) in seconds
+``Julian_year``    one Julian year (365.25 days) in seconds
+=================  ============================================================
+
+
+Length
+------
+
+=====================  ============================================================
+``inch``               one inch in meters
+``foot``               one foot in meters
+``yard``               one yard in meters
+``mile``               one mile in meters
+``mil``                one mil in meters
+``pt``                 one point in meters
+``point``              one point in meters
+``survey_foot``        one survey foot in meters
+``survey_mile``        one survey mile in meters
+``nautical_mile``      one nautical mile in meters
+``fermi``              one Fermi in meters
+``angstrom``           one Angstrom in meters
+``micron``             one micron in meters
+``au``                 one astronomical unit in meters
+``astronomical_unit``  one astronomical unit in meters
+``light_year``         one light year in meters
+``parsec``             one parsec in meters
+=====================  ============================================================
+
+Pressure
+--------
+
+=================  ============================================================
+``atm``            standard atmosphere in pascals
+``atmosphere``     standard atmosphere in pascals
+``bar``            one bar in pascals
+``torr``           one torr (mmHg) in pascals
+``mmHg``           one torr (mmHg) in pascals
+``psi``            one psi in pascals
+=================  ============================================================
+
+Area
+----
+
+=================  ============================================================
+``hectare``        one hectare in square meters
+``acre``           one acre in square meters
+=================  ============================================================
+
+
+Volume
+------
+
+===================    ========================================================
+``liter``              one liter in cubic meters
+``litre``              one liter in cubic meters
+``gallon``             one gallon (US) in cubic meters
+``gallon_US``          one gallon (US) in cubic meters
+``gallon_imp``         one gallon (UK) in cubic meters
+``fluid_ounce``        one fluid ounce (US) in cubic meters
+``fluid_ounce_US``     one fluid ounce (US) in cubic meters
+``fluid_ounce_imp``    one fluid ounce (UK) in cubic meters
+``bbl``                one barrel in cubic meters
+``barrel``             one barrel in cubic meters
+===================    ========================================================
+
+Speed
+-----
+
+==================    ==========================================================
+``kmh``               kilometers per hour in meters per second
+``mph``               miles per hour in meters per second
+``mach``              one Mach (approx., at 15 C, 1 atm) in meters per second
+``speed_of_sound``    one Mach (approx., at 15 C, 1 atm) in meters per second
+``knot``              one knot in meters per second
+==================    ==========================================================
+
+
+Temperature
+-----------
+
+=====================  =======================================================
+``zero_Celsius``       zero of Celsius scale in Kelvin
+``degree_Fahrenheit``  one Fahrenheit (only differences) in Kelvins
+=====================  =======================================================
+
+.. autosummary::
+   :toctree: generated/
+
+   convert_temperature
+
+Energy
+------
+
+====================  =======================================================
+``eV``                one electron volt in Joules
+``electron_volt``     one electron volt in Joules
+``calorie``           one calorie (thermochemical) in Joules
+``calorie_th``        one calorie (thermochemical) in Joules
+``calorie_IT``        one calorie (International Steam Table calorie, 1956) in Joules
+``erg``               one erg in Joules
+``Btu``               one British thermal unit (International Steam Table) in Joules
+``Btu_IT``            one British thermal unit (International Steam Table) in Joules
+``Btu_th``            one British thermal unit (thermochemical) in Joules
+``ton_TNT``           one ton of TNT in Joules
+====================  =======================================================
+
+Power
+-----
+
+====================  =======================================================
+``hp``                one horsepower in watts
+``horsepower``        one horsepower in watts
+====================  =======================================================
+
+Force
+-----
+
+====================  =======================================================
+``dyn``               one dyne in newtons
+``dyne``              one dyne in newtons
+``lbf``               one pound force in newtons
+``pound_force``       one pound force in newtons
+``kgf``               one kilogram force in newtons
+``kilogram_force``    one kilogram force in newtons
+====================  =======================================================
+
+Optics
+------
+
+.. autosummary::
+   :toctree: generated/
+
+   lambda2nu
+   nu2lambda
+
+References
+==========
+
+.. [CODATA2022] CODATA Recommended Values of the Fundamental
+   Physical Constants 2022.
+
+   https://physics.nist.gov/cuu/Constants/
+
+"""  # noqa: E501
+# Modules contributed by BasSw (wegwerp@gmail.com)
+from ._codata import *
+from ._constants import *
+from ._codata import _obsolete_constants, physical_constants
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import codata, constants
+
+_constant_names_list = [(_k.lower(), _k, _v)
+                        for _k, _v in physical_constants.items()
+                        if _k not in _obsolete_constants]
+_constant_names = "\n".join(["``{}``{}  {} {}".format(_x[1], " "*(66-len(_x[1])),
+                                                  _x[2][0], _x[2][1])
+                             for _x in sorted(_constant_names_list)])
+if __doc__:
+    __doc__ = __doc__ % dict(constant_names=_constant_names)
+
+del _constant_names
+del _constant_names_list
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/constants/_codata.py b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/_codata.py
new file mode 100644
index 0000000000000000000000000000000000000000..3b7e9b3779d249b834505956a9c270564c41670f
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/_codata.py
@@ -0,0 +1,2272 @@
+"""
+Fundamental Physical Constants
+------------------------------
+
+These constants are taken from CODATA Recommended Values of the Fundamental
+Physical Constants 2022.
+
+Object
+------
+physical_constants : dict
+    A dictionary containing physical constants. Keys are the names of physical
+    constants, values are tuples (value, units, precision).
+
+Functions
+---------
+value(key):
+    Returns the value of the physical constant(key).
+unit(key):
+    Returns the units of the physical constant(key).
+precision(key):
+    Returns the relative precision of the physical constant(key).
+find(sub):
+    Prints or returns list of keys containing the string sub, default is all.
+
+Source
+------
+The values of the constants provided at this site are recommended for
+international use by CODATA and are the latest available. Termed the "2018
+CODATA recommended values," they are generally recognized worldwide for use in
+all fields of science and technology. The values became available on 20 May
+2019 and replaced the 2014 CODATA set. Also available is an introduction to the
+constants for non-experts at
+
+https://physics.nist.gov/cuu/Constants/introduction.html
+
+References
+----------
+Theoretical and experimental publications relevant to the fundamental constants
+and closely related precision measurements published since the mid 1980s, but
+also including many older papers of particular interest, some of which date
+back to the 1800s. To search the bibliography, visit
+
+https://physics.nist.gov/cuu/Constants/
+
+"""
+
+# Compiled by Charles Harris, dated October 3, 2002
+# updated to 2002 values by BasSw, 2006
+# Updated to 2006 values by Vincent Davis June 2010
+# Updated to 2014 values by Joseph Booker, 2015
+# Updated to 2018 values by Jakob Jakobson, 2019
+# Updated to 2022 values by Jakob Jakobson, 2024
+
+import warnings
+import math
+
+from typing import Any
+from collections.abc import Callable
+
+from scipy._lib._array_api import xp_capabilities
+
+__all__ = ['physical_constants', 'value', 'unit', 'precision', 'find',
+           'ConstantWarning']
+
+"""
+Source:  https://physics.nist.gov/cuu/Constants/
+
+The values of the constants provided at this site are recommended for
+international use by CODATA and are the latest available. Termed the "2018
+CODATA recommended values," they are generally recognized worldwide for use in
+all fields of science and technology. The values became available on 20 May
+2019 and replaced the 2014 CODATA set.
+"""
+
+#
+# Source:  https://physics.nist.gov/cuu/Constants/
+#
+
+# Quantity                                             Value                 Uncertainty          Unit
+# ---------------------------------------------------- --------------------- -------------------- -------------
+txt2002 = """\
+Wien displacement law constant                         2.897 7685e-3         0.000 0051e-3         m K
+atomic unit of 1st hyperpolarizablity                  3.206 361 51e-53      0.000 000 28e-53      C^3 m^3 J^-2
+atomic unit of 2nd hyperpolarizablity                  6.235 3808e-65        0.000 0011e-65        C^4 m^4 J^-3
+atomic unit of electric dipole moment                  8.478 353 09e-30      0.000 000 73e-30      C m
+atomic unit of electric polarizablity                  1.648 777 274e-41     0.000 000 016e-41     C^2 m^2 J^-1
+atomic unit of electric quadrupole moment              4.486 551 24e-40      0.000 000 39e-40      C m^2
+atomic unit of magn. dipole moment                     1.854 801 90e-23      0.000 000 16e-23      J T^-1
+atomic unit of magn. flux density                      2.350 517 42e5        0.000 000 20e5        T
+deuteron magn. moment                                  0.433 073 482e-26     0.000 000 038e-26     J T^-1
+deuteron magn. moment to Bohr magneton ratio           0.466 975 4567e-3     0.000 000 0050e-3
+deuteron magn. moment to nuclear magneton ratio        0.857 438 2329        0.000 000 0092
+deuteron-electron magn. moment ratio                   -4.664 345 548e-4     0.000 000 050e-4
+deuteron-proton magn. moment ratio                     0.307 012 2084        0.000 000 0045
+deuteron-neutron magn. moment ratio                    -0.448 206 52         0.000 000 11
+electron gyromagn. ratio                               1.760 859 74e11       0.000 000 15e11       s^-1 T^-1
+electron gyromagn. ratio over 2 pi                     28 024.9532           0.0024                MHz T^-1
+electron magn. moment                                  -928.476 412e-26      0.000 080e-26         J T^-1
+electron magn. moment to Bohr magneton ratio           -1.001 159 652 1859   0.000 000 000 0038
+electron magn. moment to nuclear magneton ratio        -1838.281 971 07      0.000 000 85
+electron magn. moment anomaly                          1.159 652 1859e-3     0.000 000 0038e-3
+electron to shielded proton magn. moment ratio         -658.227 5956         0.000 0071
+electron to shielded helion magn. moment ratio         864.058 255           0.000 010
+electron-deuteron magn. moment ratio                   -2143.923 493         0.000 023
+electron-muon magn. moment ratio                       206.766 9894          0.000 0054
+electron-neutron magn. moment ratio                    960.920 50            0.000 23
+electron-proton magn. moment ratio                     -658.210 6862         0.000 0066
+magn. constant                                         12.566 370 614...e-7  (exact)               N A^-2
+magn. flux quantum                                     2.067 833 72e-15      0.000 000 18e-15      Wb
+muon magn. moment                                      -4.490 447 99e-26     0.000 000 40e-26      J T^-1
+muon magn. moment to Bohr magneton ratio               -4.841 970 45e-3      0.000 000 13e-3
+muon magn. moment to nuclear magneton ratio            -8.890 596 98         0.000 000 23
+muon-proton magn. moment ratio                         -3.183 345 118        0.000 000 089
+neutron gyromagn. ratio                                1.832 471 83e8        0.000 000 46e8        s^-1 T^-1
+neutron gyromagn. ratio over 2 pi                      29.164 6950           0.000 0073            MHz T^-1
+neutron magn. moment                                   -0.966 236 45e-26     0.000 000 24e-26      J T^-1
+neutron magn. moment to Bohr magneton ratio            -1.041 875 63e-3      0.000 000 25e-3
+neutron magn. moment to nuclear magneton ratio         -1.913 042 73         0.000 000 45
+neutron to shielded proton magn. moment ratio          -0.684 996 94         0.000 000 16
+neutron-electron magn. moment ratio                    1.040 668 82e-3       0.000 000 25e-3
+neutron-proton magn. moment ratio                      -0.684 979 34         0.000 000 16
+proton gyromagn. ratio                                 2.675 222 05e8        0.000 000 23e8        s^-1 T^-1
+proton gyromagn. ratio over 2 pi                       42.577 4813           0.000 0037            MHz T^-1
+proton magn. moment                                    1.410 606 71e-26      0.000 000 12e-26      J T^-1
+proton magn. moment to Bohr magneton ratio             1.521 032 206e-3      0.000 000 015e-3
+proton magn. moment to nuclear magneton ratio          2.792 847 351         0.000 000 028
+proton magn. shielding correction                      25.689e-6             0.015e-6
+proton-neutron magn. moment ratio                      -1.459 898 05         0.000 000 34
+shielded helion gyromagn. ratio                        2.037 894 70e8        0.000 000 18e8        s^-1 T^-1
+shielded helion gyromagn. ratio over 2 pi              32.434 1015           0.000 0028            MHz T^-1
+shielded helion magn. moment                           -1.074 553 024e-26    0.000 000 093e-26     J T^-1
+shielded helion magn. moment to Bohr magneton ratio    -1.158 671 474e-3     0.000 000 014e-3
+shielded helion magn. moment to nuclear magneton ratio -2.127 497 723        0.000 000 025
+shielded helion to proton magn. moment ratio           -0.761 766 562        0.000 000 012
+shielded helion to shielded proton magn. moment ratio  -0.761 786 1313       0.000 000 0033
+shielded helion gyromagn. ratio                        2.037 894 70e8        0.000 000 18e8        s^-1 T^-1
+shielded helion gyromagn. ratio over 2 pi              32.434 1015           0.000 0028            MHz T^-1
+shielded proton magn. moment                           1.410 570 47e-26      0.000 000 12e-26      J T^-1
+shielded proton magn. moment to Bohr magneton ratio    1.520 993 132e-3      0.000 000 016e-3
+shielded proton magn. moment to nuclear magneton ratio 2.792 775 604         0.000 000 030
+{220} lattice spacing of silicon                       192.015 5965e-12      0.000 0070e-12        m"""
+
+
+def exact2002(exact):
+    replace = {
+        'magn. constant': 4e-7 * math.pi,
+    }
+    return replace
+
+
+txt2006 = """\
+lattice spacing of silicon                             192.015 5762 e-12     0.000 0050 e-12       m
+alpha particle-electron mass ratio                     7294.299 5365         0.000 0031
+alpha particle mass                                    6.644 656 20 e-27     0.000 000 33 e-27     kg
+alpha particle mass energy equivalent                  5.971 919 17 e-10     0.000 000 30 e-10     J
+alpha particle mass energy equivalent in MeV           3727.379 109          0.000 093             MeV
+alpha particle mass in u                               4.001 506 179 127     0.000 000 000 062     u
+alpha particle molar mass                              4.001 506 179 127 e-3 0.000 000 000 062 e-3 kg mol^-1
+alpha particle-proton mass ratio                       3.972 599 689 51      0.000 000 000 41
+Angstrom star                                          1.000 014 98 e-10     0.000 000 90 e-10     m
+atomic mass constant                                   1.660 538 782 e-27    0.000 000 083 e-27    kg
+atomic mass constant energy equivalent                 1.492 417 830 e-10    0.000 000 074 e-10    J
+atomic mass constant energy equivalent in MeV          931.494 028           0.000 023             MeV
+atomic mass unit-electron volt relationship            931.494 028 e6        0.000 023 e6          eV
+atomic mass unit-hartree relationship                  3.423 177 7149 e7     0.000 000 0049 e7     E_h
+atomic mass unit-hertz relationship                    2.252 342 7369 e23    0.000 000 0032 e23    Hz
+atomic mass unit-inverse meter relationship            7.513 006 671 e14     0.000 000 011 e14     m^-1
+atomic mass unit-joule relationship                    1.492 417 830 e-10    0.000 000 074 e-10    J
+atomic mass unit-kelvin relationship                   1.080 9527 e13        0.000 0019 e13        K
+atomic mass unit-kilogram relationship                 1.660 538 782 e-27    0.000 000 083 e-27    kg
+atomic unit of 1st hyperpolarizability                 3.206 361 533 e-53    0.000 000 081 e-53    C^3 m^3 J^-2
+atomic unit of 2nd hyperpolarizability                 6.235 380 95 e-65     0.000 000 31 e-65     C^4 m^4 J^-3
+atomic unit of action                                  1.054 571 628 e-34    0.000 000 053 e-34    J s
+atomic unit of charge                                  1.602 176 487 e-19    0.000 000 040 e-19    C
+atomic unit of charge density                          1.081 202 300 e12     0.000 000 027 e12     C m^-3
+atomic unit of current                                 6.623 617 63 e-3      0.000 000 17 e-3      A
+atomic unit of electric dipole mom.                    8.478 352 81 e-30     0.000 000 21 e-30     C m
+atomic unit of electric field                          5.142 206 32 e11      0.000 000 13 e11      V m^-1
+atomic unit of electric field gradient                 9.717 361 66 e21      0.000 000 24 e21      V m^-2
+atomic unit of electric polarizability                 1.648 777 2536 e-41   0.000 000 0034 e-41   C^2 m^2 J^-1
+atomic unit of electric potential                      27.211 383 86         0.000 000 68          V
+atomic unit of electric quadrupole mom.                4.486 551 07 e-40     0.000 000 11 e-40     C m^2
+atomic unit of energy                                  4.359 743 94 e-18     0.000 000 22 e-18     J
+atomic unit of force                                   8.238 722 06 e-8      0.000 000 41 e-8      N
+atomic unit of length                                  0.529 177 208 59 e-10 0.000 000 000 36 e-10 m
+atomic unit of mag. dipole mom.                        1.854 801 830 e-23    0.000 000 046 e-23    J T^-1
+atomic unit of mag. flux density                       2.350 517 382 e5      0.000 000 059 e5      T
+atomic unit of magnetizability                         7.891 036 433 e-29    0.000 000 027 e-29    J T^-2
+atomic unit of mass                                    9.109 382 15 e-31     0.000 000 45 e-31     kg
+atomic unit of momentum                                1.992 851 565 e-24    0.000 000 099 e-24    kg m s^-1
+atomic unit of permittivity                            1.112 650 056... e-10 (exact)               F m^-1
+atomic unit of time                                    2.418 884 326 505 e-17 0.000 000 000 016 e-17 s
+atomic unit of velocity                                2.187 691 2541 e6     0.000 000 0015 e6     m s^-1
+Avogadro constant                                      6.022 141 79 e23      0.000 000 30 e23      mol^-1
+Bohr magneton                                          927.400 915 e-26      0.000 023 e-26        J T^-1
+Bohr magneton in eV/T                                  5.788 381 7555 e-5    0.000 000 0079 e-5    eV T^-1
+Bohr magneton in Hz/T                                  13.996 246 04 e9      0.000 000 35 e9       Hz T^-1
+Bohr magneton in inverse meters per tesla              46.686 4515           0.000 0012            m^-1 T^-1
+Bohr magneton in K/T                                   0.671 7131            0.000 0012            K T^-1
+Bohr radius                                            0.529 177 208 59 e-10 0.000 000 000 36 e-10 m
+Boltzmann constant                                     1.380 6504 e-23       0.000 0024 e-23       J K^-1
+Boltzmann constant in eV/K                             8.617 343 e-5         0.000 015 e-5         eV K^-1
+Boltzmann constant in Hz/K                             2.083 6644 e10        0.000 0036 e10        Hz K^-1
+Boltzmann constant in inverse meters per kelvin        69.503 56             0.000 12              m^-1 K^-1
+characteristic impedance of vacuum                     376.730 313 461...    (exact)               ohm
+classical electron radius                              2.817 940 2894 e-15   0.000 000 0058 e-15   m
+Compton wavelength                                     2.426 310 2175 e-12   0.000 000 0033 e-12   m
+Compton wavelength over 2 pi                           386.159 264 59 e-15   0.000 000 53 e-15     m
+conductance quantum                                    7.748 091 7004 e-5    0.000 000 0053 e-5    S
+conventional value of Josephson constant               483 597.9 e9          (exact)               Hz V^-1
+conventional value of von Klitzing constant            25 812.807            (exact)               ohm
+Cu x unit                                              1.002 076 99 e-13     0.000 000 28 e-13     m
+deuteron-electron mag. mom. ratio                      -4.664 345 537 e-4    0.000 000 039 e-4
+deuteron-electron mass ratio                           3670.482 9654         0.000 0016
+deuteron g factor                                      0.857 438 2308        0.000 000 0072
+deuteron mag. mom.                                     0.433 073 465 e-26    0.000 000 011 e-26    J T^-1
+deuteron mag. mom. to Bohr magneton ratio              0.466 975 4556 e-3    0.000 000 0039 e-3
+deuteron mag. mom. to nuclear magneton ratio           0.857 438 2308        0.000 000 0072
+deuteron mass                                          3.343 583 20 e-27     0.000 000 17 e-27     kg
+deuteron mass energy equivalent                        3.005 062 72 e-10     0.000 000 15 e-10     J
+deuteron mass energy equivalent in MeV                 1875.612 793          0.000 047             MeV
+deuteron mass in u                                     2.013 553 212 724     0.000 000 000 078     u
+deuteron molar mass                                    2.013 553 212 724 e-3 0.000 000 000 078 e-3 kg mol^-1
+deuteron-neutron mag. mom. ratio                       -0.448 206 52         0.000 000 11
+deuteron-proton mag. mom. ratio                        0.307 012 2070        0.000 000 0024
+deuteron-proton mass ratio                             1.999 007 501 08      0.000 000 000 22
+deuteron rms charge radius                             2.1402 e-15           0.0028 e-15           m
+electric constant                                      8.854 187 817... e-12 (exact)               F m^-1
+electron charge to mass quotient                       -1.758 820 150 e11    0.000 000 044 e11     C kg^-1
+electron-deuteron mag. mom. ratio                      -2143.923 498         0.000 018
+electron-deuteron mass ratio                           2.724 437 1093 e-4    0.000 000 0012 e-4
+electron g factor                                      -2.002 319 304 3622   0.000 000 000 0015
+electron gyromag. ratio                                1.760 859 770 e11     0.000 000 044 e11     s^-1 T^-1
+electron gyromag. ratio over 2 pi                      28 024.953 64         0.000 70              MHz T^-1
+electron mag. mom.                                     -928.476 377 e-26     0.000 023 e-26        J T^-1
+electron mag. mom. anomaly                             1.159 652 181 11 e-3  0.000 000 000 74 e-3
+electron mag. mom. to Bohr magneton ratio              -1.001 159 652 181 11 0.000 000 000 000 74
+electron mag. mom. to nuclear magneton ratio           -1838.281 970 92      0.000 000 80
+electron mass                                          9.109 382 15 e-31     0.000 000 45 e-31     kg
+electron mass energy equivalent                        8.187 104 38 e-14     0.000 000 41 e-14     J
+electron mass energy equivalent in MeV                 0.510 998 910         0.000 000 013         MeV
+electron mass in u                                     5.485 799 0943 e-4    0.000 000 0023 e-4    u
+electron molar mass                                    5.485 799 0943 e-7    0.000 000 0023 e-7    kg mol^-1
+electron-muon mag. mom. ratio                          206.766 9877          0.000 0052
+electron-muon mass ratio                               4.836 331 71 e-3      0.000 000 12 e-3
+electron-neutron mag. mom. ratio                       960.920 50            0.000 23
+electron-neutron mass ratio                            5.438 673 4459 e-4    0.000 000 0033 e-4
+electron-proton mag. mom. ratio                        -658.210 6848         0.000 0054
+electron-proton mass ratio                             5.446 170 2177 e-4    0.000 000 0024 e-4
+electron-tau mass ratio                                2.875 64 e-4          0.000 47 e-4
+electron to alpha particle mass ratio                  1.370 933 555 70 e-4  0.000 000 000 58 e-4
+electron to shielded helion mag. mom. ratio            864.058 257           0.000 010
+electron to shielded proton mag. mom. ratio            -658.227 5971         0.000 0072
+electron volt                                          1.602 176 487 e-19    0.000 000 040 e-19    J
+electron volt-atomic mass unit relationship            1.073 544 188 e-9     0.000 000 027 e-9     u
+electron volt-hartree relationship                     3.674 932 540 e-2     0.000 000 092 e-2     E_h
+electron volt-hertz relationship                       2.417 989 454 e14     0.000 000 060 e14     Hz
+electron volt-inverse meter relationship               8.065 544 65 e5       0.000 000 20 e5       m^-1
+electron volt-joule relationship                       1.602 176 487 e-19    0.000 000 040 e-19    J
+electron volt-kelvin relationship                      1.160 4505 e4         0.000 0020 e4         K
+electron volt-kilogram relationship                    1.782 661 758 e-36    0.000 000 044 e-36    kg
+elementary charge                                      1.602 176 487 e-19    0.000 000 040 e-19    C
+elementary charge over h                               2.417 989 454 e14     0.000 000 060 e14     A J^-1
+Faraday constant                                       96 485.3399           0.0024                C mol^-1
+Faraday constant for conventional electric current     96 485.3401           0.0048                C_90 mol^-1
+Fermi coupling constant                                1.166 37 e-5          0.000 01 e-5          GeV^-2
+fine-structure constant                                7.297 352 5376 e-3    0.000 000 0050 e-3
+first radiation constant                               3.741 771 18 e-16     0.000 000 19 e-16     W m^2
+first radiation constant for spectral radiance         1.191 042 759 e-16    0.000 000 059 e-16    W m^2 sr^-1
+hartree-atomic mass unit relationship                  2.921 262 2986 e-8    0.000 000 0042 e-8    u
+hartree-electron volt relationship                     27.211 383 86         0.000 000 68          eV
+Hartree energy                                         4.359 743 94 e-18     0.000 000 22 e-18     J
+Hartree energy in eV                                   27.211 383 86         0.000 000 68          eV
+hartree-hertz relationship                             6.579 683 920 722 e15 0.000 000 000 044 e15 Hz
+hartree-inverse meter relationship                     2.194 746 313 705 e7  0.000 000 000 015 e7  m^-1
+hartree-joule relationship                             4.359 743 94 e-18     0.000 000 22 e-18     J
+hartree-kelvin relationship                            3.157 7465 e5         0.000 0055 e5         K
+hartree-kilogram relationship                          4.850 869 34 e-35     0.000 000 24 e-35     kg
+helion-electron mass ratio                             5495.885 2765         0.000 0052
+helion mass                                            5.006 411 92 e-27     0.000 000 25 e-27     kg
+helion mass energy equivalent                          4.499 538 64 e-10     0.000 000 22 e-10     J
+helion mass energy equivalent in MeV                   2808.391 383          0.000 070             MeV
+helion mass in u                                       3.014 932 2473        0.000 000 0026        u
+helion molar mass                                      3.014 932 2473 e-3    0.000 000 0026 e-3    kg mol^-1
+helion-proton mass ratio                               2.993 152 6713        0.000 000 0026
+hertz-atomic mass unit relationship                    4.439 821 6294 e-24   0.000 000 0064 e-24   u
+hertz-electron volt relationship                       4.135 667 33 e-15     0.000 000 10 e-15     eV
+hertz-hartree relationship                             1.519 829 846 006 e-16 0.000 000 000010e-16 E_h
+hertz-inverse meter relationship                       3.335 640 951... e-9  (exact)               m^-1
+hertz-joule relationship                               6.626 068 96 e-34     0.000 000 33 e-34     J
+hertz-kelvin relationship                              4.799 2374 e-11       0.000 0084 e-11       K
+hertz-kilogram relationship                            7.372 496 00 e-51     0.000 000 37 e-51     kg
+inverse fine-structure constant                        137.035 999 679       0.000 000 094
+inverse meter-atomic mass unit relationship            1.331 025 0394 e-15   0.000 000 0019 e-15   u
+inverse meter-electron volt relationship               1.239 841 875 e-6     0.000 000 031 e-6     eV
+inverse meter-hartree relationship                     4.556 335 252 760 e-8 0.000 000 000 030 e-8 E_h
+inverse meter-hertz relationship                       299 792 458           (exact)               Hz
+inverse meter-joule relationship                       1.986 445 501 e-25    0.000 000 099 e-25    J
+inverse meter-kelvin relationship                      1.438 7752 e-2        0.000 0025 e-2        K
+inverse meter-kilogram relationship                    2.210 218 70 e-42     0.000 000 11 e-42     kg
+inverse of conductance quantum                         12 906.403 7787       0.000 0088            ohm
+Josephson constant                                     483 597.891 e9        0.012 e9              Hz V^-1
+joule-atomic mass unit relationship                    6.700 536 41 e9       0.000 000 33 e9       u
+joule-electron volt relationship                       6.241 509 65 e18      0.000 000 16 e18      eV
+joule-hartree relationship                             2.293 712 69 e17      0.000 000 11 e17      E_h
+joule-hertz relationship                               1.509 190 450 e33     0.000 000 075 e33     Hz
+joule-inverse meter relationship                       5.034 117 47 e24      0.000 000 25 e24      m^-1
+joule-kelvin relationship                              7.242 963 e22         0.000 013 e22         K
+joule-kilogram relationship                            1.112 650 056... e-17 (exact)               kg
+kelvin-atomic mass unit relationship                   9.251 098 e-14        0.000 016 e-14        u
+kelvin-electron volt relationship                      8.617 343 e-5         0.000 015 e-5         eV
+kelvin-hartree relationship                            3.166 8153 e-6        0.000 0055 e-6        E_h
+kelvin-hertz relationship                              2.083 6644 e10        0.000 0036 e10        Hz
+kelvin-inverse meter relationship                      69.503 56             0.000 12              m^-1
+kelvin-joule relationship                              1.380 6504 e-23       0.000 0024 e-23       J
+kelvin-kilogram relationship                           1.536 1807 e-40       0.000 0027 e-40       kg
+kilogram-atomic mass unit relationship                 6.022 141 79 e26      0.000 000 30 e26      u
+kilogram-electron volt relationship                    5.609 589 12 e35      0.000 000 14 e35      eV
+kilogram-hartree relationship                          2.061 486 16 e34      0.000 000 10 e34      E_h
+kilogram-hertz relationship                            1.356 392 733 e50     0.000 000 068 e50     Hz
+kilogram-inverse meter relationship                    4.524 439 15 e41      0.000 000 23 e41      m^-1
+kilogram-joule relationship                            8.987 551 787... e16  (exact)               J
+kilogram-kelvin relationship                           6.509 651 e39         0.000 011 e39         K
+lattice parameter of silicon                           543.102 064 e-12      0.000 014 e-12        m
+Loschmidt constant (273.15 K, 101.325 kPa)             2.686 7774 e25        0.000 0047 e25        m^-3
+mag. constant                                          12.566 370 614... e-7 (exact)               N A^-2
+mag. flux quantum                                      2.067 833 667 e-15    0.000 000 052 e-15    Wb
+molar gas constant                                     8.314 472             0.000 015             J mol^-1 K^-1
+molar mass constant                                    1 e-3                 (exact)               kg mol^-1
+molar mass of carbon-12                                12 e-3                (exact)               kg mol^-1
+molar Planck constant                                  3.990 312 6821 e-10   0.000 000 0057 e-10   J s mol^-1
+molar Planck constant times c                          0.119 626 564 72      0.000 000 000 17      J m mol^-1
+molar volume of ideal gas (273.15 K, 100 kPa)          22.710 981 e-3        0.000 040 e-3         m^3 mol^-1
+molar volume of ideal gas (273.15 K, 101.325 kPa)      22.413 996 e-3        0.000 039 e-3         m^3 mol^-1
+molar volume of silicon                                12.058 8349 e-6       0.000 0011 e-6        m^3 mol^-1
+Mo x unit                                              1.002 099 55 e-13     0.000 000 53 e-13     m
+muon Compton wavelength                                11.734 441 04 e-15    0.000 000 30 e-15     m
+muon Compton wavelength over 2 pi                      1.867 594 295 e-15    0.000 000 047 e-15    m
+muon-electron mass ratio                               206.768 2823          0.000 0052
+muon g factor                                          -2.002 331 8414       0.000 000 0012
+muon mag. mom.                                         -4.490 447 86 e-26    0.000 000 16 e-26     J T^-1
+muon mag. mom. anomaly                                 1.165 920 69 e-3      0.000 000 60 e-3
+muon mag. mom. to Bohr magneton ratio                  -4.841 970 49 e-3     0.000 000 12 e-3
+muon mag. mom. to nuclear magneton ratio               -8.890 597 05         0.000 000 23
+muon mass                                              1.883 531 30 e-28     0.000 000 11 e-28     kg
+muon mass energy equivalent                            1.692 833 510 e-11    0.000 000 095 e-11    J
+muon mass energy equivalent in MeV                     105.658 3668          0.000 0038            MeV
+muon mass in u                                         0.113 428 9256        0.000 000 0029        u
+muon molar mass                                        0.113 428 9256 e-3    0.000 000 0029 e-3    kg mol^-1
+muon-neutron mass ratio                                0.112 454 5167        0.000 000 0029
+muon-proton mag. mom. ratio                            -3.183 345 137        0.000 000 085
+muon-proton mass ratio                                 0.112 609 5261        0.000 000 0029
+muon-tau mass ratio                                    5.945 92 e-2          0.000 97 e-2
+natural unit of action                                 1.054 571 628 e-34    0.000 000 053 e-34    J s
+natural unit of action in eV s                         6.582 118 99 e-16     0.000 000 16 e-16     eV s
+natural unit of energy                                 8.187 104 38 e-14     0.000 000 41 e-14     J
+natural unit of energy in MeV                          0.510 998 910         0.000 000 013         MeV
+natural unit of length                                 386.159 264 59 e-15   0.000 000 53 e-15     m
+natural unit of mass                                   9.109 382 15 e-31     0.000 000 45 e-31     kg
+natural unit of momentum                               2.730 924 06 e-22     0.000 000 14 e-22     kg m s^-1
+natural unit of momentum in MeV/c                      0.510 998 910         0.000 000 013         MeV/c
+natural unit of time                                   1.288 088 6570 e-21   0.000 000 0018 e-21   s
+natural unit of velocity                               299 792 458           (exact)               m s^-1
+neutron Compton wavelength                             1.319 590 8951 e-15   0.000 000 0020 e-15   m
+neutron Compton wavelength over 2 pi                   0.210 019 413 82 e-15 0.000 000 000 31 e-15 m
+neutron-electron mag. mom. ratio                       1.040 668 82 e-3      0.000 000 25 e-3
+neutron-electron mass ratio                            1838.683 6605         0.000 0011
+neutron g factor                                       -3.826 085 45         0.000 000 90
+neutron gyromag. ratio                                 1.832 471 85 e8       0.000 000 43 e8       s^-1 T^-1
+neutron gyromag. ratio over 2 pi                       29.164 6954           0.000 0069            MHz T^-1
+neutron mag. mom.                                      -0.966 236 41 e-26    0.000 000 23 e-26     J T^-1
+neutron mag. mom. to Bohr magneton ratio               -1.041 875 63 e-3     0.000 000 25 e-3
+neutron mag. mom. to nuclear magneton ratio            -1.913 042 73         0.000 000 45
+neutron mass                                           1.674 927 211 e-27    0.000 000 084 e-27    kg
+neutron mass energy equivalent                         1.505 349 505 e-10    0.000 000 075 e-10    J
+neutron mass energy equivalent in MeV                  939.565 346           0.000 023             MeV
+neutron mass in u                                      1.008 664 915 97      0.000 000 000 43      u
+neutron molar mass                                     1.008 664 915 97 e-3  0.000 000 000 43 e-3  kg mol^-1
+neutron-muon mass ratio                                8.892 484 09          0.000 000 23
+neutron-proton mag. mom. ratio                         -0.684 979 34         0.000 000 16
+neutron-proton mass ratio                              1.001 378 419 18      0.000 000 000 46
+neutron-tau mass ratio                                 0.528 740             0.000 086
+neutron to shielded proton mag. mom. ratio             -0.684 996 94         0.000 000 16
+Newtonian constant of gravitation                      6.674 28 e-11         0.000 67 e-11         m^3 kg^-1 s^-2
+Newtonian constant of gravitation over h-bar c         6.708 81 e-39         0.000 67 e-39         (GeV/c^2)^-2
+nuclear magneton                                       5.050 783 24 e-27     0.000 000 13 e-27     J T^-1
+nuclear magneton in eV/T                               3.152 451 2326 e-8    0.000 000 0045 e-8    eV T^-1
+nuclear magneton in inverse meters per tesla           2.542 623 616 e-2     0.000 000 064 e-2     m^-1 T^-1
+nuclear magneton in K/T                                3.658 2637 e-4        0.000 0064 e-4        K T^-1
+nuclear magneton in MHz/T                              7.622 593 84          0.000 000 19          MHz T^-1
+Planck constant                                        6.626 068 96 e-34     0.000 000 33 e-34     J s
+Planck constant in eV s                                4.135 667 33 e-15     0.000 000 10 e-15     eV s
+Planck constant over 2 pi                              1.054 571 628 e-34    0.000 000 053 e-34    J s
+Planck constant over 2 pi in eV s                      6.582 118 99 e-16     0.000 000 16 e-16     eV s
+Planck constant over 2 pi times c in MeV fm            197.326 9631          0.000 0049            MeV fm
+Planck length                                          1.616 252 e-35        0.000 081 e-35        m
+Planck mass                                            2.176 44 e-8          0.000 11 e-8          kg
+Planck mass energy equivalent in GeV                   1.220 892 e19         0.000 061 e19         GeV
+Planck temperature                                     1.416 785 e32         0.000 071 e32         K
+Planck time                                            5.391 24 e-44         0.000 27 e-44         s
+proton charge to mass quotient                         9.578 833 92 e7       0.000 000 24 e7       C kg^-1
+proton Compton wavelength                              1.321 409 8446 e-15   0.000 000 0019 e-15   m
+proton Compton wavelength over 2 pi                    0.210 308 908 61 e-15 0.000 000 000 30 e-15 m
+proton-electron mass ratio                             1836.152 672 47       0.000 000 80
+proton g factor                                        5.585 694 713         0.000 000 046
+proton gyromag. ratio                                  2.675 222 099 e8      0.000 000 070 e8      s^-1 T^-1
+proton gyromag. ratio over 2 pi                        42.577 4821           0.000 0011            MHz T^-1
+proton mag. mom.                                       1.410 606 662 e-26    0.000 000 037 e-26    J T^-1
+proton mag. mom. to Bohr magneton ratio                1.521 032 209 e-3     0.000 000 012 e-3
+proton mag. mom. to nuclear magneton ratio             2.792 847 356         0.000 000 023
+proton mag. shielding correction                       25.694 e-6            0.014 e-6
+proton mass                                            1.672 621 637 e-27    0.000 000 083 e-27    kg
+proton mass energy equivalent                          1.503 277 359 e-10    0.000 000 075 e-10    J
+proton mass energy equivalent in MeV                   938.272 013           0.000 023             MeV
+proton mass in u                                       1.007 276 466 77      0.000 000 000 10      u
+proton molar mass                                      1.007 276 466 77 e-3  0.000 000 000 10 e-3  kg mol^-1
+proton-muon mass ratio                                 8.880 243 39          0.000 000 23
+proton-neutron mag. mom. ratio                         -1.459 898 06         0.000 000 34
+proton-neutron mass ratio                              0.998 623 478 24      0.000 000 000 46
+proton rms charge radius                               0.8768 e-15           0.0069 e-15           m
+proton-tau mass ratio                                  0.528 012             0.000 086
+quantum of circulation                                 3.636 947 5199 e-4    0.000 000 0050 e-4    m^2 s^-1
+quantum of circulation times 2                         7.273 895 040 e-4     0.000 000 010 e-4     m^2 s^-1
+Rydberg constant                                       10 973 731.568 527    0.000 073             m^-1
+Rydberg constant times c in Hz                         3.289 841 960 361 e15 0.000 000 000 022 e15 Hz
+Rydberg constant times hc in eV                        13.605 691 93         0.000 000 34          eV
+Rydberg constant times hc in J                         2.179 871 97 e-18     0.000 000 11 e-18     J
+Sackur-Tetrode constant (1 K, 100 kPa)                 -1.151 7047           0.000 0044
+Sackur-Tetrode constant (1 K, 101.325 kPa)             -1.164 8677           0.000 0044
+second radiation constant                              1.438 7752 e-2        0.000 0025 e-2        m K
+shielded helion gyromag. ratio                         2.037 894 730 e8      0.000 000 056 e8      s^-1 T^-1
+shielded helion gyromag. ratio over 2 pi               32.434 101 98         0.000 000 90          MHz T^-1
+shielded helion mag. mom.                              -1.074 552 982 e-26   0.000 000 030 e-26    J T^-1
+shielded helion mag. mom. to Bohr magneton ratio       -1.158 671 471 e-3    0.000 000 014 e-3
+shielded helion mag. mom. to nuclear magneton ratio    -2.127 497 718        0.000 000 025
+shielded helion to proton mag. mom. ratio              -0.761 766 558        0.000 000 011
+shielded helion to shielded proton mag. mom. ratio     -0.761 786 1313       0.000 000 0033
+shielded proton gyromag. ratio                         2.675 153 362 e8      0.000 000 073 e8      s^-1 T^-1
+shielded proton gyromag. ratio over 2 pi               42.576 3881           0.000 0012            MHz T^-1
+shielded proton mag. mom.                              1.410 570 419 e-26    0.000 000 038 e-26    J T^-1
+shielded proton mag. mom. to Bohr magneton ratio       1.520 993 128 e-3     0.000 000 017 e-3
+shielded proton mag. mom. to nuclear magneton ratio    2.792 775 598         0.000 000 030
+speed of light in vacuum                               299 792 458           (exact)               m s^-1
+standard acceleration of gravity                       9.806 65              (exact)               m s^-2
+standard atmosphere                                    101 325               (exact)               Pa
+Stefan-Boltzmann constant                              5.670 400 e-8         0.000 040 e-8         W m^-2 K^-4
+tau Compton wavelength                                 0.697 72 e-15         0.000 11 e-15         m
+tau Compton wavelength over 2 pi                       0.111 046 e-15        0.000 018 e-15        m
+tau-electron mass ratio                                3477.48               0.57
+tau mass                                               3.167 77 e-27         0.000 52 e-27         kg
+tau mass energy equivalent                             2.847 05 e-10         0.000 46 e-10         J
+tau mass energy equivalent in MeV                      1776.99               0.29                  MeV
+tau mass in u                                          1.907 68              0.000 31              u
+tau molar mass                                         1.907 68 e-3          0.000 31 e-3          kg mol^-1
+tau-muon mass ratio                                    16.8183               0.0027
+tau-neutron mass ratio                                 1.891 29              0.000 31
+tau-proton mass ratio                                  1.893 90              0.000 31
+Thomson cross section                                  0.665 245 8558 e-28   0.000 000 0027 e-28   m^2
+triton-electron mag. mom. ratio                        -1.620 514 423 e-3    0.000 000 021 e-3
+triton-electron mass ratio                             5496.921 5269         0.000 0051
+triton g factor                                        5.957 924 896         0.000 000 076
+triton mag. mom.                                       1.504 609 361 e-26    0.000 000 042 e-26    J T^-1
+triton mag. mom. to Bohr magneton ratio                1.622 393 657 e-3     0.000 000 021 e-3
+triton mag. mom. to nuclear magneton ratio             2.978 962 448         0.000 000 038
+triton mass                                            5.007 355 88 e-27     0.000 000 25 e-27     kg
+triton mass energy equivalent                          4.500 387 03 e-10     0.000 000 22 e-10     J
+triton mass energy equivalent in MeV                   2808.920 906          0.000 070             MeV
+triton mass in u                                       3.015 500 7134        0.000 000 0025        u
+triton molar mass                                      3.015 500 7134 e-3    0.000 000 0025 e-3    kg mol^-1
+triton-neutron mag. mom. ratio                         -1.557 185 53         0.000 000 37
+triton-proton mag. mom. ratio                          1.066 639 908         0.000 000 010
+triton-proton mass ratio                               2.993 717 0309        0.000 000 0025
+unified atomic mass unit                               1.660 538 782 e-27    0.000 000 083 e-27    kg
+von Klitzing constant                                  25 812.807 557        0.000 018             ohm
+weak mixing angle                                      0.222 55              0.000 56
+Wien frequency displacement law constant               5.878 933 e10         0.000 010 e10         Hz K^-1
+Wien wavelength displacement law constant              2.897 7685 e-3        0.000 0051 e-3        m K"""
+
+
+def exact2006(exact):
+    mu0 = 4e-7 * math.pi
+    c = exact['speed of light in vacuum']
+    epsilon0 = 1 / (mu0 * c**2)
+    replace = {
+        'mag. constant': mu0,
+        'electric constant': epsilon0,
+        'atomic unit of permittivity': 4*math.pi*epsilon0,
+        'characteristic impedance of vacuum': math.sqrt(mu0 / epsilon0),
+        'hertz-inverse meter relationship': 1/c,
+        'joule-kilogram relationship': 1/c**2,
+        'kilogram-joule relationship': c**2,
+    }
+    return replace
+
+
+txt2010 = """\
+{220} lattice spacing of silicon                       192.015 5714 e-12     0.000 0032 e-12       m
+alpha particle-electron mass ratio                     7294.299 5361         0.000 0029
+alpha particle mass                                    6.644 656 75 e-27     0.000 000 29 e-27     kg
+alpha particle mass energy equivalent                  5.971 919 67 e-10     0.000 000 26 e-10     J
+alpha particle mass energy equivalent in MeV           3727.379 240          0.000 082             MeV
+alpha particle mass in u                               4.001 506 179 125     0.000 000 000 062     u
+alpha particle molar mass                              4.001 506 179 125 e-3 0.000 000 000 062 e-3 kg mol^-1
+alpha particle-proton mass ratio                       3.972 599 689 33      0.000 000 000 36
+Angstrom star                                          1.000 014 95 e-10     0.000 000 90 e-10     m
+atomic mass constant                                   1.660 538 921 e-27    0.000 000 073 e-27    kg
+atomic mass constant energy equivalent                 1.492 417 954 e-10    0.000 000 066 e-10    J
+atomic mass constant energy equivalent in MeV          931.494 061           0.000 021             MeV
+atomic mass unit-electron volt relationship            931.494 061 e6        0.000 021 e6          eV
+atomic mass unit-hartree relationship                  3.423 177 6845 e7     0.000 000 0024 e7     E_h
+atomic mass unit-hertz relationship                    2.252 342 7168 e23    0.000 000 0016 e23    Hz
+atomic mass unit-inverse meter relationship            7.513 006 6042 e14    0.000 000 0053 e14    m^-1
+atomic mass unit-joule relationship                    1.492 417 954 e-10    0.000 000 066 e-10    J
+atomic mass unit-kelvin relationship                   1.080 954 08 e13      0.000 000 98 e13      K
+atomic mass unit-kilogram relationship                 1.660 538 921 e-27    0.000 000 073 e-27    kg
+atomic unit of 1st hyperpolarizability                 3.206 361 449 e-53    0.000 000 071 e-53    C^3 m^3 J^-2
+atomic unit of 2nd hyperpolarizability                 6.235 380 54 e-65     0.000 000 28 e-65     C^4 m^4 J^-3
+atomic unit of action                                  1.054 571 726 e-34    0.000 000 047 e-34    J s
+atomic unit of charge                                  1.602 176 565 e-19    0.000 000 035 e-19    C
+atomic unit of charge density                          1.081 202 338 e12     0.000 000 024 e12     C m^-3
+atomic unit of current                                 6.623 617 95 e-3      0.000 000 15 e-3      A
+atomic unit of electric dipole mom.                    8.478 353 26 e-30     0.000 000 19 e-30     C m
+atomic unit of electric field                          5.142 206 52 e11      0.000 000 11 e11      V m^-1
+atomic unit of electric field gradient                 9.717 362 00 e21      0.000 000 21 e21      V m^-2
+atomic unit of electric polarizability                 1.648 777 2754 e-41   0.000 000 0016 e-41   C^2 m^2 J^-1
+atomic unit of electric potential                      27.211 385 05         0.000 000 60          V
+atomic unit of electric quadrupole mom.                4.486 551 331 e-40    0.000 000 099 e-40    C m^2
+atomic unit of energy                                  4.359 744 34 e-18     0.000 000 19 e-18     J
+atomic unit of force                                   8.238 722 78 e-8      0.000 000 36 e-8      N
+atomic unit of length                                  0.529 177 210 92 e-10 0.000 000 000 17 e-10 m
+atomic unit of mag. dipole mom.                        1.854 801 936 e-23    0.000 000 041 e-23    J T^-1
+atomic unit of mag. flux density                       2.350 517 464 e5      0.000 000 052 e5      T
+atomic unit of magnetizability                         7.891 036 607 e-29    0.000 000 013 e-29    J T^-2
+atomic unit of mass                                    9.109 382 91 e-31     0.000 000 40 e-31     kg
+atomic unit of mom.um                                  1.992 851 740 e-24    0.000 000 088 e-24    kg m s^-1
+atomic unit of permittivity                            1.112 650 056... e-10 (exact)               F m^-1
+atomic unit of time                                    2.418 884 326 502e-17 0.000 000 000 012e-17 s
+atomic unit of velocity                                2.187 691 263 79 e6   0.000 000 000 71 e6   m s^-1
+Avogadro constant                                      6.022 141 29 e23      0.000 000 27 e23      mol^-1
+Bohr magneton                                          927.400 968 e-26      0.000 020 e-26        J T^-1
+Bohr magneton in eV/T                                  5.788 381 8066 e-5    0.000 000 0038 e-5    eV T^-1
+Bohr magneton in Hz/T                                  13.996 245 55 e9      0.000 000 31 e9       Hz T^-1
+Bohr magneton in inverse meters per tesla              46.686 4498           0.000 0010            m^-1 T^-1
+Bohr magneton in K/T                                   0.671 713 88          0.000 000 61          K T^-1
+Bohr radius                                            0.529 177 210 92 e-10 0.000 000 000 17 e-10 m
+Boltzmann constant                                     1.380 6488 e-23       0.000 0013 e-23       J K^-1
+Boltzmann constant in eV/K                             8.617 3324 e-5        0.000 0078 e-5        eV K^-1
+Boltzmann constant in Hz/K                             2.083 6618 e10        0.000 0019 e10        Hz K^-1
+Boltzmann constant in inverse meters per kelvin        69.503 476            0.000 063             m^-1 K^-1
+characteristic impedance of vacuum                     376.730 313 461...    (exact)               ohm
+classical electron radius                              2.817 940 3267 e-15   0.000 000 0027 e-15   m
+Compton wavelength                                     2.426 310 2389 e-12   0.000 000 0016 e-12   m
+Compton wavelength over 2 pi                           386.159 268 00 e-15   0.000 000 25 e-15     m
+conductance quantum                                    7.748 091 7346 e-5    0.000 000 0025 e-5    S
+conventional value of Josephson constant               483 597.9 e9          (exact)               Hz V^-1
+conventional value of von Klitzing constant            25 812.807            (exact)               ohm
+Cu x unit                                              1.002 076 97 e-13     0.000 000 28 e-13     m
+deuteron-electron mag. mom. ratio                      -4.664 345 537 e-4    0.000 000 039 e-4
+deuteron-electron mass ratio                           3670.482 9652         0.000 0015
+deuteron g factor                                      0.857 438 2308        0.000 000 0072
+deuteron mag. mom.                                     0.433 073 489 e-26    0.000 000 010 e-26    J T^-1
+deuteron mag. mom. to Bohr magneton ratio              0.466 975 4556 e-3    0.000 000 0039 e-3
+deuteron mag. mom. to nuclear magneton ratio           0.857 438 2308        0.000 000 0072
+deuteron mass                                          3.343 583 48 e-27     0.000 000 15 e-27     kg
+deuteron mass energy equivalent                        3.005 062 97 e-10     0.000 000 13 e-10     J
+deuteron mass energy equivalent in MeV                 1875.612 859          0.000 041             MeV
+deuteron mass in u                                     2.013 553 212 712     0.000 000 000 077     u
+deuteron molar mass                                    2.013 553 212 712 e-3 0.000 000 000 077 e-3 kg mol^-1
+deuteron-neutron mag. mom. ratio                       -0.448 206 52         0.000 000 11
+deuteron-proton mag. mom. ratio                        0.307 012 2070        0.000 000 0024
+deuteron-proton mass ratio                             1.999 007 500 97      0.000 000 000 18
+deuteron rms charge radius                             2.1424 e-15           0.0021 e-15           m
+electric constant                                      8.854 187 817... e-12 (exact)               F m^-1
+electron charge to mass quotient                       -1.758 820 088 e11    0.000 000 039 e11     C kg^-1
+electron-deuteron mag. mom. ratio                      -2143.923 498         0.000 018
+electron-deuteron mass ratio                           2.724 437 1095 e-4    0.000 000 0011 e-4
+electron g factor                                      -2.002 319 304 361 53 0.000 000 000 000 53
+electron gyromag. ratio                                1.760 859 708 e11     0.000 000 039 e11     s^-1 T^-1
+electron gyromag. ratio over 2 pi                      28 024.952 66         0.000 62              MHz T^-1
+electron-helion mass ratio                             1.819 543 0761 e-4    0.000 000 0017 e-4
+electron mag. mom.                                     -928.476 430 e-26     0.000 021 e-26        J T^-1
+electron mag. mom. anomaly                             1.159 652 180 76 e-3  0.000 000 000 27 e-3
+electron mag. mom. to Bohr magneton ratio              -1.001 159 652 180 76 0.000 000 000 000 27
+electron mag. mom. to nuclear magneton ratio           -1838.281 970 90      0.000 000 75
+electron mass                                          9.109 382 91 e-31     0.000 000 40 e-31     kg
+electron mass energy equivalent                        8.187 105 06 e-14     0.000 000 36 e-14     J
+electron mass energy equivalent in MeV                 0.510 998 928         0.000 000 011         MeV
+electron mass in u                                     5.485 799 0946 e-4    0.000 000 0022 e-4    u
+electron molar mass                                    5.485 799 0946 e-7    0.000 000 0022 e-7    kg mol^-1
+electron-muon mag. mom. ratio                          206.766 9896          0.000 0052
+electron-muon mass ratio                               4.836 331 66 e-3      0.000 000 12 e-3
+electron-neutron mag. mom. ratio                       960.920 50            0.000 23
+electron-neutron mass ratio                            5.438 673 4461 e-4    0.000 000 0032 e-4
+electron-proton mag. mom. ratio                        -658.210 6848         0.000 0054
+electron-proton mass ratio                             5.446 170 2178 e-4    0.000 000 0022 e-4
+electron-tau mass ratio                                2.875 92 e-4          0.000 26 e-4
+electron to alpha particle mass ratio                  1.370 933 555 78 e-4  0.000 000 000 55 e-4
+electron to shielded helion mag. mom. ratio            864.058 257           0.000 010
+electron to shielded proton mag. mom. ratio            -658.227 5971         0.000 0072
+electron-triton mass ratio                             1.819 200 0653 e-4    0.000 000 0017 e-4
+electron volt                                          1.602 176 565 e-19    0.000 000 035 e-19    J
+electron volt-atomic mass unit relationship            1.073 544 150 e-9     0.000 000 024 e-9     u
+electron volt-hartree relationship                     3.674 932 379 e-2     0.000 000 081 e-2     E_h
+electron volt-hertz relationship                       2.417 989 348 e14     0.000 000 053 e14     Hz
+electron volt-inverse meter relationship               8.065 544 29 e5       0.000 000 18 e5       m^-1
+electron volt-joule relationship                       1.602 176 565 e-19    0.000 000 035 e-19    J
+electron volt-kelvin relationship                      1.160 4519 e4         0.000 0011 e4         K
+electron volt-kilogram relationship                    1.782 661 845 e-36    0.000 000 039 e-36    kg
+elementary charge                                      1.602 176 565 e-19    0.000 000 035 e-19    C
+elementary charge over h                               2.417 989 348 e14     0.000 000 053 e14     A J^-1
+Faraday constant                                       96 485.3365           0.0021                C mol^-1
+Faraday constant for conventional electric current     96 485.3321           0.0043                C_90 mol^-1
+Fermi coupling constant                                1.166 364 e-5         0.000 005 e-5         GeV^-2
+fine-structure constant                                7.297 352 5698 e-3    0.000 000 0024 e-3
+first radiation constant                               3.741 771 53 e-16     0.000 000 17 e-16     W m^2
+first radiation constant for spectral radiance         1.191 042 869 e-16    0.000 000 053 e-16    W m^2 sr^-1
+hartree-atomic mass unit relationship                  2.921 262 3246 e-8    0.000 000 0021 e-8    u
+hartree-electron volt relationship                     27.211 385 05         0.000 000 60          eV
+Hartree energy                                         4.359 744 34 e-18     0.000 000 19 e-18     J
+Hartree energy in eV                                   27.211 385 05         0.000 000 60          eV
+hartree-hertz relationship                             6.579 683 920 729 e15 0.000 000 000 033 e15 Hz
+hartree-inverse meter relationship                     2.194 746 313 708 e7  0.000 000 000 011 e7  m^-1
+hartree-joule relationship                             4.359 744 34 e-18     0.000 000 19 e-18     J
+hartree-kelvin relationship                            3.157 7504 e5         0.000 0029 e5         K
+hartree-kilogram relationship                          4.850 869 79 e-35     0.000 000 21 e-35     kg
+helion-electron mass ratio                             5495.885 2754         0.000 0050
+helion g factor                                        -4.255 250 613        0.000 000 050
+helion mag. mom.                                       -1.074 617 486 e-26   0.000 000 027 e-26    J T^-1
+helion mag. mom. to Bohr magneton ratio                -1.158 740 958 e-3    0.000 000 014 e-3
+helion mag. mom. to nuclear magneton ratio             -2.127 625 306        0.000 000 025
+helion mass                                            5.006 412 34 e-27     0.000 000 22 e-27     kg
+helion mass energy equivalent                          4.499 539 02 e-10     0.000 000 20 e-10     J
+helion mass energy equivalent in MeV                   2808.391 482          0.000 062             MeV
+helion mass in u                                       3.014 932 2468        0.000 000 0025        u
+helion molar mass                                      3.014 932 2468 e-3    0.000 000 0025 e-3    kg mol^-1
+helion-proton mass ratio                               2.993 152 6707        0.000 000 0025
+hertz-atomic mass unit relationship                    4.439 821 6689 e-24   0.000 000 0031 e-24   u
+hertz-electron volt relationship                       4.135 667 516 e-15    0.000 000 091 e-15    eV
+hertz-hartree relationship                             1.519 829 8460045e-16 0.000 000 0000076e-16 E_h
+hertz-inverse meter relationship                       3.335 640 951... e-9  (exact)               m^-1
+hertz-joule relationship                               6.626 069 57 e-34     0.000 000 29 e-34     J
+hertz-kelvin relationship                              4.799 2434 e-11       0.000 0044 e-11       K
+hertz-kilogram relationship                            7.372 496 68 e-51     0.000 000 33 e-51     kg
+inverse fine-structure constant                        137.035 999 074       0.000 000 044
+inverse meter-atomic mass unit relationship            1.331 025 051 20 e-15 0.000 000 000 94 e-15 u
+inverse meter-electron volt relationship               1.239 841 930 e-6     0.000 000 027 e-6     eV
+inverse meter-hartree relationship                     4.556 335 252 755 e-8 0.000 000 000 023 e-8 E_h
+inverse meter-hertz relationship                       299 792 458           (exact)               Hz
+inverse meter-joule relationship                       1.986 445 684 e-25    0.000 000 088 e-25    J
+inverse meter-kelvin relationship                      1.438 7770 e-2        0.000 0013 e-2        K
+inverse meter-kilogram relationship                    2.210 218 902 e-42    0.000 000 098 e-42    kg
+inverse of conductance quantum                         12 906.403 7217       0.000 0042            ohm
+Josephson constant                                     483 597.870 e9        0.011 e9              Hz V^-1
+joule-atomic mass unit relationship                    6.700 535 85 e9       0.000 000 30 e9       u
+joule-electron volt relationship                       6.241 509 34 e18      0.000 000 14 e18      eV
+joule-hartree relationship                             2.293 712 48 e17      0.000 000 10 e17      E_h
+joule-hertz relationship                               1.509 190 311 e33     0.000 000 067 e33     Hz
+joule-inverse meter relationship                       5.034 117 01 e24      0.000 000 22 e24      m^-1
+joule-kelvin relationship                              7.242 9716 e22        0.000 0066 e22        K
+joule-kilogram relationship                            1.112 650 056... e-17 (exact)               kg
+kelvin-atomic mass unit relationship                   9.251 0868 e-14       0.000 0084 e-14       u
+kelvin-electron volt relationship                      8.617 3324 e-5        0.000 0078 e-5        eV
+kelvin-hartree relationship                            3.166 8114 e-6        0.000 0029 e-6        E_h
+kelvin-hertz relationship                              2.083 6618 e10        0.000 0019 e10        Hz
+kelvin-inverse meter relationship                      69.503 476            0.000 063             m^-1
+kelvin-joule relationship                              1.380 6488 e-23       0.000 0013 e-23       J
+kelvin-kilogram relationship                           1.536 1790 e-40       0.000 0014 e-40       kg
+kilogram-atomic mass unit relationship                 6.022 141 29 e26      0.000 000 27 e26      u
+kilogram-electron volt relationship                    5.609 588 85 e35      0.000 000 12 e35      eV
+kilogram-hartree relationship                          2.061 485 968 e34     0.000 000 091 e34     E_h
+kilogram-hertz relationship                            1.356 392 608 e50     0.000 000 060 e50     Hz
+kilogram-inverse meter relationship                    4.524 438 73 e41      0.000 000 20 e41      m^-1
+kilogram-joule relationship                            8.987 551 787... e16  (exact)               J
+kilogram-kelvin relationship                           6.509 6582 e39        0.000 0059 e39        K
+lattice parameter of silicon                           543.102 0504 e-12     0.000 0089 e-12       m
+Loschmidt constant (273.15 K, 100 kPa)                 2.651 6462 e25        0.000 0024 e25        m^-3
+Loschmidt constant (273.15 K, 101.325 kPa)             2.686 7805 e25        0.000 0024 e25        m^-3
+mag. constant                                          12.566 370 614... e-7 (exact)               N A^-2
+mag. flux quantum                                      2.067 833 758 e-15    0.000 000 046 e-15    Wb
+molar gas constant                                     8.314 4621            0.000 0075            J mol^-1 K^-1
+molar mass constant                                    1 e-3                 (exact)               kg mol^-1
+molar mass of carbon-12                                12 e-3                (exact)               kg mol^-1
+molar Planck constant                                  3.990 312 7176 e-10   0.000 000 0028 e-10   J s mol^-1
+molar Planck constant times c                          0.119 626 565 779     0.000 000 000 084     J m mol^-1
+molar volume of ideal gas (273.15 K, 100 kPa)          22.710 953 e-3        0.000 021 e-3         m^3 mol^-1
+molar volume of ideal gas (273.15 K, 101.325 kPa)      22.413 968 e-3        0.000 020 e-3         m^3 mol^-1
+molar volume of silicon                                12.058 833 01 e-6     0.000 000 80 e-6      m^3 mol^-1
+Mo x unit                                              1.002 099 52 e-13     0.000 000 53 e-13     m
+muon Compton wavelength                                11.734 441 03 e-15    0.000 000 30 e-15     m
+muon Compton wavelength over 2 pi                      1.867 594 294 e-15    0.000 000 047 e-15    m
+muon-electron mass ratio                               206.768 2843          0.000 0052
+muon g factor                                          -2.002 331 8418       0.000 000 0013
+muon mag. mom.                                         -4.490 448 07 e-26    0.000 000 15 e-26     J T^-1
+muon mag. mom. anomaly                                 1.165 920 91 e-3      0.000 000 63 e-3
+muon mag. mom. to Bohr magneton ratio                  -4.841 970 44 e-3     0.000 000 12 e-3
+muon mag. mom. to nuclear magneton ratio               -8.890 596 97         0.000 000 22
+muon mass                                              1.883 531 475 e-28    0.000 000 096 e-28    kg
+muon mass energy equivalent                            1.692 833 667 e-11    0.000 000 086 e-11    J
+muon mass energy equivalent in MeV                     105.658 3715          0.000 0035            MeV
+muon mass in u                                         0.113 428 9267        0.000 000 0029        u
+muon molar mass                                        0.113 428 9267 e-3    0.000 000 0029 e-3    kg mol^-1
+muon-neutron mass ratio                                0.112 454 5177        0.000 000 0028
+muon-proton mag. mom. ratio                            -3.183 345 107        0.000 000 084
+muon-proton mass ratio                                 0.112 609 5272        0.000 000 0028
+muon-tau mass ratio                                    5.946 49 e-2          0.000 54 e-2
+natural unit of action                                 1.054 571 726 e-34    0.000 000 047 e-34    J s
+natural unit of action in eV s                         6.582 119 28 e-16     0.000 000 15 e-16     eV s
+natural unit of energy                                 8.187 105 06 e-14     0.000 000 36 e-14     J
+natural unit of energy in MeV                          0.510 998 928         0.000 000 011         MeV
+natural unit of length                                 386.159 268 00 e-15   0.000 000 25 e-15     m
+natural unit of mass                                   9.109 382 91 e-31     0.000 000 40 e-31     kg
+natural unit of mom.um                                 2.730 924 29 e-22     0.000 000 12 e-22     kg m s^-1
+natural unit of mom.um in MeV/c                        0.510 998 928         0.000 000 011         MeV/c
+natural unit of time                                   1.288 088 668 33 e-21 0.000 000 000 83 e-21 s
+natural unit of velocity                               299 792 458           (exact)               m s^-1
+neutron Compton wavelength                             1.319 590 9068 e-15   0.000 000 0011 e-15   m
+neutron Compton wavelength over 2 pi                   0.210 019 415 68 e-15 0.000 000 000 17 e-15 m
+neutron-electron mag. mom. ratio                       1.040 668 82 e-3      0.000 000 25 e-3
+neutron-electron mass ratio                            1838.683 6605         0.000 0011
+neutron g factor                                       -3.826 085 45         0.000 000 90
+neutron gyromag. ratio                                 1.832 471 79 e8       0.000 000 43 e8       s^-1 T^-1
+neutron gyromag. ratio over 2 pi                       29.164 6943           0.000 0069            MHz T^-1
+neutron mag. mom.                                      -0.966 236 47 e-26    0.000 000 23 e-26     J T^-1
+neutron mag. mom. to Bohr magneton ratio               -1.041 875 63 e-3     0.000 000 25 e-3
+neutron mag. mom. to nuclear magneton ratio            -1.913 042 72         0.000 000 45
+neutron mass                                           1.674 927 351 e-27    0.000 000 074 e-27    kg
+neutron mass energy equivalent                         1.505 349 631 e-10    0.000 000 066 e-10    J
+neutron mass energy equivalent in MeV                  939.565 379           0.000 021             MeV
+neutron mass in u                                      1.008 664 916 00      0.000 000 000 43      u
+neutron molar mass                                     1.008 664 916 00 e-3  0.000 000 000 43 e-3  kg mol^-1
+neutron-muon mass ratio                                8.892 484 00          0.000 000 22
+neutron-proton mag. mom. ratio                         -0.684 979 34         0.000 000 16
+neutron-proton mass difference                         2.305 573 92 e-30     0.000 000 76 e-30
+neutron-proton mass difference energy equivalent       2.072 146 50 e-13     0.000 000 68 e-13
+neutron-proton mass difference energy equivalent in MeV 1.293 332 17          0.000 000 42
+neutron-proton mass difference in u                    0.001 388 449 19      0.000 000 000 45
+neutron-proton mass ratio                              1.001 378 419 17      0.000 000 000 45
+neutron-tau mass ratio                                 0.528 790             0.000 048
+neutron to shielded proton mag. mom. ratio             -0.684 996 94         0.000 000 16
+Newtonian constant of gravitation                      6.673 84 e-11         0.000 80 e-11         m^3 kg^-1 s^-2
+Newtonian constant of gravitation over h-bar c         6.708 37 e-39         0.000 80 e-39         (GeV/c^2)^-2
+nuclear magneton                                       5.050 783 53 e-27     0.000 000 11 e-27     J T^-1
+nuclear magneton in eV/T                               3.152 451 2605 e-8    0.000 000 0022 e-8    eV T^-1
+nuclear magneton in inverse meters per tesla           2.542 623 527 e-2     0.000 000 056 e-2     m^-1 T^-1
+nuclear magneton in K/T                                3.658 2682 e-4        0.000 0033 e-4        K T^-1
+nuclear magneton in MHz/T                              7.622 593 57          0.000 000 17          MHz T^-1
+Planck constant                                        6.626 069 57 e-34     0.000 000 29 e-34     J s
+Planck constant in eV s                                4.135 667 516 e-15    0.000 000 091 e-15    eV s
+Planck constant over 2 pi                              1.054 571 726 e-34    0.000 000 047 e-34    J s
+Planck constant over 2 pi in eV s                      6.582 119 28 e-16     0.000 000 15 e-16     eV s
+Planck constant over 2 pi times c in MeV fm            197.326 9718          0.000 0044            MeV fm
+Planck length                                          1.616 199 e-35        0.000 097 e-35        m
+Planck mass                                            2.176 51 e-8          0.000 13 e-8          kg
+Planck mass energy equivalent in GeV                   1.220 932 e19         0.000 073 e19         GeV
+Planck temperature                                     1.416 833 e32         0.000 085 e32         K
+Planck time                                            5.391 06 e-44         0.000 32 e-44         s
+proton charge to mass quotient                         9.578 833 58 e7       0.000 000 21 e7       C kg^-1
+proton Compton wavelength                              1.321 409 856 23 e-15 0.000 000 000 94 e-15 m
+proton Compton wavelength over 2 pi                    0.210 308 910 47 e-15 0.000 000 000 15 e-15 m
+proton-electron mass ratio                             1836.152 672 45       0.000 000 75
+proton g factor                                        5.585 694 713         0.000 000 046
+proton gyromag. ratio                                  2.675 222 005 e8      0.000 000 063 e8      s^-1 T^-1
+proton gyromag. ratio over 2 pi                        42.577 4806           0.000 0010            MHz T^-1
+proton mag. mom.                                       1.410 606 743 e-26    0.000 000 033 e-26    J T^-1
+proton mag. mom. to Bohr magneton ratio                1.521 032 210 e-3     0.000 000 012 e-3
+proton mag. mom. to nuclear magneton ratio             2.792 847 356         0.000 000 023
+proton mag. shielding correction                       25.694 e-6            0.014 e-6
+proton mass                                            1.672 621 777 e-27    0.000 000 074 e-27    kg
+proton mass energy equivalent                          1.503 277 484 e-10    0.000 000 066 e-10    J
+proton mass energy equivalent in MeV                   938.272 046           0.000 021             MeV
+proton mass in u                                       1.007 276 466 812     0.000 000 000 090     u
+proton molar mass                                      1.007 276 466 812 e-3 0.000 000 000 090 e-3 kg mol^-1
+proton-muon mass ratio                                 8.880 243 31          0.000 000 22
+proton-neutron mag. mom. ratio                         -1.459 898 06         0.000 000 34
+proton-neutron mass ratio                              0.998 623 478 26      0.000 000 000 45
+proton rms charge radius                               0.8775 e-15           0.0051 e-15           m
+proton-tau mass ratio                                  0.528 063             0.000 048
+quantum of circulation                                 3.636 947 5520 e-4    0.000 000 0024 e-4    m^2 s^-1
+quantum of circulation times 2                         7.273 895 1040 e-4    0.000 000 0047 e-4    m^2 s^-1
+Rydberg constant                                       10 973 731.568 539    0.000 055             m^-1
+Rydberg constant times c in Hz                         3.289 841 960 364 e15 0.000 000 000 017 e15 Hz
+Rydberg constant times hc in eV                        13.605 692 53         0.000 000 30          eV
+Rydberg constant times hc in J                         2.179 872 171 e-18    0.000 000 096 e-18    J
+Sackur-Tetrode constant (1 K, 100 kPa)                 -1.151 7078           0.000 0023
+Sackur-Tetrode constant (1 K, 101.325 kPa)             -1.164 8708           0.000 0023
+second radiation constant                              1.438 7770 e-2        0.000 0013 e-2        m K
+shielded helion gyromag. ratio                         2.037 894 659 e8      0.000 000 051 e8      s^-1 T^-1
+shielded helion gyromag. ratio over 2 pi               32.434 100 84         0.000 000 81          MHz T^-1
+shielded helion mag. mom.                              -1.074 553 044 e-26   0.000 000 027 e-26    J T^-1
+shielded helion mag. mom. to Bohr magneton ratio       -1.158 671 471 e-3    0.000 000 014 e-3
+shielded helion mag. mom. to nuclear magneton ratio    -2.127 497 718        0.000 000 025
+shielded helion to proton mag. mom. ratio              -0.761 766 558        0.000 000 011
+shielded helion to shielded proton mag. mom. ratio     -0.761 786 1313       0.000 000 0033
+shielded proton gyromag. ratio                         2.675 153 268 e8      0.000 000 066 e8      s^-1 T^-1
+shielded proton gyromag. ratio over 2 pi               42.576 3866           0.000 0010            MHz T^-1
+shielded proton mag. mom.                              1.410 570 499 e-26    0.000 000 035 e-26    J T^-1
+shielded proton mag. mom. to Bohr magneton ratio       1.520 993 128 e-3     0.000 000 017 e-3
+shielded proton mag. mom. to nuclear magneton ratio    2.792 775 598         0.000 000 030
+speed of light in vacuum                               299 792 458           (exact)               m s^-1
+standard acceleration of gravity                       9.806 65              (exact)               m s^-2
+standard atmosphere                                    101 325               (exact)               Pa
+standard-state pressure                                100 000               (exact)               Pa
+Stefan-Boltzmann constant                              5.670 373 e-8         0.000 021 e-8         W m^-2 K^-4
+tau Compton wavelength                                 0.697 787 e-15        0.000 063 e-15        m
+tau Compton wavelength over 2 pi                       0.111 056 e-15        0.000 010 e-15        m
+tau-electron mass ratio                                3477.15               0.31
+tau mass                                               3.167 47 e-27         0.000 29 e-27         kg
+tau mass energy equivalent                             2.846 78 e-10         0.000 26 e-10         J
+tau mass energy equivalent in MeV                      1776.82               0.16                  MeV
+tau mass in u                                          1.907 49              0.000 17              u
+tau molar mass                                         1.907 49 e-3          0.000 17 e-3          kg mol^-1
+tau-muon mass ratio                                    16.8167               0.0015
+tau-neutron mass ratio                                 1.891 11              0.000 17
+tau-proton mass ratio                                  1.893 72              0.000 17
+Thomson cross section                                  0.665 245 8734 e-28   0.000 000 0013 e-28   m^2
+triton-electron mass ratio                             5496.921 5267         0.000 0050
+triton g factor                                        5.957 924 896         0.000 000 076
+triton mag. mom.                                       1.504 609 447 e-26    0.000 000 038 e-26    J T^-1
+triton mag. mom. to Bohr magneton ratio                1.622 393 657 e-3     0.000 000 021 e-3
+triton mag. mom. to nuclear magneton ratio             2.978 962 448         0.000 000 038
+triton mass                                            5.007 356 30 e-27     0.000 000 22 e-27     kg
+triton mass energy equivalent                          4.500 387 41 e-10     0.000 000 20 e-10     J
+triton mass energy equivalent in MeV                   2808.921 005          0.000 062             MeV
+triton mass in u                                       3.015 500 7134        0.000 000 0025        u
+triton molar mass                                      3.015 500 7134 e-3    0.000 000 0025 e-3    kg mol^-1
+triton-proton mass ratio                               2.993 717 0308        0.000 000 0025
+unified atomic mass unit                               1.660 538 921 e-27    0.000 000 073 e-27    kg
+von Klitzing constant                                  25 812.807 4434       0.000 0084            ohm
+weak mixing angle                                      0.2223                0.0021
+Wien frequency displacement law constant               5.878 9254 e10        0.000 0053 e10        Hz K^-1
+Wien wavelength displacement law constant              2.897 7721 e-3        0.000 0026 e-3        m K"""
+
+
+exact2010 = exact2006
+
+
+txt2014 = """\
+{220} lattice spacing of silicon                       192.015 5714 e-12     0.000 0032 e-12       m
+alpha particle-electron mass ratio                     7294.299 541 36       0.000 000 24
+alpha particle mass                                    6.644 657 230 e-27    0.000 000 082 e-27    kg
+alpha particle mass energy equivalent                  5.971 920 097 e-10    0.000 000 073 e-10    J
+alpha particle mass energy equivalent in MeV           3727.379 378          0.000 023             MeV
+alpha particle mass in u                               4.001 506 179 127     0.000 000 000 063     u
+alpha particle molar mass                              4.001 506 179 127 e-3 0.000 000 000 063 e-3 kg mol^-1
+alpha particle-proton mass ratio                       3.972 599 689 07      0.000 000 000 36
+Angstrom star                                          1.000 014 95 e-10     0.000 000 90 e-10     m
+atomic mass constant                                   1.660 539 040 e-27    0.000 000 020 e-27    kg
+atomic mass constant energy equivalent                 1.492 418 062 e-10    0.000 000 018 e-10    J
+atomic mass constant energy equivalent in MeV          931.494 0954          0.000 0057            MeV
+atomic mass unit-electron volt relationship            931.494 0954 e6       0.000 0057 e6         eV
+atomic mass unit-hartree relationship                  3.423 177 6902 e7     0.000 000 0016 e7     E_h
+atomic mass unit-hertz relationship                    2.252 342 7206 e23    0.000 000 0010 e23    Hz
+atomic mass unit-inverse meter relationship            7.513 006 6166 e14    0.000 000 0034 e14    m^-1
+atomic mass unit-joule relationship                    1.492 418 062 e-10    0.000 000 018 e-10    J
+atomic mass unit-kelvin relationship                   1.080 954 38 e13      0.000 000 62 e13      K
+atomic mass unit-kilogram relationship                 1.660 539 040 e-27    0.000 000 020 e-27    kg
+atomic unit of 1st hyperpolarizability                 3.206 361 329 e-53    0.000 000 020 e-53    C^3 m^3 J^-2
+atomic unit of 2nd hyperpolarizability                 6.235 380 085 e-65    0.000 000 077 e-65    C^4 m^4 J^-3
+atomic unit of action                                  1.054 571 800 e-34    0.000 000 013 e-34    J s
+atomic unit of charge                                  1.602 176 6208 e-19   0.000 000 0098 e-19   C
+atomic unit of charge density                          1.081 202 3770 e12    0.000 000 0067 e12    C m^-3
+atomic unit of current                                 6.623 618 183 e-3     0.000 000 041 e-3     A
+atomic unit of electric dipole mom.                    8.478 353 552 e-30    0.000 000 052 e-30    C m
+atomic unit of electric field                          5.142 206 707 e11     0.000 000 032 e11     V m^-1
+atomic unit of electric field gradient                 9.717 362 356 e21     0.000 000 060 e21     V m^-2
+atomic unit of electric polarizability                 1.648 777 2731 e-41   0.000 000 0011 e-41   C^2 m^2 J^-1
+atomic unit of electric potential                      27.211 386 02         0.000 000 17          V
+atomic unit of electric quadrupole mom.                4.486 551 484 e-40    0.000 000 028 e-40    C m^2
+atomic unit of energy                                  4.359 744 650 e-18    0.000 000 054 e-18    J
+atomic unit of force                                   8.238 723 36 e-8      0.000 000 10 e-8      N
+atomic unit of length                                  0.529 177 210 67 e-10 0.000 000 000 12 e-10 m
+atomic unit of mag. dipole mom.                        1.854 801 999 e-23    0.000 000 011 e-23    J T^-1
+atomic unit of mag. flux density                       2.350 517 550 e5      0.000 000 014 e5      T
+atomic unit of magnetizability                         7.891 036 5886 e-29   0.000 000 0090 e-29   J T^-2
+atomic unit of mass                                    9.109 383 56 e-31     0.000 000 11 e-31     kg
+atomic unit of mom.um                                  1.992 851 882 e-24    0.000 000 024 e-24    kg m s^-1
+atomic unit of permittivity                            1.112 650 056... e-10 (exact)               F m^-1
+atomic unit of time                                    2.418 884 326509e-17  0.000 000 000014e-17  s
+atomic unit of velocity                                2.187 691 262 77 e6   0.000 000 000 50 e6   m s^-1
+Avogadro constant                                      6.022 140 857 e23     0.000 000 074 e23     mol^-1
+Bohr magneton                                          927.400 9994 e-26     0.000 0057 e-26       J T^-1
+Bohr magneton in eV/T                                  5.788 381 8012 e-5    0.000 000 0026 e-5    eV T^-1
+Bohr magneton in Hz/T                                  13.996 245 042 e9     0.000 000 086 e9      Hz T^-1
+Bohr magneton in inverse meters per tesla              46.686 448 14         0.000 000 29          m^-1 T^-1
+Bohr magneton in K/T                                   0.671 714 05          0.000 000 39          K T^-1
+Bohr radius                                            0.529 177 210 67 e-10 0.000 000 000 12 e-10 m
+Boltzmann constant                                     1.380 648 52 e-23     0.000 000 79 e-23     J K^-1
+Boltzmann constant in eV/K                             8.617 3303 e-5        0.000 0050 e-5        eV K^-1
+Boltzmann constant in Hz/K                             2.083 6612 e10        0.000 0012 e10        Hz K^-1
+Boltzmann constant in inverse meters per kelvin        69.503 457            0.000 040             m^-1 K^-1
+characteristic impedance of vacuum                     376.730 313 461...    (exact)               ohm
+classical electron radius                              2.817 940 3227 e-15   0.000 000 0019 e-15   m
+Compton wavelength                                     2.426 310 2367 e-12   0.000 000 0011 e-12   m
+Compton wavelength over 2 pi                           386.159 267 64 e-15   0.000 000 18 e-15     m
+conductance quantum                                    7.748 091 7310 e-5    0.000 000 0018 e-5    S
+conventional value of Josephson constant               483 597.9 e9          (exact)               Hz V^-1
+conventional value of von Klitzing constant            25 812.807            (exact)               ohm
+Cu x unit                                              1.002 076 97 e-13     0.000 000 28 e-13     m
+deuteron-electron mag. mom. ratio                      -4.664 345 535 e-4    0.000 000 026 e-4
+deuteron-electron mass ratio                           3670.482 967 85       0.000 000 13
+deuteron g factor                                      0.857 438 2311        0.000 000 0048
+deuteron mag. mom.                                     0.433 073 5040 e-26   0.000 000 0036 e-26   J T^-1
+deuteron mag. mom. to Bohr magneton ratio              0.466 975 4554 e-3    0.000 000 0026 e-3
+deuteron mag. mom. to nuclear magneton ratio           0.857 438 2311        0.000 000 0048
+deuteron mass                                          3.343 583 719 e-27    0.000 000 041 e-27    kg
+deuteron mass energy equivalent                        3.005 063 183 e-10    0.000 000 037 e-10    J
+deuteron mass energy equivalent in MeV                 1875.612 928          0.000 012             MeV
+deuteron mass in u                                     2.013 553 212 745     0.000 000 000 040     u
+deuteron molar mass                                    2.013 553 212 745 e-3 0.000 000 000 040 e-3 kg mol^-1
+deuteron-neutron mag. mom. ratio                       -0.448 206 52         0.000 000 11
+deuteron-proton mag. mom. ratio                        0.307 012 2077        0.000 000 0015
+deuteron-proton mass ratio                             1.999 007 500 87      0.000 000 000 19
+deuteron rms charge radius                             2.1413 e-15           0.0025 e-15           m
+electric constant                                      8.854 187 817... e-12 (exact)               F m^-1
+electron charge to mass quotient                       -1.758 820 024 e11    0.000 000 011 e11     C kg^-1
+electron-deuteron mag. mom. ratio                      -2143.923 499         0.000 012
+electron-deuteron mass ratio                           2.724 437 107 484 e-4 0.000 000 000 096 e-4
+electron g factor                                      -2.002 319 304 361 82 0.000 000 000 000 52
+electron gyromag. ratio                                1.760 859 644 e11     0.000 000 011 e11     s^-1 T^-1
+electron gyromag. ratio over 2 pi                      28 024.951 64         0.000 17              MHz T^-1
+electron-helion mass ratio                             1.819 543 074 854 e-4 0.000 000 000 088 e-4
+electron mag. mom.                                     -928.476 4620 e-26    0.000 0057 e-26       J T^-1
+electron mag. mom. anomaly                             1.159 652 180 91 e-3  0.000 000 000 26 e-3
+electron mag. mom. to Bohr magneton ratio              -1.001 159 652 180 91 0.000 000 000 000 26
+electron mag. mom. to nuclear magneton ratio           -1838.281 972 34      0.000 000 17
+electron mass                                          9.109 383 56 e-31     0.000 000 11 e-31     kg
+electron mass energy equivalent                        8.187 105 65 e-14     0.000 000 10 e-14     J
+electron mass energy equivalent in MeV                 0.510 998 9461        0.000 000 0031        MeV
+electron mass in u                                     5.485 799 090 70 e-4  0.000 000 000 16 e-4  u
+electron molar mass                                    5.485 799 090 70 e-7  0.000 000 000 16 e-7  kg mol^-1
+electron-muon mag. mom. ratio                          206.766 9880          0.000 0046
+electron-muon mass ratio                               4.836 331 70 e-3      0.000 000 11 e-3
+electron-neutron mag. mom. ratio                       960.920 50            0.000 23
+electron-neutron mass ratio                            5.438 673 4428 e-4    0.000 000 0027 e-4
+electron-proton mag. mom. ratio                        -658.210 6866         0.000 0020
+electron-proton mass ratio                             5.446 170 213 52 e-4  0.000 000 000 52 e-4
+electron-tau mass ratio                                2.875 92 e-4          0.000 26 e-4
+electron to alpha particle mass ratio                  1.370 933 554 798 e-4 0.000 000 000 045 e-4
+electron to shielded helion mag. mom. ratio            864.058 257           0.000 010
+electron to shielded proton mag. mom. ratio            -658.227 5971         0.000 0072
+electron-triton mass ratio                             1.819 200 062 203 e-4 0.000 000 000 084 e-4
+electron volt                                          1.602 176 6208 e-19   0.000 000 0098 e-19   J
+electron volt-atomic mass unit relationship            1.073 544 1105 e-9    0.000 000 0066 e-9    u
+electron volt-hartree relationship                     3.674 932 248 e-2     0.000 000 023 e-2     E_h
+electron volt-hertz relationship                       2.417 989 262 e14     0.000 000 015 e14     Hz
+electron volt-inverse meter relationship               8.065 544 005 e5      0.000 000 050 e5      m^-1
+electron volt-joule relationship                       1.602 176 6208 e-19   0.000 000 0098 e-19   J
+electron volt-kelvin relationship                      1.160 452 21 e4       0.000 000 67 e4       K
+electron volt-kilogram relationship                    1.782 661 907 e-36    0.000 000 011 e-36    kg
+elementary charge                                      1.602 176 6208 e-19   0.000 000 0098 e-19   C
+elementary charge over h                               2.417 989 262 e14     0.000 000 015 e14     A J^-1
+Faraday constant                                       96 485.332 89         0.000 59              C mol^-1
+Faraday constant for conventional electric current     96 485.3251           0.0012                C_90 mol^-1
+Fermi coupling constant                                1.166 3787 e-5        0.000 0006 e-5        GeV^-2
+fine-structure constant                                7.297 352 5664 e-3    0.000 000 0017 e-3
+first radiation constant                               3.741 771 790 e-16    0.000 000 046 e-16    W m^2
+first radiation constant for spectral radiance         1.191 042 953 e-16    0.000 000 015 e-16    W m^2 sr^-1
+hartree-atomic mass unit relationship                  2.921 262 3197 e-8    0.000 000 0013 e-8    u
+hartree-electron volt relationship                     27.211 386 02         0.000 000 17          eV
+Hartree energy                                         4.359 744 650 e-18    0.000 000 054 e-18    J
+Hartree energy in eV                                   27.211 386 02         0.000 000 17          eV
+hartree-hertz relationship                             6.579 683 920 711 e15 0.000 000 000 039 e15 Hz
+hartree-inverse meter relationship                     2.194 746 313 702 e7  0.000 000 000 013 e7  m^-1
+hartree-joule relationship                             4.359 744 650 e-18    0.000 000 054 e-18    J
+hartree-kelvin relationship                            3.157 7513 e5         0.000 0018 e5         K
+hartree-kilogram relationship                          4.850 870 129 e-35    0.000 000 060 e-35    kg
+helion-electron mass ratio                             5495.885 279 22       0.000 000 27
+helion g factor                                        -4.255 250 616        0.000 000 050
+helion mag. mom.                                       -1.074 617 522 e-26   0.000 000 014 e-26    J T^-1
+helion mag. mom. to Bohr magneton ratio                -1.158 740 958 e-3    0.000 000 014 e-3
+helion mag. mom. to nuclear magneton ratio             -2.127 625 308        0.000 000 025
+helion mass                                            5.006 412 700 e-27    0.000 000 062 e-27    kg
+helion mass energy equivalent                          4.499 539 341 e-10    0.000 000 055 e-10    J
+helion mass energy equivalent in MeV                   2808.391 586          0.000 017             MeV
+helion mass in u                                       3.014 932 246 73      0.000 000 000 12      u
+helion molar mass                                      3.014 932 246 73 e-3  0.000 000 000 12 e-3  kg mol^-1
+helion-proton mass ratio                               2.993 152 670 46      0.000 000 000 29
+hertz-atomic mass unit relationship                    4.439 821 6616 e-24   0.000 000 0020 e-24   u
+hertz-electron volt relationship                       4.135 667 662 e-15    0.000 000 025 e-15    eV
+hertz-hartree relationship                             1.5198298460088 e-16  0.0000000000090e-16   E_h
+hertz-inverse meter relationship                       3.335 640 951... e-9  (exact)               m^-1
+hertz-joule relationship                               6.626 070 040 e-34    0.000 000 081 e-34    J
+hertz-kelvin relationship                              4.799 2447 e-11       0.000 0028 e-11       K
+hertz-kilogram relationship                            7.372 497 201 e-51    0.000 000 091 e-51    kg
+inverse fine-structure constant                        137.035 999 139       0.000 000 031
+inverse meter-atomic mass unit relationship            1.331 025 049 00 e-15 0.000 000 000 61 e-15 u
+inverse meter-electron volt relationship               1.239 841 9739 e-6    0.000 000 0076 e-6    eV
+inverse meter-hartree relationship                     4.556 335 252 767 e-8 0.000 000 000 027 e-8 E_h
+inverse meter-hertz relationship                       299 792 458           (exact)               Hz
+inverse meter-joule relationship                       1.986 445 824 e-25    0.000 000 024 e-25    J
+inverse meter-kelvin relationship                      1.438 777 36 e-2      0.000 000 83 e-2      K
+inverse meter-kilogram relationship                    2.210 219 057 e-42    0.000 000 027 e-42    kg
+inverse of conductance quantum                         12 906.403 7278       0.000 0029            ohm
+Josephson constant                                     483 597.8525 e9       0.0030 e9             Hz V^-1
+joule-atomic mass unit relationship                    6.700 535 363 e9      0.000 000 082 e9      u
+joule-electron volt relationship                       6.241 509 126 e18     0.000 000 038 e18     eV
+joule-hartree relationship                             2.293 712 317 e17     0.000 000 028 e17     E_h
+joule-hertz relationship                               1.509 190 205 e33     0.000 000 019 e33     Hz
+joule-inverse meter relationship                       5.034 116 651 e24     0.000 000 062 e24     m^-1
+joule-kelvin relationship                              7.242 9731 e22        0.000 0042 e22        K
+joule-kilogram relationship                            1.112 650 056... e-17 (exact)               kg
+kelvin-atomic mass unit relationship                   9.251 0842 e-14       0.000 0053 e-14       u
+kelvin-electron volt relationship                      8.617 3303 e-5        0.000 0050 e-5        eV
+kelvin-hartree relationship                            3.166 8105 e-6        0.000 0018 e-6        E_h
+kelvin-hertz relationship                              2.083 6612 e10        0.000 0012 e10        Hz
+kelvin-inverse meter relationship                      69.503 457            0.000 040             m^-1
+kelvin-joule relationship                              1.380 648 52 e-23     0.000 000 79 e-23     J
+kelvin-kilogram relationship                           1.536 178 65 e-40     0.000 000 88 e-40     kg
+kilogram-atomic mass unit relationship                 6.022 140 857 e26     0.000 000 074 e26     u
+kilogram-electron volt relationship                    5.609 588 650 e35     0.000 000 034 e35     eV
+kilogram-hartree relationship                          2.061 485 823 e34     0.000 000 025 e34     E_h
+kilogram-hertz relationship                            1.356 392 512 e50     0.000 000 017 e50     Hz
+kilogram-inverse meter relationship                    4.524 438 411 e41     0.000 000 056 e41     m^-1
+kilogram-joule relationship                            8.987 551 787... e16  (exact)               J
+kilogram-kelvin relationship                           6.509 6595 e39        0.000 0037 e39        K
+lattice parameter of silicon                           543.102 0504 e-12     0.000 0089 e-12       m
+Loschmidt constant (273.15 K, 100 kPa)                 2.651 6467 e25        0.000 0015 e25        m^-3
+Loschmidt constant (273.15 K, 101.325 kPa)             2.686 7811 e25        0.000 0015 e25        m^-3
+mag. constant                                          12.566 370 614... e-7 (exact)               N A^-2
+mag. flux quantum                                      2.067 833 831 e-15    0.000 000 013 e-15    Wb
+molar gas constant                                     8.314 4598            0.000 0048            J mol^-1 K^-1
+molar mass constant                                    1 e-3                 (exact)               kg mol^-1
+molar mass of carbon-12                                12 e-3                (exact)               kg mol^-1
+molar Planck constant                                  3.990 312 7110 e-10   0.000 000 0018 e-10   J s mol^-1
+molar Planck constant times c                          0.119 626 565 582     0.000 000 000 054     J m mol^-1
+molar volume of ideal gas (273.15 K, 100 kPa)          22.710 947 e-3        0.000 013 e-3         m^3 mol^-1
+molar volume of ideal gas (273.15 K, 101.325 kPa)      22.413 962 e-3        0.000 013 e-3         m^3 mol^-1
+molar volume of silicon                                12.058 832 14 e-6     0.000 000 61 e-6      m^3 mol^-1
+Mo x unit                                              1.002 099 52 e-13     0.000 000 53 e-13     m
+muon Compton wavelength                                11.734 441 11 e-15    0.000 000 26 e-15     m
+muon Compton wavelength over 2 pi                      1.867 594 308 e-15    0.000 000 042 e-15    m
+muon-electron mass ratio                               206.768 2826          0.000 0046
+muon g factor                                          -2.002 331 8418       0.000 000 0013
+muon mag. mom.                                         -4.490 448 26 e-26    0.000 000 10 e-26     J T^-1
+muon mag. mom. anomaly                                 1.165 920 89 e-3      0.000 000 63 e-3
+muon mag. mom. to Bohr magneton ratio                  -4.841 970 48 e-3     0.000 000 11 e-3
+muon mag. mom. to nuclear magneton ratio               -8.890 597 05         0.000 000 20
+muon mass                                              1.883 531 594 e-28    0.000 000 048 e-28    kg
+muon mass energy equivalent                            1.692 833 774 e-11    0.000 000 043 e-11    J
+muon mass energy equivalent in MeV                     105.658 3745          0.000 0024            MeV
+muon mass in u                                         0.113 428 9257        0.000 000 0025        u
+muon molar mass                                        0.113 428 9257 e-3    0.000 000 0025 e-3    kg mol^-1
+muon-neutron mass ratio                                0.112 454 5167        0.000 000 0025
+muon-proton mag. mom. ratio                            -3.183 345 142        0.000 000 071
+muon-proton mass ratio                                 0.112 609 5262        0.000 000 0025
+muon-tau mass ratio                                    5.946 49 e-2          0.000 54 e-2
+natural unit of action                                 1.054 571 800 e-34    0.000 000 013 e-34    J s
+natural unit of action in eV s                         6.582 119 514 e-16    0.000 000 040 e-16    eV s
+natural unit of energy                                 8.187 105 65 e-14     0.000 000 10 e-14     J
+natural unit of energy in MeV                          0.510 998 9461        0.000 000 0031        MeV
+natural unit of length                                 386.159 267 64 e-15   0.000 000 18 e-15     m
+natural unit of mass                                   9.109 383 56 e-31     0.000 000 11 e-31     kg
+natural unit of mom.um                                 2.730 924 488 e-22    0.000 000 034 e-22    kg m s^-1
+natural unit of mom.um in MeV/c                        0.510 998 9461        0.000 000 0031        MeV/c
+natural unit of time                                   1.288 088 667 12 e-21 0.000 000 000 58 e-21 s
+natural unit of velocity                               299 792 458           (exact)               m s^-1
+neutron Compton wavelength                             1.319 590 904 81 e-15 0.000 000 000 88 e-15 m
+neutron Compton wavelength over 2 pi                   0.210 019 415 36 e-15 0.000 000 000 14 e-15 m
+neutron-electron mag. mom. ratio                       1.040 668 82 e-3      0.000 000 25 e-3
+neutron-electron mass ratio                            1838.683 661 58       0.000 000 90
+neutron g factor                                       -3.826 085 45         0.000 000 90
+neutron gyromag. ratio                                 1.832 471 72 e8       0.000 000 43 e8       s^-1 T^-1
+neutron gyromag. ratio over 2 pi                       29.164 6933           0.000 0069            MHz T^-1
+neutron mag. mom.                                      -0.966 236 50 e-26    0.000 000 23 e-26     J T^-1
+neutron mag. mom. to Bohr magneton ratio               -1.041 875 63 e-3     0.000 000 25 e-3
+neutron mag. mom. to nuclear magneton ratio            -1.913 042 73         0.000 000 45
+neutron mass                                           1.674 927 471 e-27    0.000 000 021 e-27    kg
+neutron mass energy equivalent                         1.505 349 739 e-10    0.000 000 019 e-10    J
+neutron mass energy equivalent in MeV                  939.565 4133          0.000 0058            MeV
+neutron mass in u                                      1.008 664 915 88      0.000 000 000 49      u
+neutron molar mass                                     1.008 664 915 88 e-3  0.000 000 000 49 e-3  kg mol^-1
+neutron-muon mass ratio                                8.892 484 08          0.000 000 20
+neutron-proton mag. mom. ratio                         -0.684 979 34         0.000 000 16
+neutron-proton mass difference                         2.305 573 77 e-30     0.000 000 85 e-30
+neutron-proton mass difference energy equivalent       2.072 146 37 e-13     0.000 000 76 e-13
+neutron-proton mass difference energy equivalent in MeV 1.293 332 05         0.000 000 48
+neutron-proton mass difference in u                    0.001 388 449 00      0.000 000 000 51
+neutron-proton mass ratio                              1.001 378 418 98      0.000 000 000 51
+neutron-tau mass ratio                                 0.528 790             0.000 048
+neutron to shielded proton mag. mom. ratio             -0.684 996 94         0.000 000 16
+Newtonian constant of gravitation                      6.674 08 e-11         0.000 31 e-11         m^3 kg^-1 s^-2
+Newtonian constant of gravitation over h-bar c         6.708 61 e-39         0.000 31 e-39         (GeV/c^2)^-2
+nuclear magneton                                       5.050 783 699 e-27    0.000 000 031 e-27    J T^-1
+nuclear magneton in eV/T                               3.152 451 2550 e-8    0.000 000 0015 e-8    eV T^-1
+nuclear magneton in inverse meters per tesla           2.542 623 432 e-2     0.000 000 016 e-2     m^-1 T^-1
+nuclear magneton in K/T                                3.658 2690 e-4        0.000 0021 e-4        K T^-1
+nuclear magneton in MHz/T                              7.622 593 285         0.000 000 047         MHz T^-1
+Planck constant                                        6.626 070 040 e-34    0.000 000 081 e-34    J s
+Planck constant in eV s                                4.135 667 662 e-15    0.000 000 025 e-15    eV s
+Planck constant over 2 pi                              1.054 571 800 e-34    0.000 000 013 e-34    J s
+Planck constant over 2 pi in eV s                      6.582 119 514 e-16    0.000 000 040 e-16    eV s
+Planck constant over 2 pi times c in MeV fm            197.326 9788          0.000 0012            MeV fm
+Planck length                                          1.616 229 e-35        0.000 038 e-35        m
+Planck mass                                            2.176 470 e-8         0.000 051 e-8         kg
+Planck mass energy equivalent in GeV                   1.220 910 e19         0.000 029 e19         GeV
+Planck temperature                                     1.416 808 e32         0.000 033 e32         K
+Planck time                                            5.391 16 e-44         0.000 13 e-44         s
+proton charge to mass quotient                         9.578 833 226 e7      0.000 000 059 e7      C kg^-1
+proton Compton wavelength                              1.321 409 853 96 e-15 0.000 000 000 61 e-15 m
+proton Compton wavelength over 2 pi                    0.210 308910109e-15   0.000 000 000097e-15  m
+proton-electron mass ratio                             1836.152 673 89       0.000 000 17
+proton g factor                                        5.585 694 702         0.000 000 017
+proton gyromag. ratio                                  2.675 221 900 e8      0.000 000 018 e8      s^-1 T^-1
+proton gyromag. ratio over 2 pi                        42.577 478 92         0.000 000 29          MHz T^-1
+proton mag. mom.                                       1.410 606 7873 e-26   0.000 000 0097 e-26   J T^-1
+proton mag. mom. to Bohr magneton ratio                1.521 032 2053 e-3    0.000 000 0046 e-3
+proton mag. mom. to nuclear magneton ratio             2.792 847 3508        0.000 000 0085
+proton mag. shielding correction                       25.691 e-6            0.011 e-6
+proton mass                                            1.672 621 898 e-27    0.000 000 021 e-27    kg
+proton mass energy equivalent                          1.503 277 593 e-10    0.000 000 018 e-10    J
+proton mass energy equivalent in MeV                   938.272 0813          0.000 0058            MeV
+proton mass in u                                       1.007 276 466 879     0.000 000 000 091     u
+proton molar mass                                      1.007 276 466 879 e-3 0.000 000 000 091 e-3 kg mol^-1
+proton-muon mass ratio                                 8.880 243 38          0.000 000 20
+proton-neutron mag. mom. ratio                         -1.459 898 05         0.000 000 34
+proton-neutron mass ratio                              0.998 623 478 44      0.000 000 000 51
+proton rms charge radius                               0.8751 e-15           0.0061 e-15           m
+proton-tau mass ratio                                  0.528 063             0.000 048
+quantum of circulation                                 3.636 947 5486 e-4    0.000 000 0017 e-4    m^2 s^-1
+quantum of circulation times 2                         7.273 895 0972 e-4    0.000 000 0033 e-4    m^2 s^-1
+Rydberg constant                                       10 973 731.568 508    0.000 065             m^-1
+Rydberg constant times c in Hz                         3.289 841 960 355 e15 0.000 000 000 019 e15 Hz
+Rydberg constant times hc in eV                        13.605 693 009        0.000 000 084         eV
+Rydberg constant times hc in J                         2.179 872 325 e-18    0.000 000 027 e-18    J
+Sackur-Tetrode constant (1 K, 100 kPa)                 -1.151 7084           0.000 0014
+Sackur-Tetrode constant (1 K, 101.325 kPa)             -1.164 8714           0.000 0014
+second radiation constant                              1.438 777 36 e-2      0.000 000 83 e-2      m K
+shielded helion gyromag. ratio                         2.037 894 585 e8      0.000 000 027 e8      s^-1 T^-1
+shielded helion gyromag. ratio over 2 pi               32.434 099 66         0.000 000 43          MHz T^-1
+shielded helion mag. mom.                              -1.074 553 080 e-26   0.000 000 014 e-26    J T^-1
+shielded helion mag. mom. to Bohr magneton ratio       -1.158 671 471 e-3    0.000 000 014 e-3
+shielded helion mag. mom. to nuclear magneton ratio    -2.127 497 720        0.000 000 025
+shielded helion to proton mag. mom. ratio              -0.761 766 5603       0.000 000 0092
+shielded helion to shielded proton mag. mom. ratio     -0.761 786 1313       0.000 000 0033
+shielded proton gyromag. ratio                         2.675 153 171 e8      0.000 000 033 e8      s^-1 T^-1
+shielded proton gyromag. ratio over 2 pi               42.576 385 07         0.000 000 53          MHz T^-1
+shielded proton mag. mom.                              1.410 570 547 e-26    0.000 000 018 e-26    J T^-1
+shielded proton mag. mom. to Bohr magneton ratio       1.520 993 128 e-3     0.000 000 017 e-3
+shielded proton mag. mom. to nuclear magneton ratio    2.792 775 600         0.000 000 030
+speed of light in vacuum                               299 792 458           (exact)               m s^-1
+standard acceleration of gravity                       9.806 65              (exact)               m s^-2
+standard atmosphere                                    101 325               (exact)               Pa
+standard-state pressure                                100 000               (exact)               Pa
+Stefan-Boltzmann constant                              5.670 367 e-8         0.000 013 e-8         W m^-2 K^-4
+tau Compton wavelength                                 0.697 787 e-15        0.000 063 e-15        m
+tau Compton wavelength over 2 pi                       0.111 056 e-15        0.000 010 e-15        m
+tau-electron mass ratio                                3477.15               0.31
+tau mass                                               3.167 47 e-27         0.000 29 e-27         kg
+tau mass energy equivalent                             2.846 78 e-10         0.000 26 e-10         J
+tau mass energy equivalent in MeV                      1776.82               0.16                  MeV
+tau mass in u                                          1.907 49              0.000 17              u
+tau molar mass                                         1.907 49 e-3          0.000 17 e-3          kg mol^-1
+tau-muon mass ratio                                    16.8167               0.0015
+tau-neutron mass ratio                                 1.891 11              0.000 17
+tau-proton mass ratio                                  1.893 72              0.000 17
+Thomson cross section                                  0.665 245 871 58 e-28 0.000 000 000 91 e-28 m^2
+triton-electron mass ratio                             5496.921 535 88       0.000 000 26
+triton g factor                                        5.957 924 920         0.000 000 028
+triton mag. mom.                                       1.504 609 503 e-26    0.000 000 012 e-26    J T^-1
+triton mag. mom. to Bohr magneton ratio                1.622 393 6616 e-3    0.000 000 0076 e-3
+triton mag. mom. to nuclear magneton ratio             2.978 962 460         0.000 000 014
+triton mass                                            5.007 356 665 e-27    0.000 000 062 e-27    kg
+triton mass energy equivalent                          4.500 387 735 e-10    0.000 000 055 e-10    J
+triton mass energy equivalent in MeV                   2808.921 112          0.000 017             MeV
+triton mass in u                                       3.015 500 716 32      0.000 000 000 11      u
+triton molar mass                                      3.015 500 716 32 e-3  0.000 000 000 11 e-3  kg mol^-1
+triton-proton mass ratio                               2.993 717 033 48      0.000 000 000 22
+unified atomic mass unit                               1.660 539 040 e-27    0.000 000 020 e-27    kg
+von Klitzing constant                                  25 812.807 4555       0.000 0059            ohm
+weak mixing angle                                      0.2223                0.0021
+Wien frequency displacement law constant               5.878 9238 e10        0.000 0034 e10        Hz K^-1
+Wien wavelength displacement law constant              2.897 7729 e-3        0.000 0017 e-3        m K"""
+
+
+exact2014 = exact2010
+
+
+txt2018 = """\
+alpha particle-electron mass ratio                          7294.299 541 42          0.000 000 24
+alpha particle mass                                         6.644 657 3357 e-27      0.000 000 0020 e-27      kg
+alpha particle mass energy equivalent                       5.971 920 1914 e-10      0.000 000 0018 e-10      J
+alpha particle mass energy equivalent in MeV                3727.379 4066            0.000 0011               MeV
+alpha particle mass in u                                    4.001 506 179 127        0.000 000 000 063        u
+alpha particle molar mass                                   4.001 506 1777 e-3       0.000 000 0012 e-3       kg mol^-1
+alpha particle-proton mass ratio                            3.972 599 690 09         0.000 000 000 22
+alpha particle relative atomic mass                         4.001 506 179 127        0.000 000 000 063
+Angstrom star                                               1.000 014 95 e-10        0.000 000 90 e-10        m
+atomic mass constant                                        1.660 539 066 60 e-27    0.000 000 000 50 e-27    kg
+atomic mass constant energy equivalent                      1.492 418 085 60 e-10    0.000 000 000 45 e-10    J
+atomic mass constant energy equivalent in MeV               931.494 102 42           0.000 000 28             MeV
+atomic mass unit-electron volt relationship                 9.314 941 0242 e8        0.000 000 0028 e8        eV
+atomic mass unit-hartree relationship                       3.423 177 6874 e7        0.000 000 0010 e7        E_h
+atomic mass unit-hertz relationship                         2.252 342 718 71 e23     0.000 000 000 68 e23     Hz
+atomic mass unit-inverse meter relationship                 7.513 006 6104 e14       0.000 000 0023 e14       m^-1
+atomic mass unit-joule relationship                         1.492 418 085 60 e-10    0.000 000 000 45 e-10    J
+atomic mass unit-kelvin relationship                        1.080 954 019 16 e13     0.000 000 000 33 e13     K
+atomic mass unit-kilogram relationship                      1.660 539 066 60 e-27    0.000 000 000 50 e-27    kg
+atomic unit of 1st hyperpolarizability                      3.206 361 3061 e-53      0.000 000 0015 e-53      C^3 m^3 J^-2
+atomic unit of 2nd hyperpolarizability                      6.235 379 9905 e-65      0.000 000 0038 e-65      C^4 m^4 J^-3
+atomic unit of action                                       1.054 571 817... e-34    (exact)                  J s
+atomic unit of charge                                       1.602 176 634 e-19       (exact)                  C
+atomic unit of charge density                               1.081 202 384 57 e12     0.000 000 000 49 e12     C m^-3
+atomic unit of current                                      6.623 618 237 510 e-3    0.000 000 000 013 e-3    A
+atomic unit of electric dipole mom.                         8.478 353 6255 e-30      0.000 000 0013 e-30      C m
+atomic unit of electric field                               5.142 206 747 63 e11     0.000 000 000 78 e11     V m^-1
+atomic unit of electric field gradient                      9.717 362 4292 e21       0.000 000 0029 e21       V m^-2
+atomic unit of electric polarizability                      1.648 777 274 36 e-41    0.000 000 000 50 e-41    C^2 m^2 J^-1
+atomic unit of electric potential                           27.211 386 245 988       0.000 000 000 053        V
+atomic unit of electric quadrupole mom.                     4.486 551 5246 e-40      0.000 000 0014 e-40      C m^2
+atomic unit of energy                                       4.359 744 722 2071 e-18  0.000 000 000 0085 e-18  J
+atomic unit of force                                        8.238 723 4983 e-8       0.000 000 0012 e-8       N
+atomic unit of length                                       5.291 772 109 03 e-11    0.000 000 000 80 e-11    m
+atomic unit of mag. dipole mom.                             1.854 802 015 66 e-23    0.000 000 000 56 e-23    J T^-1
+atomic unit of mag. flux density                            2.350 517 567 58 e5      0.000 000 000 71 e5      T
+atomic unit of magnetizability                              7.891 036 6008 e-29      0.000 000 0048 e-29      J T^-2
+atomic unit of mass                                         9.109 383 7015 e-31      0.000 000 0028 e-31      kg
+atomic unit of momentum                                     1.992 851 914 10 e-24    0.000 000 000 30 e-24    kg m s^-1
+atomic unit of permittivity                                 1.112 650 055 45 e-10    0.000 000 000 17 e-10    F m^-1
+atomic unit of time                                         2.418 884 326 5857 e-17  0.000 000 000 0047 e-17  s
+atomic unit of velocity                                     2.187 691 263 64 e6      0.000 000 000 33 e6      m s^-1
+Avogadro constant                                           6.022 140 76 e23         (exact)                  mol^-1
+Bohr magneton                                               9.274 010 0783 e-24      0.000 000 0028 e-24      J T^-1
+Bohr magneton in eV/T                                       5.788 381 8060 e-5       0.000 000 0017 e-5       eV T^-1
+Bohr magneton in Hz/T                                       1.399 624 493 61 e10     0.000 000 000 42 e10     Hz T^-1
+Bohr magneton in inverse meter per tesla                    46.686 447 783           0.000 000 014            m^-1 T^-1
+Bohr magneton in K/T                                        0.671 713 815 63         0.000 000 000 20         K T^-1
+Bohr radius                                                 5.291 772 109 03 e-11    0.000 000 000 80 e-11    m
+Boltzmann constant                                          1.380 649 e-23           (exact)                  J K^-1
+Boltzmann constant in eV/K                                  8.617 333 262... e-5     (exact)                  eV K^-1
+Boltzmann constant in Hz/K                                  2.083 661 912... e10     (exact)                  Hz K^-1
+Boltzmann constant in inverse meter per kelvin              69.503 480 04...         (exact)                  m^-1 K^-1
+characteristic impedance of vacuum                          376.730 313 668          0.000 000 057            ohm
+classical electron radius                                   2.817 940 3262 e-15      0.000 000 0013 e-15      m
+Compton wavelength                                          2.426 310 238 67 e-12    0.000 000 000 73 e-12    m
+conductance quantum                                         7.748 091 729... e-5     (exact)                  S
+conventional value of ampere-90                             1.000 000 088 87...      (exact)                  A
+conventional value of coulomb-90                            1.000 000 088 87...      (exact)                  C
+conventional value of farad-90                              0.999 999 982 20...      (exact)                  F
+conventional value of henry-90                              1.000 000 017 79...      (exact)                  H
+conventional value of Josephson constant                    483 597.9 e9             (exact)                  Hz V^-1
+conventional value of ohm-90                                1.000 000 017 79...      (exact)                  ohm
+conventional value of volt-90                               1.000 000 106 66...      (exact)                  V
+conventional value of von Klitzing constant                 25 812.807               (exact)                  ohm
+conventional value of watt-90                               1.000 000 195 53...      (exact)                  W
+Cu x unit                                                   1.002 076 97 e-13        0.000 000 28 e-13        m
+deuteron-electron mag. mom. ratio                           -4.664 345 551 e-4       0.000 000 012 e-4
+deuteron-electron mass ratio                                3670.482 967 88          0.000 000 13
+deuteron g factor                                           0.857 438 2338           0.000 000 0022
+deuteron mag. mom.                                          4.330 735 094 e-27       0.000 000 011 e-27       J T^-1
+deuteron mag. mom. to Bohr magneton ratio                   4.669 754 570 e-4        0.000 000 012 e-4
+deuteron mag. mom. to nuclear magneton ratio                0.857 438 2338           0.000 000 0022
+deuteron mass                                               3.343 583 7724 e-27      0.000 000 0010 e-27      kg
+deuteron mass energy equivalent                             3.005 063 231 02 e-10    0.000 000 000 91 e-10    J
+deuteron mass energy equivalent in MeV                      1875.612 942 57          0.000 000 57             MeV
+deuteron mass in u                                          2.013 553 212 745        0.000 000 000 040        u
+deuteron molar mass                                         2.013 553 212 05 e-3     0.000 000 000 61 e-3     kg mol^-1
+deuteron-neutron mag. mom. ratio                            -0.448 206 53            0.000 000 11
+deuteron-proton mag. mom. ratio                             0.307 012 209 39         0.000 000 000 79
+deuteron-proton mass ratio                                  1.999 007 501 39         0.000 000 000 11
+deuteron relative atomic mass                               2.013 553 212 745        0.000 000 000 040
+deuteron rms charge radius                                  2.127 99 e-15            0.000 74 e-15            m
+electron charge to mass quotient                            -1.758 820 010 76 e11    0.000 000 000 53 e11     C kg^-1
+electron-deuteron mag. mom. ratio                           -2143.923 4915           0.000 0056
+electron-deuteron mass ratio                                2.724 437 107 462 e-4    0.000 000 000 096 e-4
+electron g factor                                           -2.002 319 304 362 56    0.000 000 000 000 35
+electron gyromag. ratio                                     1.760 859 630 23 e11     0.000 000 000 53 e11     s^-1 T^-1
+electron gyromag. ratio in MHz/T                            28 024.951 4242          0.000 0085               MHz T^-1
+electron-helion mass ratio                                  1.819 543 074 573 e-4    0.000 000 000 079 e-4
+electron mag. mom.                                          -9.284 764 7043 e-24     0.000 000 0028 e-24      J T^-1
+electron mag. mom. anomaly                                  1.159 652 181 28 e-3     0.000 000 000 18 e-3
+electron mag. mom. to Bohr magneton ratio                   -1.001 159 652 181 28    0.000 000 000 000 18
+electron mag. mom. to nuclear magneton ratio                -1838.281 971 88         0.000 000 11
+electron mass                                               9.109 383 7015 e-31      0.000 000 0028 e-31      kg
+electron mass energy equivalent                             8.187 105 7769 e-14      0.000 000 0025 e-14      J
+electron mass energy equivalent in MeV                      0.510 998 950 00         0.000 000 000 15         MeV
+electron mass in u                                          5.485 799 090 65 e-4     0.000 000 000 16 e-4     u
+electron molar mass                                         5.485 799 0888 e-7       0.000 000 0017 e-7       kg mol^-1
+electron-muon mag. mom. ratio                               206.766 9883             0.000 0046
+electron-muon mass ratio                                    4.836 331 69 e-3         0.000 000 11 e-3
+electron-neutron mag. mom. ratio                            960.920 50               0.000 23
+electron-neutron mass ratio                                 5.438 673 4424 e-4       0.000 000 0026 e-4
+electron-proton mag. mom. ratio                             -658.210 687 89          0.000 000 20
+electron-proton mass ratio                                  5.446 170 214 87 e-4     0.000 000 000 33 e-4
+electron relative atomic mass                               5.485 799 090 65 e-4     0.000 000 000 16 e-4
+electron-tau mass ratio                                     2.875 85 e-4             0.000 19 e-4
+electron to alpha particle mass ratio                       1.370 933 554 787 e-4    0.000 000 000 045 e-4
+electron to shielded helion mag. mom. ratio                 864.058 257              0.000 010
+electron to shielded proton mag. mom. ratio                 -658.227 5971            0.000 0072
+electron-triton mass ratio                                  1.819 200 062 251 e-4    0.000 000 000 090 e-4
+electron volt                                               1.602 176 634 e-19       (exact)                  J
+electron volt-atomic mass unit relationship                 1.073 544 102 33 e-9     0.000 000 000 32 e-9     u
+electron volt-hartree relationship                          3.674 932 217 5655 e-2   0.000 000 000 0071 e-2   E_h
+electron volt-hertz relationship                            2.417 989 242... e14     (exact)                  Hz
+electron volt-inverse meter relationship                    8.065 543 937... e5      (exact)                  m^-1
+electron volt-joule relationship                            1.602 176 634 e-19       (exact)                  J
+electron volt-kelvin relationship                           1.160 451 812... e4      (exact)                  K
+electron volt-kilogram relationship                         1.782 661 921... e-36    (exact)                  kg
+elementary charge                                           1.602 176 634 e-19       (exact)                  C
+elementary charge over h-bar                                1.519 267 447... e15     (exact)                  A J^-1
+Faraday constant                                            96 485.332 12...         (exact)                  C mol^-1
+Fermi coupling constant                                     1.166 3787 e-5           0.000 0006 e-5           GeV^-2
+fine-structure constant                                     7.297 352 5693 e-3       0.000 000 0011 e-3
+first radiation constant                                    3.741 771 852... e-16    (exact)                  W m^2
+first radiation constant for spectral radiance              1.191 042 972... e-16    (exact)                  W m^2 sr^-1
+hartree-atomic mass unit relationship                       2.921 262 322 05 e-8     0.000 000 000 88 e-8     u
+hartree-electron volt relationship                          27.211 386 245 988       0.000 000 000 053        eV
+Hartree energy                                              4.359 744 722 2071 e-18  0.000 000 000 0085 e-18  J
+Hartree energy in eV                                        27.211 386 245 988       0.000 000 000 053        eV
+hartree-hertz relationship                                  6.579 683 920 502 e15    0.000 000 000 013 e15    Hz
+hartree-inverse meter relationship                          2.194 746 313 6320 e7    0.000 000 000 0043 e7    m^-1
+hartree-joule relationship                                  4.359 744 722 2071 e-18  0.000 000 000 0085 e-18  J
+hartree-kelvin relationship                                 3.157 750 248 0407 e5    0.000 000 000 0061 e5    K
+hartree-kilogram relationship                               4.850 870 209 5432 e-35  0.000 000 000 0094 e-35  kg
+helion-electron mass ratio                                  5495.885 280 07          0.000 000 24
+helion g factor                                             -4.255 250 615           0.000 000 050
+helion mag. mom.                                            -1.074 617 532 e-26      0.000 000 013 e-26       J T^-1
+helion mag. mom. to Bohr magneton ratio                     -1.158 740 958 e-3       0.000 000 014 e-3
+helion mag. mom. to nuclear magneton ratio                  -2.127 625 307           0.000 000 025
+helion mass                                                 5.006 412 7796 e-27      0.000 000 0015 e-27      kg
+helion mass energy equivalent                               4.499 539 4125 e-10      0.000 000 0014 e-10      J
+helion mass energy equivalent in MeV                        2808.391 607 43          0.000 000 85             MeV
+helion mass in u                                            3.014 932 247 175        0.000 000 000 097        u
+helion molar mass                                           3.014 932 246 13 e-3     0.000 000 000 91 e-3     kg mol^-1
+helion-proton mass ratio                                    2.993 152 671 67         0.000 000 000 13
+helion relative atomic mass                                 3.014 932 247 175        0.000 000 000 097
+helion shielding shift                                      5.996 743 e-5            0.000 010 e-5
+hertz-atomic mass unit relationship                         4.439 821 6652 e-24      0.000 000 0013 e-24      u
+hertz-electron volt relationship                            4.135 667 696... e-15    (exact)                  eV
+hertz-hartree relationship                                  1.519 829 846 0570 e-16  0.000 000 000 0029 e-16  E_h
+hertz-inverse meter relationship                            3.335 640 951... e-9     (exact)                  m^-1
+hertz-joule relationship                                    6.626 070 15 e-34        (exact)                  J
+hertz-kelvin relationship                                   4.799 243 073... e-11    (exact)                  K
+hertz-kilogram relationship                                 7.372 497 323... e-51    (exact)                  kg
+hyperfine transition frequency of Cs-133                    9 192 631 770            (exact)                  Hz
+inverse fine-structure constant                             137.035 999 084          0.000 000 021
+inverse meter-atomic mass unit relationship                 1.331 025 050 10 e-15    0.000 000 000 40 e-15    u
+inverse meter-electron volt relationship                    1.239 841 984... e-6     (exact)                  eV
+inverse meter-hartree relationship                          4.556 335 252 9120 e-8   0.000 000 000 0088 e-8   E_h
+inverse meter-hertz relationship                            299 792 458              (exact)                  Hz
+inverse meter-joule relationship                            1.986 445 857... e-25    (exact)                  J
+inverse meter-kelvin relationship                           1.438 776 877... e-2     (exact)                  K
+inverse meter-kilogram relationship                         2.210 219 094... e-42    (exact)                  kg
+inverse of conductance quantum                              12 906.403 72...         (exact)                  ohm
+Josephson constant                                          483 597.848 4... e9      (exact)                  Hz V^-1
+joule-atomic mass unit relationship                         6.700 535 2565 e9        0.000 000 0020 e9        u
+joule-electron volt relationship                            6.241 509 074... e18     (exact)                  eV
+joule-hartree relationship                                  2.293 712 278 3963 e17   0.000 000 000 0045 e17   E_h
+joule-hertz relationship                                    1.509 190 179... e33     (exact)                  Hz
+joule-inverse meter relationship                            5.034 116 567... e24     (exact)                  m^-1
+joule-kelvin relationship                                   7.242 970 516... e22     (exact)                  K
+joule-kilogram relationship                                 1.112 650 056... e-17    (exact)                  kg
+kelvin-atomic mass unit relationship                        9.251 087 3014 e-14      0.000 000 0028 e-14      u
+kelvin-electron volt relationship                           8.617 333 262... e-5     (exact)                  eV
+kelvin-hartree relationship                                 3.166 811 563 4556 e-6   0.000 000 000 0061 e-6   E_h
+kelvin-hertz relationship                                   2.083 661 912... e10     (exact)                  Hz
+kelvin-inverse meter relationship                           69.503 480 04...         (exact)                  m^-1
+kelvin-joule relationship                                   1.380 649 e-23           (exact)                  J
+kelvin-kilogram relationship                                1.536 179 187... e-40    (exact)                  kg
+kilogram-atomic mass unit relationship                      6.022 140 7621 e26       0.000 000 0018 e26       u
+kilogram-electron volt relationship                         5.609 588 603... e35     (exact)                  eV
+kilogram-hartree relationship                               2.061 485 788 7409 e34   0.000 000 000 0040 e34   E_h
+kilogram-hertz relationship                                 1.356 392 489... e50     (exact)                  Hz
+kilogram-inverse meter relationship                         4.524 438 335... e41     (exact)                  m^-1
+kilogram-joule relationship                                 8.987 551 787... e16     (exact)                  J
+kilogram-kelvin relationship                                6.509 657 260... e39     (exact)                  K
+lattice parameter of silicon                                5.431 020 511 e-10       0.000 000 089 e-10       m
+lattice spacing of ideal Si (220)                           1.920 155 716 e-10       0.000 000 032 e-10       m
+Loschmidt constant (273.15 K, 100 kPa)                      2.651 645 804... e25     (exact)                  m^-3
+Loschmidt constant (273.15 K, 101.325 kPa)                  2.686 780 111... e25     (exact)                  m^-3
+luminous efficacy                                           683                      (exact)                  lm W^-1
+mag. flux quantum                                           2.067 833 848... e-15    (exact)                  Wb
+molar gas constant                                          8.314 462 618...         (exact)                  J mol^-1 K^-1
+molar mass constant                                         0.999 999 999 65 e-3     0.000 000 000 30 e-3     kg mol^-1
+molar mass of carbon-12                                     11.999 999 9958 e-3      0.000 000 0036 e-3       kg mol^-1
+molar Planck constant                                       3.990 312 712... e-10    (exact)                  J Hz^-1 mol^-1
+molar volume of ideal gas (273.15 K, 100 kPa)               22.710 954 64... e-3     (exact)                  m^3 mol^-1
+molar volume of ideal gas (273.15 K, 101.325 kPa)           22.413 969 54... e-3     (exact)                  m^3 mol^-1
+molar volume of silicon                                     1.205 883 199 e-5        0.000 000 060 e-5        m^3 mol^-1
+Mo x unit                                                   1.002 099 52 e-13        0.000 000 53 e-13        m
+muon Compton wavelength                                     1.173 444 110 e-14       0.000 000 026 e-14       m
+muon-electron mass ratio                                    206.768 2830             0.000 0046
+muon g factor                                               -2.002 331 8418          0.000 000 0013
+muon mag. mom.                                              -4.490 448 30 e-26       0.000 000 10 e-26        J T^-1
+muon mag. mom. anomaly                                      1.165 920 89 e-3         0.000 000 63 e-3
+muon mag. mom. to Bohr magneton ratio                       -4.841 970 47 e-3        0.000 000 11 e-3
+muon mag. mom. to nuclear magneton ratio                    -8.890 597 03            0.000 000 20
+muon mass                                                   1.883 531 627 e-28       0.000 000 042 e-28       kg
+muon mass energy equivalent                                 1.692 833 804 e-11       0.000 000 038 e-11       J
+muon mass energy equivalent in MeV                          105.658 3755             0.000 0023               MeV
+muon mass in u                                              0.113 428 9259           0.000 000 0025           u
+muon molar mass                                             1.134 289 259 e-4        0.000 000 025 e-4        kg mol^-1
+muon-neutron mass ratio                                     0.112 454 5170           0.000 000 0025
+muon-proton mag. mom. ratio                                 -3.183 345 142           0.000 000 071
+muon-proton mass ratio                                      0.112 609 5264           0.000 000 0025
+muon-tau mass ratio                                         5.946 35 e-2             0.000 40 e-2
+natural unit of action                                      1.054 571 817... e-34    (exact)                  J s
+natural unit of action in eV s                              6.582 119 569... e-16    (exact)                  eV s
+natural unit of energy                                      8.187 105 7769 e-14      0.000 000 0025 e-14      J
+natural unit of energy in MeV                               0.510 998 950 00         0.000 000 000 15         MeV
+natural unit of length                                      3.861 592 6796 e-13      0.000 000 0012 e-13      m
+natural unit of mass                                        9.109 383 7015 e-31      0.000 000 0028 e-31      kg
+natural unit of momentum                                    2.730 924 530 75 e-22    0.000 000 000 82 e-22    kg m s^-1
+natural unit of momentum in MeV/c                           0.510 998 950 00         0.000 000 000 15         MeV/c
+natural unit of time                                        1.288 088 668 19 e-21    0.000 000 000 39 e-21    s
+natural unit of velocity                                    299 792 458              (exact)                  m s^-1
+neutron Compton wavelength                                  1.319 590 905 81 e-15    0.000 000 000 75 e-15    m
+neutron-electron mag. mom. ratio                            1.040 668 82 e-3         0.000 000 25 e-3
+neutron-electron mass ratio                                 1838.683 661 73          0.000 000 89
+neutron g factor                                            -3.826 085 45            0.000 000 90
+neutron gyromag. ratio                                      1.832 471 71 e8          0.000 000 43 e8          s^-1 T^-1
+neutron gyromag. ratio in MHz/T                             29.164 6931              0.000 0069               MHz T^-1
+neutron mag. mom.                                           -9.662 3651 e-27         0.000 0023 e-27          J T^-1
+neutron mag. mom. to Bohr magneton ratio                    -1.041 875 63 e-3        0.000 000 25 e-3
+neutron mag. mom. to nuclear magneton ratio                 -1.913 042 73            0.000 000 45
+neutron mass                                                1.674 927 498 04 e-27    0.000 000 000 95 e-27    kg
+neutron mass energy equivalent                              1.505 349 762 87 e-10    0.000 000 000 86 e-10    J
+neutron mass energy equivalent in MeV                       939.565 420 52           0.000 000 54             MeV
+neutron mass in u                                           1.008 664 915 95         0.000 000 000 49         u
+neutron molar mass                                          1.008 664 915 60 e-3     0.000 000 000 57 e-3     kg mol^-1
+neutron-muon mass ratio                                     8.892 484 06             0.000 000 20
+neutron-proton mag. mom. ratio                              -0.684 979 34            0.000 000 16
+neutron-proton mass difference                              2.305 574 35 e-30        0.000 000 82 e-30        kg
+neutron-proton mass difference energy equivalent            2.072 146 89 e-13        0.000 000 74 e-13        J
+neutron-proton mass difference energy equivalent in MeV     1.293 332 36             0.000 000 46             MeV
+neutron-proton mass difference in u                         1.388 449 33 e-3         0.000 000 49 e-3         u
+neutron-proton mass ratio                                   1.001 378 419 31         0.000 000 000 49
+neutron relative atomic mass                                1.008 664 915 95         0.000 000 000 49
+neutron-tau mass ratio                                      0.528 779                0.000 036
+neutron to shielded proton mag. mom. ratio                  -0.684 996 94            0.000 000 16
+Newtonian constant of gravitation                           6.674 30 e-11            0.000 15 e-11            m^3 kg^-1 s^-2
+Newtonian constant of gravitation over h-bar c              6.708 83 e-39            0.000 15 e-39            (GeV/c^2)^-2
+nuclear magneton                                            5.050 783 7461 e-27      0.000 000 0015 e-27      J T^-1
+nuclear magneton in eV/T                                    3.152 451 258 44 e-8     0.000 000 000 96 e-8     eV T^-1
+nuclear magneton in inverse meter per tesla                 2.542 623 413 53 e-2     0.000 000 000 78 e-2     m^-1 T^-1
+nuclear magneton in K/T                                     3.658 267 7756 e-4       0.000 000 0011 e-4       K T^-1
+nuclear magneton in MHz/T                                   7.622 593 2291           0.000 000 0023           MHz T^-1
+Planck constant                                             6.626 070 15 e-34        (exact)                  J Hz^-1
+Planck constant in eV/Hz                                    4.135 667 696... e-15    (exact)                  eV Hz^-1
+Planck length                                               1.616 255 e-35           0.000 018 e-35           m
+Planck mass                                                 2.176 434 e-8            0.000 024 e-8            kg
+Planck mass energy equivalent in GeV                        1.220 890 e19            0.000 014 e19            GeV
+Planck temperature                                          1.416 784 e32            0.000 016 e32            K
+Planck time                                                 5.391 247 e-44           0.000 060 e-44           s
+proton charge to mass quotient                              9.578 833 1560 e7        0.000 000 0029 e7        C kg^-1
+proton Compton wavelength                                   1.321 409 855 39 e-15    0.000 000 000 40 e-15    m
+proton-electron mass ratio                                  1836.152 673 43          0.000 000 11
+proton g factor                                             5.585 694 6893           0.000 000 0016
+proton gyromag. ratio                                       2.675 221 8744 e8        0.000 000 0011 e8        s^-1 T^-1
+proton gyromag. ratio in MHz/T                              42.577 478 518           0.000 000 018            MHz T^-1
+proton mag. mom.                                            1.410 606 797 36 e-26    0.000 000 000 60 e-26    J T^-1
+proton mag. mom. to Bohr magneton ratio                     1.521 032 202 30 e-3     0.000 000 000 46 e-3
+proton mag. mom. to nuclear magneton ratio                  2.792 847 344 63         0.000 000 000 82
+proton mag. shielding correction                            2.5689 e-5               0.0011 e-5
+proton mass                                                 1.672 621 923 69 e-27    0.000 000 000 51 e-27    kg
+proton mass energy equivalent                               1.503 277 615 98 e-10    0.000 000 000 46 e-10    J
+proton mass energy equivalent in MeV                        938.272 088 16           0.000 000 29             MeV
+proton mass in u                                            1.007 276 466 621        0.000 000 000 053        u
+proton molar mass                                           1.007 276 466 27 e-3     0.000 000 000 31 e-3     kg mol^-1
+proton-muon mass ratio                                      8.880 243 37             0.000 000 20
+proton-neutron mag. mom. ratio                              -1.459 898 05            0.000 000 34
+proton-neutron mass ratio                                   0.998 623 478 12         0.000 000 000 49
+proton relative atomic mass                                 1.007 276 466 621        0.000 000 000 053
+proton rms charge radius                                    8.414 e-16               0.019 e-16               m
+proton-tau mass ratio                                       0.528 051                0.000 036
+quantum of circulation                                      3.636 947 5516 e-4       0.000 000 0011 e-4       m^2 s^-1
+quantum of circulation times 2                              7.273 895 1032 e-4       0.000 000 0022 e-4       m^2 s^-1
+reduced Compton wavelength                                  3.861 592 6796 e-13      0.000 000 0012 e-13      m
+reduced muon Compton wavelength                             1.867 594 306 e-15       0.000 000 042 e-15       m
+reduced neutron Compton wavelength                          2.100 194 1552 e-16      0.000 000 0012 e-16      m
+reduced Planck constant                                     1.054 571 817... e-34    (exact)                  J s
+reduced Planck constant in eV s                             6.582 119 569... e-16    (exact)                  eV s
+reduced Planck constant times c in MeV fm                   197.326 980 4...         (exact)                  MeV fm
+reduced proton Compton wavelength                           2.103 089 103 36 e-16    0.000 000 000 64 e-16    m
+reduced tau Compton wavelength                              1.110 538 e-16           0.000 075 e-16           m
+Rydberg constant                                            10 973 731.568 160       0.000 021                m^-1
+Rydberg constant times c in Hz                              3.289 841 960 2508 e15   0.000 000 000 0064 e15   Hz
+Rydberg constant times hc in eV                             13.605 693 122 994       0.000 000 000 026        eV
+Rydberg constant times hc in J                              2.179 872 361 1035 e-18  0.000 000 000 0042 e-18  J
+Sackur-Tetrode constant (1 K, 100 kPa)                      -1.151 707 537 06        0.000 000 000 45
+Sackur-Tetrode constant (1 K, 101.325 kPa)                  -1.164 870 523 58        0.000 000 000 45
+second radiation constant                                   1.438 776 877... e-2     (exact)                  m K
+shielded helion gyromag. ratio                              2.037 894 569 e8         0.000 000 024 e8         s^-1 T^-1
+shielded helion gyromag. ratio in MHz/T                     32.434 099 42            0.000 000 38             MHz T^-1
+shielded helion mag. mom.                                   -1.074 553 090 e-26      0.000 000 013 e-26       J T^-1
+shielded helion mag. mom. to Bohr magneton ratio            -1.158 671 471 e-3       0.000 000 014 e-3
+shielded helion mag. mom. to nuclear magneton ratio         -2.127 497 719           0.000 000 025
+shielded helion to proton mag. mom. ratio                   -0.761 766 5618          0.000 000 0089
+shielded helion to shielded proton mag. mom. ratio          -0.761 786 1313          0.000 000 0033
+shielded proton gyromag. ratio                              2.675 153 151 e8         0.000 000 029 e8         s^-1 T^-1
+shielded proton gyromag. ratio in MHz/T                     42.576 384 74            0.000 000 46             MHz T^-1
+shielded proton mag. mom.                                   1.410 570 560 e-26       0.000 000 015 e-26       J T^-1
+shielded proton mag. mom. to Bohr magneton ratio            1.520 993 128 e-3        0.000 000 017 e-3
+shielded proton mag. mom. to nuclear magneton ratio         2.792 775 599            0.000 000 030
+shielding difference of d and p in HD                       2.0200 e-8               0.0020 e-8
+shielding difference of t and p in HT                       2.4140 e-8               0.0020 e-8
+speed of light in vacuum                                    299 792 458              (exact)                  m s^-1
+standard acceleration of gravity                            9.806 65                 (exact)                  m s^-2
+standard atmosphere                                         101 325                  (exact)                  Pa
+standard-state pressure                                     100 000                  (exact)                  Pa
+Stefan-Boltzmann constant                                   5.670 374 419... e-8     (exact)                  W m^-2 K^-4
+tau Compton wavelength                                      6.977 71 e-16            0.000 47 e-16            m
+tau-electron mass ratio                                     3477.23                  0.23
+tau energy equivalent                                       1776.86                  0.12                     MeV
+tau mass                                                    3.167 54 e-27            0.000 21 e-27            kg
+tau mass energy equivalent                                  2.846 84 e-10            0.000 19 e-10            J
+tau mass in u                                               1.907 54                 0.000 13                 u
+tau molar mass                                              1.907 54 e-3             0.000 13 e-3             kg mol^-1
+tau-muon mass ratio                                         16.8170                  0.0011
+tau-neutron mass ratio                                      1.891 15                 0.000 13
+tau-proton mass ratio                                       1.893 76                 0.000 13
+Thomson cross section                                       6.652 458 7321 e-29      0.000 000 0060 e-29      m^2
+triton-electron mass ratio                                  5496.921 535 73          0.000 000 27
+triton g factor                                             5.957 924 931            0.000 000 012
+triton mag. mom.                                            1.504 609 5202 e-26      0.000 000 0030 e-26      J T^-1
+triton mag. mom. to Bohr magneton ratio                     1.622 393 6651 e-3       0.000 000 0032 e-3
+triton mag. mom. to nuclear magneton ratio                  2.978 962 4656           0.000 000 0059
+triton mass                                                 5.007 356 7446 e-27      0.000 000 0015 e-27      kg
+triton mass energy equivalent                               4.500 387 8060 e-10      0.000 000 0014 e-10      J
+triton mass energy equivalent in MeV                        2808.921 132 98          0.000 000 85             MeV
+triton mass in u                                            3.015 500 716 21         0.000 000 000 12         u
+triton molar mass                                           3.015 500 715 17 e-3     0.000 000 000 92 e-3     kg mol^-1
+triton-proton mass ratio                                    2.993 717 034 14         0.000 000 000 15
+triton relative atomic mass                                 3.015 500 716 21         0.000 000 000 12
+triton to proton mag. mom. ratio                            1.066 639 9191           0.000 000 0021
+unified atomic mass unit                                    1.660 539 066 60 e-27    0.000 000 000 50 e-27    kg
+vacuum electric permittivity                                8.854 187 8128 e-12      0.000 000 0013 e-12      F m^-1
+vacuum mag. permeability                                    1.256 637 062 12 e-6     0.000 000 000 19 e-6     N A^-2
+von Klitzing constant                                       25 812.807 45...         (exact)                  ohm
+weak mixing angle                                           0.222 90                 0.000 30
+Wien frequency displacement law constant                    5.878 925 757... e10     (exact)                  Hz K^-1
+Wien wavelength displacement law constant                   2.897 771 955... e-3     (exact)                  m K
+W to Z mass ratio                                           0.881 53                 0.000 17                   """
+
+
+def exact2018(exact):
+    # SI base constants
+    c = exact['speed of light in vacuum']
+    h = exact['Planck constant']
+    e = exact['elementary charge']
+    k = exact['Boltzmann constant']
+    N_A = exact['Avogadro constant']
+
+    # Other useful constants
+    R = N_A * k
+    hbar = h / (2*math.pi)
+    G_0 = 2 * e**2 / h
+
+    # Wien law numerical constants: https://en.wikipedia.org/wiki/Wien%27s_displacement_law
+    # (alpha - 3)*exp(alpha) + 3 = 0
+    # (x - 5)*exp(x) + 5 = 0
+    alpha_W = 2.821439372122078893403  # 3 + lambertw(-3 * exp(-3))
+    x_W = 4.965114231744276303699  # 5 + lambertw(-5 * exp(-5))
+
+    # Conventional electrical unit
+    # See https://en.wikipedia.org/wiki/Conventional_electrical_unit
+    K_J90 = exact['conventional value of Josephson constant']
+    K_J = 2 * e / h
+    R_K90 = exact['conventional value of von Klitzing constant']
+    R_K = h / e**2
+    V_90 = K_J90 / K_J
+    ohm_90 = R_K / R_K90
+    A_90 = V_90 / ohm_90
+
+    replace = {
+        'atomic unit of action': hbar,
+        'Boltzmann constant in eV/K': k / e,
+        'Boltzmann constant in Hz/K': k / h,
+        'Boltzmann constant in inverse meter per kelvin': k / (h * c),
+        'conductance quantum': G_0,
+        'conventional value of ampere-90': A_90,
+        'conventional value of coulomb-90': A_90,
+        'conventional value of farad-90': 1 / ohm_90,
+        'conventional value of henry-90': ohm_90,
+        'conventional value of ohm-90': ohm_90,
+        'conventional value of volt-90': V_90,
+        'conventional value of watt-90': V_90**2 / ohm_90,
+        'electron volt-hertz relationship': e / h,
+        'electron volt-inverse meter relationship': e / (h * c),
+        'electron volt-kelvin relationship': e / k,
+        'electron volt-kilogram relationship': e / c**2,
+        'elementary charge over h-bar': e / hbar,
+        'Faraday constant': e * N_A,
+        'first radiation constant': 2 * math.pi * h * c**2,
+        'first radiation constant for spectral radiance': 2 * h * c**2,
+        'hertz-electron volt relationship': h / e,
+        'hertz-inverse meter relationship': 1 / c,
+        'hertz-kelvin relationship': h / k,
+        'hertz-kilogram relationship': h / c**2,
+        'inverse meter-electron volt relationship': (h * c) / e,
+        'inverse meter-joule relationship': h * c,
+        'inverse meter-kelvin relationship': h * c / k,
+        'inverse meter-kilogram relationship': h / c,
+        'inverse of conductance quantum': 1 / G_0,
+        'Josephson constant': K_J,
+        'joule-electron volt relationship': 1 / e,
+        'joule-hertz relationship': 1 / h,
+        'joule-inverse meter relationship': 1 / (h * c),
+        'joule-kelvin relationship': 1 / k,
+        'joule-kilogram relationship': 1 / c**2,
+        'kelvin-electron volt relationship': k / e,
+        'kelvin-hertz relationship': k / h,
+        'kelvin-inverse meter relationship': k / (h * c),
+        'kelvin-kilogram relationship': k / c**2,
+        'kilogram-electron volt relationship': c**2 / e,
+        'kilogram-hertz relationship': c**2 / h,
+        'kilogram-inverse meter relationship': c / h,
+        'kilogram-joule relationship': c**2,
+        'kilogram-kelvin relationship': c**2 / k,
+        'Loschmidt constant (273.15 K, 100 kPa)': 100e3 / 273.15 / k,
+        'Loschmidt constant (273.15 K, 101.325 kPa)': 101.325e3 / 273.15 / k,
+        'mag. flux quantum': h / (2 * e),
+        'molar gas constant': R,
+        'molar Planck constant': h * N_A,
+        'molar volume of ideal gas (273.15 K, 100 kPa)': R * 273.15 / 100e3,
+        'molar volume of ideal gas (273.15 K, 101.325 kPa)': R * 273.15 / 101.325e3,
+        'natural unit of action': hbar,
+        'natural unit of action in eV s': hbar / e,
+        'Planck constant in eV/Hz': h / e,
+        'reduced Planck constant': hbar,
+        'reduced Planck constant in eV s': hbar / e,
+        'reduced Planck constant times c in MeV fm': hbar * c / (e * 1e6 * 1e-15),
+        'second radiation constant': h * c / k,
+        'Stefan-Boltzmann constant': 2 * math.pi**5 * k**4 / (15 * h**3 * c**2),
+        'von Klitzing constant': R_K,
+        'Wien frequency displacement law constant': alpha_W * k / h,
+        'Wien wavelength displacement law constant': h * c / (x_W * k),
+    }
+    return replace
+
+
+txt2022 = """\
+alpha particle-electron mass ratio                          7294.299 541 71          0.000 000 17             
+alpha particle mass                                         6.644 657 3450 e-27      0.000 000 0021 e-27      kg
+alpha particle mass energy equivalent                       5.971 920 1997 e-10      0.000 000 0019 e-10      J
+alpha particle mass energy equivalent in MeV                3727.379 4118            0.000 0012               MeV
+alpha particle mass in u                                    4.001 506 179 129        0.000 000 000 062        u
+alpha particle molar mass                                   4.001 506 1833 e-3       0.000 000 0012 e-3       kg mol^-1
+alpha particle-proton mass ratio                            3.972 599 690 252        0.000 000 000 070        
+alpha particle relative atomic mass                         4.001 506 179 129        0.000 000 000 062        
+alpha particle rms charge radius                            1.6785 e-15              0.0021 e-15              m
+Angstrom star                                               1.000 014 95 e-10        0.000 000 90 e-10        m
+atomic mass constant                                        1.660 539 068 92 e-27    0.000 000 000 52 e-27    kg
+atomic mass constant energy equivalent                      1.492 418 087 68 e-10    0.000 000 000 46 e-10    J
+atomic mass constant energy equivalent in MeV               931.494 103 72           0.000 000 29             MeV
+atomic mass unit-electron volt relationship                 9.314 941 0372 e8        0.000 000 0029 e8        eV
+atomic mass unit-hartree relationship                       3.423 177 6922 e7        0.000 000 0011 e7        E_h
+atomic mass unit-hertz relationship                         2.252 342 721 85 e23     0.000 000 000 70 e23     Hz
+atomic mass unit-inverse meter relationship                 7.513 006 6209 e14       0.000 000 0023 e14       m^-1
+atomic mass unit-joule relationship                         1.492 418 087 68 e-10    0.000 000 000 46 e-10    J
+atomic mass unit-kelvin relationship                        1.080 954 020 67 e13     0.000 000 000 34 e13     K
+atomic mass unit-kilogram relationship                      1.660 539 068 92 e-27    0.000 000 000 52 e-27    kg
+atomic unit of 1st hyperpolarizability                      3.206 361 2996 e-53      0.000 000 0015 e-53      C^3 m^3 J^-2
+atomic unit of 2nd hyperpolarizability                      6.235 379 9735 e-65      0.000 000 0039 e-65      C^4 m^4 J^-3
+atomic unit of action                                       1.054 571 817... e-34    (exact)                  J s
+atomic unit of charge                                       1.602 176 634 e-19       (exact)                  C
+atomic unit of charge density                               1.081 202 386 77 e12     0.000 000 000 51 e12     C m^-3
+atomic unit of current                                      6.623 618 237 5082 e-3   0.000 000 000 0072 e-3   A
+atomic unit of electric dipole mom.                         8.478 353 6198 e-30      0.000 000 0013 e-30      C m
+atomic unit of electric field                               5.142 206 751 12 e11     0.000 000 000 80 e11     V m^-1
+atomic unit of electric field gradient                      9.717 362 4424 e21       0.000 000 0030 e21       V m^-2
+atomic unit of electric polarizability                      1.648 777 272 12 e-41    0.000 000 000 51 e-41    C^2 m^2 J^-1
+atomic unit of electric potential                           27.211 386 245 981       0.000 000 000 030        V
+atomic unit of electric quadrupole mom.                     4.486 551 5185 e-40      0.000 000 0014 e-40      C m^2
+atomic unit of energy                                       4.359 744 722 2060 e-18  0.000 000 000 0048 e-18  J
+atomic unit of force                                        8.238 723 5038 e-8       0.000 000 0013 e-8       N
+atomic unit of length                                       5.291 772 105 44 e-11    0.000 000 000 82 e-11    m
+atomic unit of mag. dipole mom.                             1.854 802 013 15 e-23    0.000 000 000 58 e-23    J T^-1
+atomic unit of mag. flux density                            2.350 517 570 77 e5      0.000 000 000 73 e5      T
+atomic unit of magnetizability                              7.891 036 5794 e-29      0.000 000 0049 e-29      J T^-2
+atomic unit of mass                                         9.109 383 7139 e-31      0.000 000 0028 e-31      kg
+atomic unit of momentum                                     1.992 851 915 45 e-24    0.000 000 000 31 e-24    kg m s^-1
+atomic unit of permittivity                                 1.112 650 056 20 e-10    0.000 000 000 17 e-10    F m^-1
+atomic unit of time                                         2.418 884 326 5864 e-17  0.000 000 000 0026 e-17  s
+atomic unit of velocity                                     2.187 691 262 16 e6      0.000 000 000 34 e6      m s^-1
+Avogadro constant                                           6.022 140 76 e23         (exact)                  mol^-1
+Bohr magneton                                               9.274 010 0657 e-24      0.000 000 0029 e-24      J T^-1
+Bohr magneton in eV/T                                       5.788 381 7982 e-5       0.000 000 0018 e-5       eV T^-1
+Bohr magneton in Hz/T                                       1.399 624 491 71 e10     0.000 000 000 44 e10     Hz T^-1
+Bohr magneton in inverse meter per tesla                    46.686 447 719           0.000 000 015            m^-1 T^-1
+Bohr magneton in K/T                                        0.671 713 814 72         0.000 000 000 21         K T^-1
+Bohr radius                                                 5.291 772 105 44 e-11    0.000 000 000 82 e-11    m
+Boltzmann constant                                          1.380 649 e-23           (exact)                  J K^-1
+Boltzmann constant in eV/K                                  8.617 333 262... e-5     (exact)                  eV K^-1
+Boltzmann constant in Hz/K                                  2.083 661 912... e10     (exact)                  Hz K^-1
+Boltzmann constant in inverse meter per kelvin              69.503 480 04...         (exact)                  m^-1 K^-1
+characteristic impedance of vacuum                          376.730 313 412          0.000 000 059            ohm
+classical electron radius                                   2.817 940 3205 e-15      0.000 000 0013 e-15      m
+Compton wavelength                                          2.426 310 235 38 e-12    0.000 000 000 76 e-12    m
+conductance quantum                                         7.748 091 729... e-5     (exact)                  S
+conventional value of ampere-90                             1.000 000 088 87...      (exact)                  A
+conventional value of coulomb-90                            1.000 000 088 87...      (exact)                  C
+conventional value of farad-90                              0.999 999 982 20...      (exact)                  F
+conventional value of henry-90                              1.000 000 017 79...      (exact)                  H
+conventional value of Josephson constant                    483 597.9 e9             (exact)                  Hz V^-1
+conventional value of ohm-90                                1.000 000 017 79...      (exact)                  ohm
+conventional value of volt-90                               1.000 000 106 66...      (exact)                  V
+conventional value of von Klitzing constant                 25 812.807               (exact)                  ohm
+conventional value of watt-90                               1.000 000 195 53...      (exact)                  W
+Copper x unit                                               1.002 076 97 e-13        0.000 000 28 e-13        m
+deuteron-electron mag. mom. ratio                           -4.664 345 550 e-4       0.000 000 012 e-4        
+deuteron-electron mass ratio                                3670.482 967 655         0.000 000 063            
+deuteron g factor                                           0.857 438 2335           0.000 000 0022           
+deuteron mag. mom.                                          4.330 735 087 e-27       0.000 000 011 e-27       J T^-1
+deuteron mag. mom. to Bohr magneton ratio                   4.669 754 568 e-4        0.000 000 012 e-4        
+deuteron mag. mom. to nuclear magneton ratio                0.857 438 2335           0.000 000 0022           
+deuteron mass                                               3.343 583 7768 e-27      0.000 000 0010 e-27      kg
+deuteron mass energy equivalent                             3.005 063 234 91 e-10    0.000 000 000 94 e-10    J
+deuteron mass energy equivalent in MeV                      1875.612 945 00          0.000 000 58             MeV
+deuteron mass in u                                          2.013 553 212 544        0.000 000 000 015        u
+deuteron molar mass                                         2.013 553 214 66 e-3     0.000 000 000 63 e-3     kg mol^-1
+deuteron-neutron mag. mom. ratio                            -0.448 206 52            0.000 000 11             
+deuteron-proton mag. mom. ratio                             0.307 012 209 30         0.000 000 000 79         
+deuteron-proton mass ratio                                  1.999 007 501 2699       0.000 000 000 0084       
+deuteron relative atomic mass                               2.013 553 212 544        0.000 000 000 015        
+deuteron rms charge radius                                  2.127 78 e-15            0.000 27 e-15            m
+electron charge to mass quotient                            -1.758 820 008 38 e11    0.000 000 000 55 e11     C kg^-1
+electron-deuteron mag. mom. ratio                           -2143.923 4921           0.000 0056               
+electron-deuteron mass ratio                                2.724 437 107 629 e-4    0.000 000 000 047 e-4    
+electron g factor                                           -2.002 319 304 360 92    0.000 000 000 000 36     
+electron gyromag. ratio                                     1.760 859 627 84 e11     0.000 000 000 55 e11     s^-1 T^-1
+electron gyromag. ratio in MHz/T                            28 024.951 3861          0.000 0087               MHz T^-1
+electron-helion mass ratio                                  1.819 543 074 649 e-4    0.000 000 000 053 e-4    
+electron mag. mom.                                          -9.284 764 6917 e-24     0.000 000 0029 e-24      J T^-1
+electron mag. mom. anomaly                                  1.159 652 180 46 e-3     0.000 000 000 18 e-3     
+electron mag. mom. to Bohr magneton ratio                   -1.001 159 652 180 46    0.000 000 000 000 18     
+electron mag. mom. to nuclear magneton ratio                -1838.281 971 877        0.000 000 032            
+electron mass                                               9.109 383 7139 e-31      0.000 000 0028 e-31      kg
+electron mass energy equivalent                             8.187 105 7880 e-14      0.000 000 0026 e-14      J
+electron mass energy equivalent in MeV                      0.510 998 950 69         0.000 000 000 16         MeV
+electron mass in u                                          5.485 799 090 441 e-4    0.000 000 000 097 e-4    u
+electron molar mass                                         5.485 799 0962 e-7       0.000 000 0017 e-7       kg mol^-1
+electron-muon mag. mom. ratio                               206.766 9881             0.000 0046               
+electron-muon mass ratio                                    4.836 331 70 e-3         0.000 000 11 e-3         
+electron-neutron mag. mom. ratio                            960.920 48               0.000 23                 
+electron-neutron mass ratio                                 5.438 673 4416 e-4       0.000 000 0022 e-4       
+electron-proton mag. mom. ratio                             -658.210 687 89          0.000 000 19             
+electron-proton mass ratio                                  5.446 170 214 889 e-4    0.000 000 000 094 e-4    
+electron relative atomic mass                               5.485 799 090 441 e-4    0.000 000 000 097 e-4    
+electron-tau mass ratio                                     2.875 85 e-4             0.000 19 e-4             
+electron to alpha particle mass ratio                       1.370 933 554 733 e-4    0.000 000 000 032 e-4    
+electron to shielded helion mag. mom. ratio                 864.058 239 86           0.000 000 70             
+electron to shielded proton mag. mom. ratio                 -658.227 5856            0.000 0027               
+electron-triton mass ratio                                  1.819 200 062 327 e-4    0.000 000 000 068 e-4    
+electron volt                                               1.602 176 634 e-19       (exact)                  J
+electron volt-atomic mass unit relationship                 1.073 544 100 83 e-9     0.000 000 000 33 e-9     u
+electron volt-hartree relationship                          3.674 932 217 5665 e-2   0.000 000 000 0040 e-2   E_h
+electron volt-hertz relationship                            2.417 989 242... e14     (exact)                  Hz
+electron volt-inverse meter relationship                    8.065 543 937... e5      (exact)                  m^-1
+electron volt-joule relationship                            1.602 176 634 e-19       (exact)                  J
+electron volt-kelvin relationship                           1.160 451 812... e4      (exact)                  K
+electron volt-kilogram relationship                         1.782 661 921... e-36    (exact)                  kg
+elementary charge                                           1.602 176 634 e-19       (exact)                  C
+elementary charge over h-bar                                1.519 267 447... e15     (exact)                  A J^-1
+Faraday constant                                            96 485.332 12...         (exact)                  C mol^-1
+Fermi coupling constant                                     1.166 3787 e-5           0.000 0006 e-5           GeV^-2
+fine-structure constant                                     7.297 352 5643 e-3       0.000 000 0011 e-3       
+first radiation constant                                    3.741 771 852... e-16    (exact)                  W m^2
+first radiation constant for spectral radiance              1.191 042 972... e-16    (exact)                  W m^2 sr^-1
+hartree-atomic mass unit relationship                       2.921 262 317 97 e-8     0.000 000 000 91 e-8     u
+hartree-electron volt relationship                          27.211 386 245 981       0.000 000 000 030        eV
+Hartree energy                                              4.359 744 722 2060 e-18  0.000 000 000 0048 e-18  J
+Hartree energy in eV                                        27.211 386 245 981       0.000 000 000 030        eV
+hartree-hertz relationship                                  6.579 683 920 4999 e15   0.000 000 000 0072 e15   Hz
+hartree-inverse meter relationship                          2.194 746 313 6314 e7    0.000 000 000 0024 e7    m^-1
+hartree-joule relationship                                  4.359 744 722 2060 e-18  0.000 000 000 0048 e-18  J
+hartree-kelvin relationship                                 3.157 750 248 0398 e5    0.000 000 000 0034 e5    K
+hartree-kilogram relationship                               4.850 870 209 5419 e-35  0.000 000 000 0053 e-35  kg
+helion-electron mass ratio                                  5495.885 279 84          0.000 000 16             
+helion g factor                                             -4.255 250 6995          0.000 000 0034           
+helion mag. mom.                                            -1.074 617 551 98 e-26   0.000 000 000 93 e-26    J T^-1
+helion mag. mom. to Bohr magneton ratio                     -1.158 740 980 83 e-3    0.000 000 000 94 e-3     
+helion mag. mom. to nuclear magneton ratio                  -2.127 625 3498          0.000 000 0017           
+helion mass                                                 5.006 412 7862 e-27      0.000 000 0016 e-27      kg
+helion mass energy equivalent                               4.499 539 4185 e-10      0.000 000 0014 e-10      J
+helion mass energy equivalent in MeV                        2808.391 611 12          0.000 000 88             MeV
+helion mass in u                                            3.014 932 246 932        0.000 000 000 074        u
+helion molar mass                                           3.014 932 250 10 e-3     0.000 000 000 94 e-3     kg mol^-1
+helion-proton mass ratio                                    2.993 152 671 552        0.000 000 000 070        
+helion relative atomic mass                                 3.014 932 246 932        0.000 000 000 074        
+helion shielding shift                                      5.996 7029 e-5           0.000 0023 e-5           
+hertz-atomic mass unit relationship                         4.439 821 6590 e-24      0.000 000 0014 e-24      u
+hertz-electron volt relationship                            4.135 667 696... e-15    (exact)                  eV
+hertz-hartree relationship                                  1.519 829 846 0574 e-16  0.000 000 000 0017 e-16  E_h
+hertz-inverse meter relationship                            3.335 640 951... e-9     (exact)                  m^-1
+hertz-joule relationship                                    6.626 070 15 e-34        (exact)                  J
+hertz-kelvin relationship                                   4.799 243 073... e-11    (exact)                  K
+hertz-kilogram relationship                                 7.372 497 323... e-51    (exact)                  kg
+hyperfine transition frequency of Cs-133                    9 192 631 770            (exact)                  Hz
+inverse fine-structure constant                             137.035 999 177          0.000 000 021            
+inverse meter-atomic mass unit relationship                 1.331 025 048 24 e-15    0.000 000 000 41 e-15    u
+inverse meter-electron volt relationship                    1.239 841 984... e-6     (exact)                  eV
+inverse meter-hartree relationship                          4.556 335 252 9132 e-8   0.000 000 000 0050 e-8   E_h
+inverse meter-hertz relationship                            299 792 458              (exact)                  Hz
+inverse meter-joule relationship                            1.986 445 857... e-25    (exact)                  J
+inverse meter-kelvin relationship                           1.438 776 877... e-2     (exact)                  K
+inverse meter-kilogram relationship                         2.210 219 094... e-42    (exact)                  kg
+inverse of conductance quantum                              12 906.403 72...         (exact)                  ohm
+Josephson constant                                          483 597.848 4... e9      (exact)                  Hz V^-1
+joule-atomic mass unit relationship                         6.700 535 2471 e9        0.000 000 0021 e9        u
+joule-electron volt relationship                            6.241 509 074... e18     (exact)                  eV
+joule-hartree relationship                                  2.293 712 278 3969 e17   0.000 000 000 0025 e17   E_h
+joule-hertz relationship                                    1.509 190 179... e33     (exact)                  Hz
+joule-inverse meter relationship                            5.034 116 567... e24     (exact)                  m^-1
+joule-kelvin relationship                                   7.242 970 516... e22     (exact)                  K
+joule-kilogram relationship                                 1.112 650 056... e-17    (exact)                  kg
+kelvin-atomic mass unit relationship                        9.251 087 2884 e-14      0.000 000 0029 e-14      u
+kelvin-electron volt relationship                           8.617 333 262... e-5     (exact)                  eV
+kelvin-hartree relationship                                 3.166 811 563 4564 e-6   0.000 000 000 0035 e-6   E_h
+kelvin-hertz relationship                                   2.083 661 912... e10     (exact)                  Hz
+kelvin-inverse meter relationship                           69.503 480 04...         (exact)                  m^-1
+kelvin-joule relationship                                   1.380 649 e-23           (exact)                  J
+kelvin-kilogram relationship                                1.536 179 187... e-40    (exact)                  kg
+kilogram-atomic mass unit relationship                      6.022 140 7537 e26       0.000 000 0019 e26       u
+kilogram-electron volt relationship                         5.609 588 603... e35     (exact)                  eV
+kilogram-hartree relationship                               2.061 485 788 7415 e34   0.000 000 000 0022 e34   E_h
+kilogram-hertz relationship                                 1.356 392 489... e50     (exact)                  Hz
+kilogram-inverse meter relationship                         4.524 438 335... e41     (exact)                  m^-1
+kilogram-joule relationship                                 8.987 551 787... e16     (exact)                  J
+kilogram-kelvin relationship                                6.509 657 260... e39     (exact)                  K
+lattice parameter of silicon                                5.431 020 511 e-10       0.000 000 089 e-10       m
+lattice spacing of ideal Si (220)                           1.920 155 716 e-10       0.000 000 032 e-10       m
+Loschmidt constant (273.15 K, 100 kPa)                      2.651 645 804... e25     (exact)                  m^-3
+Loschmidt constant (273.15 K, 101.325 kPa)                  2.686 780 111... e25     (exact)                  m^-3
+luminous efficacy                                           683                      (exact)                  lm W^-1
+mag. flux quantum                                           2.067 833 848... e-15    (exact)                  Wb
+molar gas constant                                          8.314 462 618...         (exact)                  J mol^-1 K^-1
+molar mass constant                                         1.000 000 001 05 e-3     0.000 000 000 31 e-3     kg mol^-1
+molar mass of carbon-12                                     12.000 000 0126 e-3      0.000 000 0037 e-3       kg mol^-1
+molar Planck constant                                       3.990 312 712... e-10    (exact)                  J Hz^-1 mol^-1
+molar volume of ideal gas (273.15 K, 100 kPa)               22.710 954 64... e-3     (exact)                  m^3 mol^-1
+molar volume of ideal gas (273.15 K, 101.325 kPa)           22.413 969 54... e-3     (exact)                  m^3 mol^-1
+molar volume of silicon                                     1.205 883 199 e-5        0.000 000 060 e-5        m^3 mol^-1
+Molybdenum x unit                                           1.002 099 52 e-13        0.000 000 53 e-13        m
+muon Compton wavelength                                     1.173 444 110 e-14       0.000 000 026 e-14       m
+muon-electron mass ratio                                    206.768 2827             0.000 0046               
+muon g factor                                               -2.002 331 841 23        0.000 000 000 82         
+muon mag. mom.                                              -4.490 448 30 e-26       0.000 000 10 e-26        J T^-1
+muon mag. mom. anomaly                                      1.165 920 62 e-3         0.000 000 41 e-3         
+muon mag. mom. to Bohr magneton ratio                       -4.841 970 48 e-3        0.000 000 11 e-3         
+muon mag. mom. to nuclear magneton ratio                    -8.890 597 04            0.000 000 20             
+muon mass                                                   1.883 531 627 e-28       0.000 000 042 e-28       kg
+muon mass energy equivalent                                 1.692 833 804 e-11       0.000 000 038 e-11       J
+muon mass energy equivalent in MeV                          105.658 3755             0.000 0023               MeV
+muon mass in u                                              0.113 428 9257           0.000 000 0025           u
+muon molar mass                                             1.134 289 258 e-4        0.000 000 025 e-4        kg mol^-1
+muon-neutron mass ratio                                     0.112 454 5168           0.000 000 0025           
+muon-proton mag. mom. ratio                                 -3.183 345 146           0.000 000 071            
+muon-proton mass ratio                                      0.112 609 5262           0.000 000 0025           
+muon-tau mass ratio                                         5.946 35 e-2             0.000 40 e-2             
+natural unit of action                                      1.054 571 817... e-34    (exact)                  J s
+natural unit of action in eV s                              6.582 119 569... e-16    (exact)                  eV s
+natural unit of energy                                      8.187 105 7880 e-14      0.000 000 0026 e-14      J
+natural unit of energy in MeV                               0.510 998 950 69         0.000 000 000 16         MeV
+natural unit of length                                      3.861 592 6744 e-13      0.000 000 0012 e-13      m
+natural unit of mass                                        9.109 383 7139 e-31      0.000 000 0028 e-31      kg
+natural unit of momentum                                    2.730 924 534 46 e-22    0.000 000 000 85 e-22    kg m s^-1
+natural unit of momentum in MeV/c                           0.510 998 950 69         0.000 000 000 16         MeV/c
+natural unit of time                                        1.288 088 666 44 e-21    0.000 000 000 40 e-21    s
+natural unit of velocity                                    299 792 458              (exact)                  m s^-1
+neutron Compton wavelength                                  1.319 590 903 82 e-15    0.000 000 000 67 e-15    m
+neutron-electron mag. mom. ratio                            1.040 668 84 e-3         0.000 000 24 e-3         
+neutron-electron mass ratio                                 1838.683 662 00          0.000 000 74             
+neutron g factor                                            -3.826 085 52            0.000 000 90             
+neutron gyromag. ratio                                      1.832 471 74 e8          0.000 000 43 e8          s^-1 T^-1
+neutron gyromag. ratio in MHz/T                             29.164 6935              0.000 0069               MHz T^-1
+neutron mag. mom.                                           -9.662 3653 e-27         0.000 0023 e-27          J T^-1
+neutron mag. mom. to Bohr magneton ratio                    -1.041 875 65 e-3        0.000 000 25 e-3         
+neutron mag. mom. to nuclear magneton ratio                 -1.913 042 76            0.000 000 45             
+neutron mass                                                1.674 927 500 56 e-27    0.000 000 000 85 e-27    kg
+neutron mass energy equivalent                              1.505 349 765 14 e-10    0.000 000 000 76 e-10    J
+neutron mass energy equivalent in MeV                       939.565 421 94           0.000 000 48             MeV
+neutron mass in u                                           1.008 664 916 06         0.000 000 000 40         u
+neutron molar mass                                          1.008 664 917 12 e-3     0.000 000 000 51 e-3     kg mol^-1
+neutron-muon mass ratio                                     8.892 484 08             0.000 000 20             
+neutron-proton mag. mom. ratio                              -0.684 979 35            0.000 000 16             
+neutron-proton mass difference                              2.305 574 61 e-30        0.000 000 67 e-30        kg
+neutron-proton mass difference energy equivalent            2.072 147 12 e-13        0.000 000 60 e-13        J
+neutron-proton mass difference energy equivalent in MeV     1.293 332 51             0.000 000 38             MeV
+neutron-proton mass difference in u                         1.388 449 48 e-3         0.000 000 40 e-3         u
+neutron-proton mass ratio                                   1.001 378 419 46         0.000 000 000 40         
+neutron relative atomic mass                                1.008 664 916 06         0.000 000 000 40         
+neutron-tau mass ratio                                      0.528 779                0.000 036                
+neutron to shielded proton mag. mom. ratio                  -0.684 996 94            0.000 000 16             
+Newtonian constant of gravitation                           6.674 30 e-11            0.000 15 e-11            m^3 kg^-1 s^-2
+Newtonian constant of gravitation over h-bar c              6.708 83 e-39            0.000 15 e-39            (GeV/c^2)^-2
+nuclear magneton                                            5.050 783 7393 e-27      0.000 000 0016 e-27      J T^-1
+nuclear magneton in eV/T                                    3.152 451 254 17 e-8     0.000 000 000 98 e-8     eV T^-1
+nuclear magneton in inverse meter per tesla                 2.542 623 410 09 e-2     0.000 000 000 79 e-2     m^-1 T^-1
+nuclear magneton in K/T                                     3.658 267 7706 e-4       0.000 000 0011 e-4       K T^-1
+nuclear magneton in MHz/T                                   7.622 593 2188           0.000 000 0024           MHz T^-1
+Planck constant                                             6.626 070 15 e-34        (exact)                  J Hz^-1
+Planck constant in eV/Hz                                    4.135 667 696... e-15    (exact)                  eV Hz^-1
+Planck length                                               1.616 255 e-35           0.000 018 e-35           m
+Planck mass                                                 2.176 434 e-8            0.000 024 e-8            kg
+Planck mass energy equivalent in GeV                        1.220 890 e19            0.000 014 e19            GeV
+Planck temperature                                          1.416 784 e32            0.000 016 e32            K
+Planck time                                                 5.391 247 e-44           0.000 060 e-44           s
+proton charge to mass quotient                              9.578 833 1430 e7        0.000 000 0030 e7        C kg^-1
+proton Compton wavelength                                   1.321 409 853 60 e-15    0.000 000 000 41 e-15    m
+proton-electron mass ratio                                  1836.152 673 426         0.000 000 032            
+proton g factor                                             5.585 694 6893           0.000 000 0016           
+proton gyromag. ratio                                       2.675 221 8708 e8        0.000 000 0011 e8        s^-1 T^-1
+proton gyromag. ratio in MHz/T                              42.577 478 461           0.000 000 018            MHz T^-1
+proton mag. mom.                                            1.410 606 795 45 e-26    0.000 000 000 60 e-26    J T^-1
+proton mag. mom. to Bohr magneton ratio                     1.521 032 202 30 e-3     0.000 000 000 45 e-3     
+proton mag. mom. to nuclear magneton ratio                  2.792 847 344 63         0.000 000 000 82         
+proton mag. shielding correction                            2.567 15 e-5             0.000 41 e-5             
+proton mass                                                 1.672 621 925 95 e-27    0.000 000 000 52 e-27    kg
+proton mass energy equivalent                               1.503 277 618 02 e-10    0.000 000 000 47 e-10    J
+proton mass energy equivalent in MeV                        938.272 089 43           0.000 000 29             MeV
+proton mass in u                                            1.007 276 466 5789       0.000 000 000 0083       u
+proton molar mass                                           1.007 276 467 64 e-3     0.000 000 000 31 e-3     kg mol^-1
+proton-muon mass ratio                                      8.880 243 38             0.000 000 20             
+proton-neutron mag. mom. ratio                              -1.459 898 02            0.000 000 34             
+proton-neutron mass ratio                                   0.998 623 477 97         0.000 000 000 40         
+proton relative atomic mass                                 1.007 276 466 5789       0.000 000 000 0083       
+proton rms charge radius                                    8.4075 e-16              0.0064 e-16              m
+proton-tau mass ratio                                       0.528 051                0.000 036                
+quantum of circulation                                      3.636 947 5467 e-4       0.000 000 0011 e-4       m^2 s^-1
+quantum of circulation times 2                              7.273 895 0934 e-4       0.000 000 0023 e-4       m^2 s^-1
+reduced Compton wavelength                                  3.861 592 6744 e-13      0.000 000 0012 e-13      m
+reduced muon Compton wavelength                             1.867 594 306 e-15       0.000 000 042 e-15       m
+reduced neutron Compton wavelength                          2.100 194 1520 e-16      0.000 000 0011 e-16      m
+reduced Planck constant                                     1.054 571 817... e-34    (exact)                  J s
+reduced Planck constant in eV s                             6.582 119 569... e-16    (exact)                  eV s
+reduced Planck constant times c in MeV fm                   197.326 980 4...         (exact)                  MeV fm
+reduced proton Compton wavelength                           2.103 089 100 51 e-16    0.000 000 000 66 e-16    m
+reduced tau Compton wavelength                              1.110 538 e-16           0.000 075 e-16           m
+Rydberg constant                                            10 973 731.568 157       0.000 012                m^-1
+Rydberg constant times c in Hz                              3.289 841 960 2500 e15   0.000 000 000 0036 e15   Hz
+Rydberg constant times hc in eV                             13.605 693 122 990       0.000 000 000 015        eV
+Rydberg constant times hc in J                              2.179 872 361 1030 e-18  0.000 000 000 0024 e-18  J
+Sackur-Tetrode constant (1 K, 100 kPa)                      -1.151 707 534 96        0.000 000 000 47         
+Sackur-Tetrode constant (1 K, 101.325 kPa)                  -1.164 870 521 49        0.000 000 000 47         
+second radiation constant                                   1.438 776 877... e-2     (exact)                  m K
+shielded helion gyromag. ratio                              2.037 894 6078 e8        0.000 000 0018 e8        s^-1 T^-1
+shielded helion gyromag. ratio in MHz/T                     32.434 100 033           0.000 000 028            MHz T^-1
+shielded helion mag. mom.                                   -1.074 553 110 35 e-26   0.000 000 000 93 e-26    J T^-1
+shielded helion mag. mom. to Bohr magneton ratio            -1.158 671 494 57 e-3    0.000 000 000 94 e-3     
+shielded helion mag. mom. to nuclear magneton ratio         -2.127 497 7624          0.000 000 0017           
+shielded helion to proton mag. mom. ratio                   -0.761 766 577 21        0.000 000 000 66         
+shielded helion to shielded proton mag. mom. ratio          -0.761 786 1334          0.000 000 0031           
+shielded proton gyromag. ratio                              2.675 153 194 e8         0.000 000 011 e8         s^-1 T^-1
+shielded proton gyromag. ratio in MHz/T                     42.576 385 43            0.000 000 17             MHz T^-1
+shielded proton mag. mom.                                   1.410 570 5830 e-26      0.000 000 0058 e-26      J T^-1
+shielded proton mag. mom. to Bohr magneton ratio            1.520 993 1551 e-3       0.000 000 0062 e-3       
+shielded proton mag. mom. to nuclear magneton ratio         2.792 775 648            0.000 000 011            
+shielding difference of d and p in HD                       1.987 70 e-8             0.000 10 e-8             
+shielding difference of t and p in HT                       2.394 50 e-8             0.000 20 e-8             
+speed of light in vacuum                                    299 792 458              (exact)                  m s^-1
+standard acceleration of gravity                            9.806 65                 (exact)                  m s^-2
+standard atmosphere                                         101 325                  (exact)                  Pa
+standard-state pressure                                     100 000                  (exact)                  Pa
+Stefan-Boltzmann constant                                   5.670 374 419... e-8     (exact)                  W m^-2 K^-4
+tau Compton wavelength                                      6.977 71 e-16            0.000 47 e-16            m
+tau-electron mass ratio                                     3477.23                  0.23                     
+tau energy equivalent                                       1776.86                  0.12                     MeV
+tau mass                                                    3.167 54 e-27            0.000 21 e-27            kg
+tau mass energy equivalent                                  2.846 84 e-10            0.000 19 e-10            J
+tau mass in u                                               1.907 54                 0.000 13                 u
+tau molar mass                                              1.907 54 e-3             0.000 13 e-3             kg mol^-1
+tau-muon mass ratio                                         16.8170                  0.0011                   
+tau-neutron mass ratio                                      1.891 15                 0.000 13                 
+tau-proton mass ratio                                       1.893 76                 0.000 13                 
+Thomson cross section                                       6.652 458 7051 e-29      0.000 000 0062 e-29      m^2
+triton-electron mass ratio                                  5496.921 535 51          0.000 000 21             
+triton g factor                                             5.957 924 930            0.000 000 012            
+triton mag. mom.                                            1.504 609 5178 e-26      0.000 000 0030 e-26      J T^-1
+triton mag. mom. to Bohr magneton ratio                     1.622 393 6648 e-3       0.000 000 0032 e-3       
+triton mag. mom. to nuclear magneton ratio                  2.978 962 4650           0.000 000 0059           
+triton mass                                                 5.007 356 7512 e-27      0.000 000 0016 e-27      kg
+triton mass energy equivalent                               4.500 387 8119 e-10      0.000 000 0014 e-10      J
+triton mass energy equivalent in MeV                        2808.921 136 68          0.000 000 88             MeV
+triton mass in u                                            3.015 500 715 97         0.000 000 000 10         u
+triton molar mass                                           3.015 500 719 13 e-3     0.000 000 000 94 e-3     kg mol^-1
+triton-proton mass ratio                                    2.993 717 034 03         0.000 000 000 10         
+triton relative atomic mass                                 3.015 500 715 97         0.000 000 000 10         
+triton to proton mag. mom. ratio                            1.066 639 9189           0.000 000 0021           
+unified atomic mass unit                                    1.660 539 068 92 e-27    0.000 000 000 52 e-27    kg
+vacuum electric permittivity                                8.854 187 8188 e-12      0.000 000 0014 e-12      F m^-1
+vacuum mag. permeability                                    1.256 637 061 27 e-6     0.000 000 000 20 e-6     N A^-2
+von Klitzing constant                                       25 812.807 45...         (exact)                  ohm
+weak mixing angle                                           0.223 05                 0.000 23                 
+Wien frequency displacement law constant                    5.878 925 757... e10     (exact)                  Hz K^-1
+Wien wavelength displacement law constant                   2.897 771 955... e-3     (exact)                  m K
+W to Z mass ratio                                           0.881 45                 0.000 13                    """
+
+
+exact2022 = exact2018
+
+
+# -----------------------------------------------------------------------------
+
+
+def parse_constants_2002to2014(
+    d: str, exact_func: Callable[[Any], Any]
+) -> dict[str, tuple[float, str, float]]:
+    constants: dict[str, tuple[float, str, float]] = {}
+    exact: dict[str, float] = {}
+    need_replace = set()
+    for line in d.split('\n'):
+        name = line[:55].rstrip()
+        val = float(line[55:77].replace(' ', '').replace('...', ''))
+        is_truncated = '...' in line[55:77]
+        is_exact = '(exact)' in line[77:99]
+        if is_truncated and is_exact:
+            # missing decimals, use computed exact value
+            need_replace.add(name)
+        elif is_exact:
+            exact[name] = val
+        else:
+            assert not is_truncated
+        uncert = float(line[77:99].replace(' ', '').replace('(exact)', '0'))
+        units = line[99:].rstrip()
+        constants[name] = (val, units, uncert)
+    replace = exact_func(exact)
+    replace_exact(constants, need_replace, replace)
+    return constants
+
+
+def parse_constants_2018toXXXX(
+    d: str, exact_func: Callable[[Any], Any]
+) -> dict[str, tuple[float, str, float]]:
+    constants: dict[str, tuple[float, str, float]] = {}
+    exact: dict[str, float] = {}
+    need_replace = set()
+    for line in d.split('\n'):
+        name = line[:60].rstrip()
+        val = float(line[60:85].replace(' ', '').replace('...', ''))
+        is_truncated = '...' in line[60:85]
+        is_exact = '(exact)' in line[85:110]
+        if is_truncated and is_exact:
+            # missing decimals, use computed exact value
+            need_replace.add(name)
+        elif is_exact:
+            exact[name] = val
+        else:
+            assert not is_truncated
+        uncert = float(line[85:110].replace(' ', '').replace('(exact)', '0'))
+        units = line[110:].rstrip()
+        constants[name] = (val, units, uncert)
+    replace = exact_func(exact)
+    replace_exact(constants, need_replace, replace)
+    return constants
+
+
+def replace_exact(d, to_replace, exact):
+    for name in to_replace:
+        assert name in exact, f'Missing exact value: {name}'
+        assert abs(exact[name]/d[name][0] - 1) <= 1e-9, \
+            f'Bad exact value: {name}: { exact[name]}, {d[name][0]}'
+        d[name] = (exact[name],) + d[name][1:]
+    assert set(exact.keys()) == set(to_replace)
+
+
+_physical_constants_2002 = parse_constants_2002to2014(txt2002, exact2002)
+_physical_constants_2006 = parse_constants_2002to2014(txt2006, exact2006)
+_physical_constants_2010 = parse_constants_2002to2014(txt2010, exact2010)
+_physical_constants_2014 = parse_constants_2002to2014(txt2014, exact2014)
+_physical_constants_2018 = parse_constants_2018toXXXX(txt2018, exact2018)
+_physical_constants_2022 = parse_constants_2018toXXXX(txt2022, exact2022)
+
+physical_constants: dict[str, tuple[float, str, float]] = {}
+physical_constants.update(_physical_constants_2002)
+physical_constants.update(_physical_constants_2006)
+physical_constants.update(_physical_constants_2010)
+physical_constants.update(_physical_constants_2014)
+physical_constants.update(_physical_constants_2018)
+physical_constants.update(_physical_constants_2022)
+_current_constants = _physical_constants_2022
+_current_codata = "CODATA 2022"
+
+# check obsolete values
+_obsolete_constants = {}
+for k in physical_constants:
+    if k not in _current_constants:
+        _obsolete_constants[k] = True
+
+# generate some additional aliases
+_aliases = {}
+for k in _physical_constants_2002:
+    if 'magn.' in k:
+        _aliases[k] = k.replace('magn.', 'mag.')
+for k in _physical_constants_2006:
+    if 'momentum' in k:
+        _aliases[k] = k.replace('momentum', 'mom.um')
+for k in _physical_constants_2018:
+    if 'momentum' in k:
+        _aliases[k] = k.replace('momentum', 'mom.um')
+for k in _physical_constants_2022:
+    if 'momentum' in k:
+        _aliases[k] = k.replace('momentum', 'mom.um')        
+
+# CODATA 2018 and 2022: renamed and no longer exact; use as aliases
+_aliases['mag. constant'] = 'vacuum mag. permeability'
+_aliases['electric constant'] = 'vacuum electric permittivity'
+
+
+_extra_alias_keys = ['natural unit of velocity',
+                     'natural unit of action',
+                     'natural unit of action in eV s',
+                     'natural unit of mass',
+                     'natural unit of energy',
+                     'natural unit of energy in MeV',
+                     'natural unit of mom.um',
+                     'natural unit of mom.um in MeV/c',
+                     'natural unit of length',
+                     'natural unit of time']
+
+# finally, insert aliases for values
+for k, v in list(_aliases.items()):
+    if v in _current_constants or v in _extra_alias_keys:
+        physical_constants[k] = physical_constants[v]
+    else:
+        del _aliases[k]
+
+
+class ConstantWarning(DeprecationWarning):
+    """Accessing a constant no longer in current CODATA data set"""
+    pass
+
+
+def _check_obsolete(key: str) -> None:
+    if key in _obsolete_constants and key not in _aliases:
+        warnings.warn(f"Constant '{key}' is not in current {_current_codata} data set",
+                      ConstantWarning, stacklevel=3)
+
+
+@xp_capabilities(out_of_scope=True)
+def value(key: str) -> float:
+    """
+    Value in physical_constants indexed by key
+
+    Parameters
+    ----------
+    key : Python string
+        Key in dictionary `physical_constants`
+
+    Returns
+    -------
+    value : float
+        Value in `physical_constants` corresponding to `key`
+
+    Examples
+    --------
+    >>> from scipy import constants
+    >>> constants.value('elementary charge')
+    1.602176634e-19
+
+    """
+    _check_obsolete(key)
+    return physical_constants[key][0]
+
+
+@xp_capabilities(out_of_scope=True)
+def unit(key: str) -> str:
+    """
+    Unit in physical_constants indexed by key
+
+    Parameters
+    ----------
+    key : Python string
+        Key in dictionary `physical_constants`
+
+    Returns
+    -------
+    unit : Python string
+        Unit in `physical_constants` corresponding to `key`
+
+    Examples
+    --------
+    >>> from scipy import constants
+    >>> constants.unit('proton mass')
+    'kg'
+
+    """
+    _check_obsolete(key)
+    return physical_constants[key][1]
+
+
+@xp_capabilities(out_of_scope=True)
+def precision(key: str) -> float:
+    """
+    Relative precision in physical_constants indexed by key
+
+    Parameters
+    ----------
+    key : Python string
+        Key in dictionary `physical_constants`
+
+    Returns
+    -------
+    prec : float
+        Relative precision in `physical_constants` corresponding to `key`
+
+    Examples
+    --------
+    >>> from scipy import constants
+    >>> constants.precision('proton mass')
+    5.1e-37
+
+    """
+    _check_obsolete(key)
+    return physical_constants[key][2] / physical_constants[key][0]
+
+
+@xp_capabilities(out_of_scope=True)
+def find(sub: str | None = None, disp: bool = False) -> Any:
+    """
+    Return list of physical_constant keys containing a given string.
+
+    Parameters
+    ----------
+    sub : str
+        Sub-string to search keys for. By default, return all keys.
+    disp : bool
+        If True, print the keys that are found and return None.
+        Otherwise, return the list of keys without printing anything.
+
+    Returns
+    -------
+    keys : list or None
+        If `disp` is False, the list of keys is returned.
+        Otherwise, None is returned.
+
+    Examples
+    --------
+    >>> from scipy.constants import find, physical_constants
+
+    Which keys in the ``physical_constants`` dictionary contain 'boltzmann'?
+
+    >>> find('boltzmann')
+    ['Boltzmann constant',
+     'Boltzmann constant in Hz/K',
+     'Boltzmann constant in eV/K',
+     'Boltzmann constant in inverse meter per kelvin',
+     'Stefan-Boltzmann constant']
+
+    Get the constant called 'Boltzmann constant in Hz/K':
+
+    >>> physical_constants['Boltzmann constant in Hz/K']
+    (20836619120.0, 'Hz K^-1', 0.0)
+
+    Find constants with 'radius' in the key:
+
+    >>> find('radius')
+    ['Bohr radius',
+     'alpha particle rms charge radius',
+     'classical electron radius',
+     'deuteron rms charge radius',
+     'proton rms charge radius']
+    >>> physical_constants['classical electron radius']
+    (2.8179403262e-15, 'm', 1.3e-24)
+
+    """
+    if sub is None:
+        result = list(_current_constants.keys())
+    else:
+        result = [key for key in _current_constants
+                  if sub.lower() in key.lower()]
+
+    result.sort()
+    if disp:
+        for key in result:
+            print(key)
+        return
+    else:
+        return result
+
+# This is not used here, but it must be defined to pass
+# scipy/_lib/tests/test_public_api.py::test_private_but_present_deprecation
+c = value('speed of light in vacuum')
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/constants/_constants.py b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/_constants.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc4bdf83d60e37e039b9b830f74f7024c1759d32
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/_constants.py
@@ -0,0 +1,369 @@
+"""
+Collection of physical constants and conversion factors.
+
+Most constants are in SI units, so you can do
+print '10 mile per minute is', 10*mile/minute, 'm/s or', 10*mile/(minute*knot), 'knots'
+
+The list is not meant to be comprehensive, but just convenient for everyday use.
+"""
+
+import math as _math
+from typing import TYPE_CHECKING, Any
+
+from ._codata import value as _cd
+
+if TYPE_CHECKING:
+    import numpy.typing as npt
+
+from scipy._lib._array_api import array_namespace, _asarray, xp_capabilities
+
+
+"""
+BasSw 2006
+physical constants: imported from CODATA
+unit conversion: see e.g., NIST special publication 811
+Use at own risk: double-check values before calculating your Mars orbit-insertion burn.
+Some constants exist in a few variants, which are marked with suffixes.
+The ones without any suffix should be the most common ones.
+"""
+
+__all__ = [
+    'Avogadro', 'Boltzmann', 'Btu', 'Btu_IT', 'Btu_th', 'G',
+    'Julian_year', 'N_A', 'Planck', 'R', 'Rydberg',
+    'Stefan_Boltzmann', 'Wien', 'acre', 'alpha',
+    'angstrom', 'arcmin', 'arcminute', 'arcsec',
+    'arcsecond', 'astronomical_unit', 'atm',
+    'atmosphere', 'atomic_mass', 'atto', 'au', 'bar',
+    'barrel', 'bbl', 'blob', 'c', 'calorie',
+    'calorie_IT', 'calorie_th', 'carat', 'centi',
+    'convert_temperature', 'day', 'deci', 'degree',
+    'degree_Fahrenheit', 'deka', 'dyn', 'dyne', 'e',
+    'eV', 'electron_mass', 'electron_volt',
+    'elementary_charge', 'epsilon_0', 'erg',
+    'exa', 'exbi', 'femto', 'fermi', 'fine_structure',
+    'fluid_ounce', 'fluid_ounce_US', 'fluid_ounce_imp',
+    'foot', 'g', 'gallon', 'gallon_US', 'gallon_imp',
+    'gas_constant', 'gibi', 'giga', 'golden', 'golden_ratio',
+    'grain', 'gram', 'gravitational_constant', 'h', 'hbar',
+    'hectare', 'hecto', 'horsepower', 'hour', 'hp',
+    'inch', 'k', 'kgf', 'kibi', 'kilo', 'kilogram_force',
+    'kmh', 'knot', 'lambda2nu', 'lb', 'lbf',
+    'light_year', 'liter', 'litre', 'long_ton', 'm_e',
+    'm_n', 'm_p', 'm_u', 'mach', 'mebi', 'mega',
+    'metric_ton', 'micro', 'micron', 'mil', 'mile',
+    'milli', 'minute', 'mmHg', 'mph', 'mu_0', 'nano',
+    'nautical_mile', 'neutron_mass', 'nu2lambda',
+    'ounce', 'oz', 'parsec', 'pebi', 'peta',
+    'pi', 'pico', 'point', 'pound', 'pound_force',
+    'proton_mass', 'psi', 'pt', 'quecto', 'quetta', 'ronna', 'ronto',
+    'short_ton', 'sigma', 'slinch', 'slug', 'speed_of_light',
+    'speed_of_sound', 'stone', 'survey_foot',
+    'survey_mile', 'tebi', 'tera', 'ton_TNT',
+    'torr', 'troy_ounce', 'troy_pound', 'u',
+    'week', 'yard', 'year', 'yobi', 'yocto',
+    'yotta', 'zebi', 'zepto', 'zero_Celsius', 'zetta'
+]
+
+
+# mathematical constants
+pi = _math.pi
+golden = golden_ratio = (1 + _math.sqrt(5)) / 2
+
+# SI prefixes
+quetta = 1e30
+ronna = 1e27
+yotta = 1e24
+zetta = 1e21
+exa = 1e18
+peta = 1e15
+tera = 1e12
+giga = 1e9
+mega = 1e6
+kilo = 1e3
+hecto = 1e2
+deka = 1e1
+deci = 1e-1
+centi = 1e-2
+milli = 1e-3
+micro = 1e-6
+nano = 1e-9
+pico = 1e-12
+femto = 1e-15
+atto = 1e-18
+zepto = 1e-21
+yocto = 1e-24
+ronto = 1e-27
+quecto = 1e-30
+
+# binary prefixes
+kibi = 2**10
+mebi = 2**20
+gibi = 2**30
+tebi = 2**40
+pebi = 2**50
+exbi = 2**60
+zebi = 2**70
+yobi = 2**80
+
+# physical constants
+c = speed_of_light = _cd('speed of light in vacuum')
+mu_0 = _cd('vacuum mag. permeability')
+epsilon_0 = _cd('vacuum electric permittivity')
+h = Planck = _cd('Planck constant')
+hbar = _cd('reduced Planck constant')
+G = gravitational_constant = _cd('Newtonian constant of gravitation')
+g = _cd('standard acceleration of gravity')
+e = elementary_charge = _cd('elementary charge')
+R = gas_constant = _cd('molar gas constant')
+alpha = fine_structure = _cd('fine-structure constant')
+N_A = Avogadro = _cd('Avogadro constant')
+k = Boltzmann = _cd('Boltzmann constant')
+sigma = Stefan_Boltzmann = _cd('Stefan-Boltzmann constant')
+Wien = _cd('Wien wavelength displacement law constant')
+Rydberg = _cd('Rydberg constant')
+
+# mass in kg
+gram = 1e-3
+metric_ton = 1e3
+grain = 64.79891e-6
+lb = pound = 7000 * grain  # avoirdupois
+blob = slinch = pound * g / 0.0254  # lbf*s**2/in (added in 1.0.0)
+slug = blob / 12  # lbf*s**2/foot (added in 1.0.0)
+oz = ounce = pound / 16
+stone = 14 * pound
+long_ton = 2240 * pound
+short_ton = 2000 * pound
+
+troy_ounce = 480 * grain  # only for metals / gems
+troy_pound = 12 * troy_ounce
+carat = 200e-6
+
+m_e = electron_mass = _cd('electron mass')
+m_p = proton_mass = _cd('proton mass')
+m_n = neutron_mass = _cd('neutron mass')
+m_u = u = atomic_mass = _cd('atomic mass constant')
+
+# angle in rad
+degree = pi / 180
+arcmin = arcminute = degree / 60
+arcsec = arcsecond = arcmin / 60
+
+# time in second
+minute = 60.0
+hour = 60 * minute
+day = 24 * hour
+week = 7 * day
+year = 365 * day
+Julian_year = 365.25 * day
+
+# length in meter
+inch = 0.0254
+foot = 12 * inch
+yard = 3 * foot
+mile = 1760 * yard
+mil = inch / 1000
+pt = point = inch / 72  # typography
+survey_foot = 1200.0 / 3937
+survey_mile = 5280 * survey_foot
+nautical_mile = 1852.0
+fermi = 1e-15
+angstrom = 1e-10
+micron = 1e-6
+au = astronomical_unit = 149597870700.0
+light_year = Julian_year * c
+parsec = au / arcsec
+
+# pressure in pascal
+atm = atmosphere = _cd('standard atmosphere')
+bar = 1e5
+torr = mmHg = atm / 760
+psi = pound * g / (inch * inch)
+
+# area in meter**2
+hectare = 1e4
+acre = 43560 * foot**2
+
+# volume in meter**3
+litre = liter = 1e-3
+gallon = gallon_US = 231 * inch**3  # US
+# pint = gallon_US / 8
+fluid_ounce = fluid_ounce_US = gallon_US / 128
+bbl = barrel = 42 * gallon_US  # for oil
+
+gallon_imp = 4.54609e-3  # UK
+fluid_ounce_imp = gallon_imp / 160
+
+# speed in meter per second
+kmh = 1e3 / hour
+mph = mile / hour
+# approx value of mach at 15 degrees in 1 atm. Is this a common value?
+mach = speed_of_sound = 340.5
+knot = nautical_mile / hour
+
+# temperature in kelvin
+zero_Celsius = 273.15
+degree_Fahrenheit = 1/1.8  # only for differences
+
+# energy in joule
+eV = electron_volt = elementary_charge  # * 1 Volt
+calorie = calorie_th = 4.184
+calorie_IT = 4.1868
+erg = 1e-7
+Btu_th = pound * degree_Fahrenheit * calorie_th / gram
+Btu = Btu_IT = pound * degree_Fahrenheit * calorie_IT / gram
+ton_TNT = 1e9 * calorie_th
+# Wh = watt_hour
+
+# power in watt
+hp = horsepower = 550 * foot * pound * g
+
+# force in newton
+dyn = dyne = 1e-5
+lbf = pound_force = pound * g
+kgf = kilogram_force = g  # * 1 kg
+
+# functions for conversions that are not linear
+
+
+@xp_capabilities()
+def convert_temperature(
+    val: "npt.ArrayLike",
+    old_scale: str,
+    new_scale: str,
+) -> Any:
+    """
+    Convert from a temperature scale to another one among Celsius, Kelvin,
+    Fahrenheit, and Rankine scales.
+
+    Parameters
+    ----------
+    val : array_like
+        Value(s) of the temperature(s) to be converted expressed in the
+        original scale.
+    old_scale : str
+        Specifies as a string the original scale from which the temperature
+        value(s) will be converted. Supported scales are Celsius ('Celsius',
+        'celsius', 'C' or 'c'), Kelvin ('Kelvin', 'kelvin', 'K', 'k'),
+        Fahrenheit ('Fahrenheit', 'fahrenheit', 'F' or 'f'), and Rankine
+        ('Rankine', 'rankine', 'R', 'r').
+    new_scale : str
+        Specifies as a string the new scale to which the temperature
+        value(s) will be converted. Supported scales are Celsius ('Celsius',
+        'celsius', 'C' or 'c'), Kelvin ('Kelvin', 'kelvin', 'K', 'k'),
+        Fahrenheit ('Fahrenheit', 'fahrenheit', 'F' or 'f'), and Rankine
+        ('Rankine', 'rankine', 'R', 'r').
+
+    Returns
+    -------
+    res : float or array of floats
+        Value(s) of the converted temperature(s) expressed in the new scale.
+
+    Notes
+    -----
+    .. versionadded:: 0.18.0
+
+    Examples
+    --------
+    >>> from scipy.constants import convert_temperature
+    >>> import numpy as np
+    >>> convert_temperature(np.array([-40, 40]), 'Celsius', 'Kelvin')
+    array([ 233.15,  313.15])
+
+    """
+    xp = array_namespace(val)
+    _val = _asarray(val, xp=xp, subok=True)
+    # Convert from `old_scale` to Kelvin
+    if old_scale.lower() in ['celsius', 'c']:
+        tempo = _val + zero_Celsius
+    elif old_scale.lower() in ['kelvin', 'k']:
+        tempo = _val
+    elif old_scale.lower() in ['fahrenheit', 'f']:
+        tempo = (_val - 32) * 5 / 9 + zero_Celsius
+    elif old_scale.lower() in ['rankine', 'r']:
+        tempo = _val * 5 / 9
+    else:
+        raise NotImplementedError(f"{old_scale=} is unsupported: supported scales "
+                                   "are Celsius, Kelvin, Fahrenheit, and "
+                                   "Rankine")
+    # and from Kelvin to `new_scale`.
+    if new_scale.lower() in ['celsius', 'c']:
+        res = tempo - zero_Celsius
+    elif new_scale.lower() in ['kelvin', 'k']:
+        res = tempo
+    elif new_scale.lower() in ['fahrenheit', 'f']:
+        res = (tempo - zero_Celsius) * 9 / 5 + 32
+    elif new_scale.lower() in ['rankine', 'r']:
+        res = tempo * 9 / 5
+    else:
+        raise NotImplementedError(f"{new_scale=} is unsupported: supported "
+                                   "scales are 'Celsius', 'Kelvin', "
+                                   "'Fahrenheit', and 'Rankine'")
+
+    return res
+
+
+# optics
+
+
+@xp_capabilities()
+def lambda2nu(lambda_: "npt.ArrayLike") -> Any:
+    """
+    Convert wavelength to optical frequency
+
+    Parameters
+    ----------
+    lambda_ : array_like
+        Wavelength(s) to be converted.
+
+    Returns
+    -------
+    nu : float or array of floats
+        Equivalent optical frequency.
+
+    Notes
+    -----
+    Computes ``nu = c / lambda`` where c = 299792458.0, i.e., the
+    (vacuum) speed of light in meters/second.
+
+    Examples
+    --------
+    >>> from scipy.constants import lambda2nu, speed_of_light
+    >>> import numpy as np
+    >>> lambda2nu(np.array((1, speed_of_light)))
+    array([  2.99792458e+08,   1.00000000e+00])
+
+    """
+    xp = array_namespace(lambda_)
+    return c / _asarray(lambda_, xp=xp, subok=True)
+
+
+@xp_capabilities()
+def nu2lambda(nu: "npt.ArrayLike") -> Any:
+    """
+    Convert optical frequency to wavelength.
+
+    Parameters
+    ----------
+    nu : array_like
+        Optical frequency to be converted.
+
+    Returns
+    -------
+    lambda : float or array of floats
+        Equivalent wavelength(s).
+
+    Notes
+    -----
+    Computes ``lambda = c / nu`` where c = 299792458.0, i.e., the
+    (vacuum) speed of light in meters/second.
+
+    Examples
+    --------
+    >>> from scipy.constants import nu2lambda, speed_of_light
+    >>> import numpy as np
+    >>> nu2lambda(np.array((1, speed_of_light)))
+    array([  2.99792458e+08,   1.00000000e+00])
+
+    """
+    xp = array_namespace(nu)
+    return c / _asarray(nu, xp=xp, subok=True)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/constants/codata.py b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/codata.py
new file mode 100644
index 0000000000000000000000000000000000000000..912e0bbf7c4f14d23ced4546b6704f7789996d97
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/codata.py
@@ -0,0 +1,21 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.constants` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'physical_constants', 'value', 'unit', 'precision', 'find',
+    'ConstantWarning', 'k', 'c',
+
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="constants", module="codata",
+                                   private_modules=["_codata"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/constants/constants.py b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/constants.py
new file mode 100644
index 0000000000000000000000000000000000000000..855901ba802881090b99b7e8972de741331c7ab9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/constants.py
@@ -0,0 +1,53 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.constants` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'Avogadro', 'Boltzmann', 'Btu', 'Btu_IT', 'Btu_th', 'G',
+    'Julian_year', 'N_A', 'Planck', 'R', 'Rydberg',
+    'Stefan_Boltzmann', 'Wien', 'acre', 'alpha',
+    'angstrom', 'arcmin', 'arcminute', 'arcsec',
+    'arcsecond', 'astronomical_unit', 'atm',
+    'atmosphere', 'atomic_mass', 'atto', 'au', 'bar',
+    'barrel', 'bbl', 'blob', 'c', 'calorie',
+    'calorie_IT', 'calorie_th', 'carat', 'centi',
+    'convert_temperature', 'day', 'deci', 'degree',
+    'degree_Fahrenheit', 'deka', 'dyn', 'dyne', 'e',
+    'eV', 'electron_mass', 'electron_volt',
+    'elementary_charge', 'epsilon_0', 'erg',
+    'exa', 'exbi', 'femto', 'fermi', 'fine_structure',
+    'fluid_ounce', 'fluid_ounce_US', 'fluid_ounce_imp',
+    'foot', 'g', 'gallon', 'gallon_US', 'gallon_imp',
+    'gas_constant', 'gibi', 'giga', 'golden', 'golden_ratio',
+    'grain', 'gram', 'gravitational_constant', 'h', 'hbar',
+    'hectare', 'hecto', 'horsepower', 'hour', 'hp',
+    'inch', 'k', 'kgf', 'kibi', 'kilo', 'kilogram_force',
+    'kmh', 'knot', 'lambda2nu', 'lb', 'lbf',
+    'light_year', 'liter', 'litre', 'long_ton', 'm_e',
+    'm_n', 'm_p', 'm_u', 'mach', 'mebi', 'mega',
+    'metric_ton', 'micro', 'micron', 'mil', 'mile',
+    'milli', 'minute', 'mmHg', 'mph', 'mu_0', 'nano',
+    'nautical_mile', 'neutron_mass', 'nu2lambda',
+    'ounce', 'oz', 'parsec', 'pebi', 'peta',
+    'pi', 'pico', 'point', 'pound', 'pound_force',
+    'proton_mass', 'psi', 'pt', 'short_ton',
+    'sigma', 'slinch', 'slug', 'speed_of_light',
+    'speed_of_sound', 'stone', 'survey_foot',
+    'survey_mile', 'tebi', 'tera', 'ton_TNT',
+    'torr', 'troy_ounce', 'troy_pound', 'u',
+    'week', 'yard', 'year', 'yobi', 'yocto',
+    'yotta', 'zebi', 'zepto', 'zero_Celsius', 'zetta'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="constants", module="constants",
+                                   private_modules=["_constants"], all=__all__,
+                                   attribute=name)
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/constants/tests/test_codata.py b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/tests/test_codata.py
new file mode 100644
index 0000000000000000000000000000000000000000..ece796136a43ef6f3078272e4d0223263c9e31e8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/tests/test_codata.py
@@ -0,0 +1,78 @@
+from scipy.constants import find, value, c, speed_of_light, precision
+from numpy.testing import assert_equal, assert_, assert_almost_equal
+import scipy.constants._codata as _cd
+from scipy import constants
+
+
+def test_find():
+    keys = find('weak mixing', disp=False)
+    assert_equal(keys, ['weak mixing angle'])
+
+    keys = find('qwertyuiop', disp=False)
+    assert_equal(keys, [])
+
+    keys = find('natural unit', disp=False)
+    assert_equal(keys, sorted(['natural unit of velocity',
+                                'natural unit of action',
+                                'natural unit of action in eV s',
+                                'natural unit of mass',
+                                'natural unit of energy',
+                                'natural unit of energy in MeV',
+                                'natural unit of momentum',
+                                'natural unit of momentum in MeV/c',
+                                'natural unit of length',
+                                'natural unit of time']))
+
+
+def test_basic_table_parse():
+    c_s = 'speed of light in vacuum'
+    assert_equal(value(c_s), c)
+    assert_equal(value(c_s), speed_of_light)
+
+
+def test_basic_lookup():
+    assert_equal('{} {}'.format(int(_cd.value('speed of light in vacuum')),
+                                _cd.unit('speed of light in vacuum')),
+                 '299792458 m s^-1')
+
+
+def test_find_all():
+    assert_(len(find(disp=False)) > 300)
+
+
+def test_find_single():
+    assert_equal(find('Wien freq', disp=False)[0],
+                 'Wien frequency displacement law constant')
+
+
+def test_2002_vs_2006():
+    assert_almost_equal(value('magn. flux quantum'),
+                        value('mag. flux quantum'))
+
+
+def test_exact_values():
+    # Check that updating stored values with exact ones worked.
+    exact = dict((k, v[0]) for k, v in _cd._physical_constants_2018.items())
+    replace = _cd.exact2018(exact)
+    for key, val in replace.items():
+        assert_equal(val, value(key))
+        assert precision(key) == 0
+
+
+def test_gh11341():
+    # gh-11341 noted that these three constants should exist (for backward
+    # compatibility) and should always have the same value:
+    a = constants.epsilon_0
+    b = constants.physical_constants['electric constant'][0]
+    c = constants.physical_constants['vacuum electric permittivity'][0]
+    assert a == b == c
+
+
+def test_gh14467():
+    # gh-14467 noted that some physical constants in CODATA are rounded
+    # to only ten significant figures even though they are supposed to be
+    # exact. Check that (at least) the case mentioned in the issue is resolved.
+    res = constants.physical_constants['Boltzmann constant in eV/K'][0]
+    ref = (constants.physical_constants['Boltzmann constant'][0]
+           / constants.physical_constants['elementary charge'][0])
+    assert res == ref
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/constants/tests/test_constants.py b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/tests/test_constants.py
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/constants/tests/test_constants.py
@@ -0,0 +1,83 @@
+import pytest
+
+import scipy.constants as sc
+from scipy._lib._array_api_no_0d import xp_assert_equal, xp_assert_close
+from scipy._lib._array_api import make_xp_test_case
+
+lazy_xp_modules = [sc]
+
+
+@make_xp_test_case(sc.convert_temperature)
+class TestConvertTemperature:
+    def test_convert_temperature(self, xp):
+        xp_assert_equal(sc.convert_temperature(xp.asarray(32.), 'f', 'Celsius'),
+                        xp.asarray(0.0))
+        xp_assert_equal(sc.convert_temperature(xp.asarray([0., 0.]),
+                                               'celsius', 'Kelvin'),
+                        xp.asarray([273.15, 273.15]))
+        xp_assert_equal(sc.convert_temperature(xp.asarray([0., 0.]), 'kelvin', 'c'),
+                        xp.asarray([-273.15, -273.15]))
+        xp_assert_equal(sc.convert_temperature(xp.asarray([32., 32.]), 'f', 'k'),
+                        xp.asarray([273.15, 273.15]))
+        xp_assert_equal(sc.convert_temperature(xp.asarray([273.15, 273.15]),
+                                               'kelvin', 'F'),
+                        xp.asarray([32., 32.]))
+        xp_assert_equal(sc.convert_temperature(xp.asarray([0., 0.]), 'C', 'fahrenheit'),
+                        xp.asarray([32., 32.]))
+        xp_assert_close(sc.convert_temperature(xp.asarray([0., 0.], dtype=xp.float64),
+                                               'c', 'r'),
+                        xp.asarray([491.67, 491.67], dtype=xp.float64),
+                        rtol=0., atol=1e-13)
+        xp_assert_close(sc.convert_temperature(xp.asarray([491.67, 491.67],
+                                                        dtype=xp.float64),
+                                               'Rankine', 'C'),
+                        xp.asarray([0., 0.], dtype=xp.float64), rtol=0., atol=1e-13)
+        xp_assert_close(sc.convert_temperature(xp.asarray([491.67, 491.67],
+                                                        dtype=xp.float64),
+                                               'r', 'F'),
+                        xp.asarray([32., 32.], dtype=xp.float64), rtol=0., atol=1e-13)
+        xp_assert_close(sc.convert_temperature(xp.asarray([32., 32.], dtype=xp.float64),
+                                               'fahrenheit', 'R'),
+                        xp.asarray([491.67, 491.67], dtype=xp.float64),
+                        rtol=0., atol=1e-13)
+        xp_assert_close(sc.convert_temperature(xp.asarray([273.15, 273.15],
+                                                        dtype=xp.float64),
+                                               'K', 'R'),
+                        xp.asarray([491.67, 491.67], dtype=xp.float64),
+                        rtol=0., atol=1e-13)
+        xp_assert_close(sc.convert_temperature(xp.asarray([491.67, 0.],
+                                                          dtype=xp.float64),
+                                               'rankine', 'kelvin'),
+                        xp.asarray([273.15, 0.], dtype=xp.float64), rtol=0., atol=1e-13)
+
+    def test_convert_temperature_array_like(self):
+        xp_assert_close(sc.convert_temperature([491.67, 0.], 'rankine', 'kelvin'),
+                        [273.15, 0.], rtol=0., atol=1e-13)
+
+
+    def test_convert_temperature_errors(self):
+        with pytest.raises(NotImplementedError, match="old_scale="):
+            sc.convert_temperature(1, old_scale="cheddar", new_scale="kelvin")
+        with pytest.raises(NotImplementedError, match="new_scale="):
+            sc.convert_temperature(1, old_scale="kelvin", new_scale="brie")
+
+
+@make_xp_test_case(sc.lambda2nu)
+class TestLambdaToNu:
+    def test_lambda_to_nu(self, xp):
+        xp_assert_equal(sc.lambda2nu(xp.asarray([sc.speed_of_light, 1])),
+                        xp.asarray([1, sc.speed_of_light]))
+
+
+    def test_lambda_to_nu_array_like(self):
+        xp_assert_close(sc.lambda2nu([sc.speed_of_light, 1]), [1, sc.speed_of_light])
+
+
+@make_xp_test_case(sc.nu2lambda)
+class TestNuToLambda:
+    def test_nu_to_lambda(self, xp):
+        xp_assert_equal(sc.nu2lambda(xp.asarray([sc.speed_of_light, 1])),
+                        xp.asarray([1, sc.speed_of_light]))
+
+    def test_nu_to_lambda_array_like(self):
+        xp_assert_close(sc.nu2lambda([sc.speed_of_light, 1]), [1, sc.speed_of_light])
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/__init__.py
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index 0000000000000000000000000000000000000000..fdd4ffebec4c57f6d399a0f76df2b66056f0b225
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/__init__.py
@@ -0,0 +1,90 @@
+"""
+================================
+Datasets (:mod:`scipy.datasets`)
+================================
+
+.. currentmodule:: scipy.datasets
+
+Dataset Methods
+===============
+
+.. autosummary::
+   :toctree: generated/
+
+   ascent
+   face
+   electrocardiogram
+
+Utility Methods
+===============
+
+.. autosummary::
+   :toctree: generated/
+
+   download_all    -- Download all the dataset files to specified path.
+   clear_cache     -- Clear cached dataset directory.
+
+
+Usage of Datasets
+=================
+
+SciPy dataset methods can be simply called as follows: ``'()'``
+This downloads the dataset files over the network once, and saves the cache,
+before returning a `numpy.ndarray` object representing the dataset.
+
+Note that the return data structure and data type might be different for
+different dataset methods. For a more detailed example on usage, please look
+into the particular dataset method documentation above.
+
+
+How dataset retrieval and storage works
+=======================================
+
+SciPy dataset files are stored within individual GitHub repositories under the
+SciPy GitHub organization, following a naming convention as
+``'dataset-'``, for example `scipy.datasets.face` files live at
+https://github.com/scipy/dataset-face.  The `scipy.datasets` submodule utilizes
+and depends on `Pooch `_, a Python
+package built to simplify fetching data files. Pooch uses these repos to
+retrieve the respective dataset files when calling the dataset function.
+
+A registry of all the datasets, essentially a mapping of filenames with their
+SHA256 hash and repo urls are maintained, which Pooch uses to handle and verify
+the downloads on function call. After downloading the dataset once, the files
+are saved in the system cache directory under ``'scipy-data'``.
+
+Dataset cache locations may vary on different platforms.
+
+For macOS::
+
+    '~/Library/Caches/scipy-data'
+
+For Linux and other Unix-like platforms::
+
+    '~/.cache/scipy-data'  # or the value of the XDG_CACHE_HOME env var, if defined
+
+For Windows::
+
+    'C:\\Users\\\\AppData\\Local\\\\scipy-data\\Cache'
+
+
+In environments with constrained network connectivity for various security
+reasons or on systems without continuous internet connections, one may manually
+load the cache of the datasets by placing the contents of the dataset repo in
+the above mentioned cache directory to avoid fetching dataset errors without
+the internet connectivity.
+
+"""
+
+
+from ._fetchers import face, ascent, electrocardiogram
+from ._download_all import download_all
+from ._utils import clear_cache
+
+__all__ = ['ascent', 'electrocardiogram', 'face',
+           'download_all', 'clear_cache']
+
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_download_all.py b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_download_all.py
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index 0000000000000000000000000000000000000000..d410e968f4d4e25d788b93913c8901d1cd74b521
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_download_all.py
@@ -0,0 +1,74 @@
+"""
+Platform independent script to download all the
+`scipy.datasets` module data files.
+This doesn't require a full scipy build.
+
+Run: python _download_all.py 
+"""
+
+from scipy._lib._array_api import xp_capabilities
+
+import argparse
+try:
+    import pooch
+except ImportError:
+    pooch = None
+
+
+if __package__ is None or __package__ == '':
+    # Running as python script, use absolute import
+    import _registry  # type: ignore
+else:
+    # Running as python module, use relative import
+    from . import _registry
+
+
+@xp_capabilities(out_of_scope=True)
+def download_all(path=None):
+    """
+    Utility method to download all the dataset files
+    for `scipy.datasets` module.
+
+    Parameters
+    ----------
+    path : str, optional
+        Directory path to download all the dataset files.
+        If None, default to the system cache_dir detected by pooch.
+
+    Examples
+    --------
+    Download the datasets to the default cache location:
+
+    >>> from scipy import datasets
+    >>> datasets.download_all()
+
+    Download the datasets to the current directory:
+
+    >>> datasets.download_all(".")
+
+    """
+    if pooch is None:
+        raise ImportError("Missing optional dependency 'pooch' required "
+                          "for scipy.datasets module. Please use pip or "
+                          "conda to install 'pooch'.")
+    if path is None:
+        path = pooch.os_cache('scipy-data')
+    # https://github.com/scipy/scipy/issues/21879
+    downloader = pooch.HTTPDownloader(headers={"User-Agent": "SciPy"})
+    for dataset_name, dataset_hash in _registry.registry.items():
+        pooch.retrieve(url=_registry.registry_urls[dataset_name],
+                       known_hash=dataset_hash,
+                       fname=dataset_name, path=path, downloader=downloader)
+
+
+def main():
+    parser = argparse.ArgumentParser(description='Download SciPy data files.')
+    parser.add_argument("path", nargs='?', type=str,
+                        default=pooch.os_cache('scipy-data'),
+                        help="Directory path to download all the data files.")
+    args = parser.parse_args()
+    download_all(args.path)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_fetchers.py b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_fetchers.py
new file mode 100644
index 0000000000000000000000000000000000000000..f6389a0ca5da32ce86b018ac7f92b1e49300645b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_fetchers.py
@@ -0,0 +1,229 @@
+import sys
+
+from numpy import array, frombuffer, load
+from ._registry import registry, registry_urls
+
+from scipy._lib._array_api import xp_capabilities
+
+try:
+    import pooch
+except ImportError:
+    pooch = None
+    data_fetcher = None
+else:
+    data_fetcher = pooch.create(
+        # Use the default cache folder for the operating system
+        # Pooch uses appdirs (https://github.com/ActiveState/appdirs) to
+        # select an appropriate directory for the cache on each platform.
+        path=pooch.os_cache("scipy-data"),
+
+        # The remote data is on Github
+        # base_url is a required param, even though we override this
+        # using individual urls in the registry.
+        base_url="https://github.com/scipy/",
+        registry=registry,
+        urls=registry_urls
+    )
+
+
+def fetch_data(dataset_name, data_fetcher=data_fetcher):
+    if data_fetcher is None:
+        raise ImportError("Missing optional dependency 'pooch' required "
+                          "for scipy.datasets module. Please use pip or "
+                          "conda to install 'pooch'.")
+    # https://github.com/scipy/scipy/issues/21879
+    downloader = pooch.HTTPDownloader(
+        headers={"User-Agent": f"SciPy {sys.modules['scipy'].__version__}"}
+    )
+    # The "fetch" method returns the full path to the downloaded data file.
+    return data_fetcher.fetch(dataset_name, downloader=downloader)
+
+
+@xp_capabilities(out_of_scope=True)
+def ascent():
+    """
+    Get an 8-bit grayscale bit-depth, 512 x 512 derived image for easy
+    use in demos.
+
+    The image is derived from
+    https://pixnio.com/people/accent-to-the-top
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    ascent : ndarray
+       convenient image to use for testing and demonstration
+
+    Examples
+    --------
+    >>> import scipy.datasets
+    >>> ascent = scipy.datasets.ascent()
+    >>> ascent.shape
+    (512, 512)
+    >>> ascent.max()
+    np.uint8(255)
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.gray()
+    >>> plt.imshow(ascent)
+    >>> plt.show()
+
+    """
+    import pickle
+
+    # The file will be downloaded automatically the first time this is run,
+    # returning the path to the downloaded file. Afterwards, Pooch finds
+    # it in the local cache and doesn't repeat the download.
+    fname = fetch_data("ascent.dat")
+    # Now we just need to load it with our standard Python tools.
+    with open(fname, 'rb') as f:
+        ascent = array(pickle.load(f))
+    return ascent
+
+
+@xp_capabilities(out_of_scope=True)
+def electrocardiogram():
+    """
+    Load an electrocardiogram as an example for a 1-D signal.
+
+    The returned signal is a 5 minute long electrocardiogram (ECG), a medical
+    recording of the heart's electrical activity, sampled at 360 Hz.
+
+    Returns
+    -------
+    ecg : ndarray
+        The electrocardiogram in millivolt (mV) sampled at 360 Hz.
+
+    Notes
+    -----
+    The provided signal is an excerpt (19:35 to 24:35) from the `record 208`_
+    (lead MLII) provided by the MIT-BIH Arrhythmia Database [1]_ on
+    PhysioNet [2]_. The excerpt includes noise induced artifacts, typical
+    heartbeats as well as pathological changes.
+
+    .. _record 208: https://physionet.org/physiobank/database/html/mitdbdir/records.htm#208
+
+    .. versionadded:: 1.1.0
+
+    References
+    ----------
+    .. [1] Moody GB, Mark RG. The impact of the MIT-BIH Arrhythmia Database.
+           IEEE Eng in Med and Biol 20(3):45-50 (May-June 2001).
+           (PMID: 11446209); :doi:`10.13026/C2F305`
+    .. [2] Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh,
+           Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank,
+           PhysioToolkit, and PhysioNet: Components of a New Research Resource
+           for Complex Physiologic Signals. Circulation 101(23):e215-e220;
+           :doi:`10.1161/01.CIR.101.23.e215`
+
+    Examples
+    --------
+    >>> from scipy.datasets import electrocardiogram
+    >>> ecg = electrocardiogram()
+    >>> ecg
+    array([-0.245, -0.215, -0.185, ..., -0.405, -0.395, -0.385], shape=(108000,))
+    >>> ecg.shape, ecg.mean(), ecg.std()
+    ((108000,), -0.16510875, 0.5992473991177294)
+
+    As stated the signal features several areas with a different morphology.
+    E.g., the first few seconds show the electrical activity of a heart in
+    normal sinus rhythm as seen below.
+
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> fs = 360
+    >>> time = np.arange(ecg.size) / fs
+    >>> plt.plot(time, ecg)
+    >>> plt.xlabel("time in s")
+    >>> plt.ylabel("ECG in mV")
+    >>> plt.xlim(9, 10.2)
+    >>> plt.ylim(-1, 1.5)
+    >>> plt.show()
+
+    After second 16, however, the first premature ventricular contractions,
+    also called extrasystoles, appear. These have a different morphology
+    compared to typical heartbeats. The difference can easily be observed
+    in the following plot.
+
+    >>> plt.plot(time, ecg)
+    >>> plt.xlabel("time in s")
+    >>> plt.ylabel("ECG in mV")
+    >>> plt.xlim(46.5, 50)
+    >>> plt.ylim(-2, 1.5)
+    >>> plt.show()
+
+    At several points large artifacts disturb the recording, e.g.:
+
+    >>> plt.plot(time, ecg)
+    >>> plt.xlabel("time in s")
+    >>> plt.ylabel("ECG in mV")
+    >>> plt.xlim(207, 215)
+    >>> plt.ylim(-2, 3.5)
+    >>> plt.show()
+
+    Finally, examining the power spectrum reveals that most of the biosignal is
+    made up of lower frequencies. At 60 Hz the noise induced by the mains
+    electricity can be clearly observed.
+
+    >>> from scipy.signal import welch
+    >>> f, Pxx = welch(ecg, fs=fs, nperseg=2048, scaling="spectrum")
+    >>> plt.semilogy(f, Pxx)
+    >>> plt.xlabel("Frequency in Hz")
+    >>> plt.ylabel("Power spectrum of the ECG in mV**2")
+    >>> plt.xlim(f[[0, -1]])
+    >>> plt.show()
+    """
+    fname = fetch_data("ecg.dat")
+    with load(fname) as file:
+        ecg = file["ecg"].astype(int)  # np.uint16 -> int
+    # Convert raw output of ADC to mV: (ecg - adc_zero) / adc_gain
+    ecg = (ecg - 1024) / 200.0
+    return ecg
+
+
+@xp_capabilities(out_of_scope=True)
+def face(gray=False):
+    """
+    Get a 1024 x 768, color image of a raccoon face.
+
+    The image is derived from
+    https://pixnio.com/fauna-animals/raccoons/raccoon-procyon-lotor
+
+    Parameters
+    ----------
+    gray : bool, optional
+        If True return 8-bit grey-scale image, otherwise return a color image
+
+    Returns
+    -------
+    face : ndarray
+        image of a raccoon face
+
+    Examples
+    --------
+    >>> import scipy.datasets
+    >>> face = scipy.datasets.face()
+    >>> face.shape
+    (768, 1024, 3)
+    >>> face.max()
+    np.uint8(255)
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.gray()
+    >>> plt.imshow(face)
+    >>> plt.show()
+
+    """
+    import bz2
+    fname = fetch_data("face.dat")
+    with open(fname, 'rb') as f:
+        rawdata = f.read()
+    face_data = bz2.decompress(rawdata)
+    face = frombuffer(face_data, dtype='uint8').reshape((768, 1024, 3))
+    if gray is True:
+        face = (0.21 * face[:, :, 0] + 0.71 * face[:, :, 1] +
+                0.07 * face[:, :, 2]).astype('uint8')
+    return face
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_registry.py b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_registry.py
new file mode 100644
index 0000000000000000000000000000000000000000..969384ad9843159e766100bfa9755aed8102dd09
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_registry.py
@@ -0,0 +1,26 @@
+##########################################################################
+# This file serves as the dataset registry for SciPy Datasets SubModule.
+##########################################################################
+
+
+# To generate the SHA256 hash, use the command
+# openssl sha256 
+registry = {
+    "ascent.dat": "03ce124c1afc880f87b55f6b061110e2e1e939679184f5614e38dacc6c1957e2",
+    "ecg.dat": "f20ad3365fb9b7f845d0e5c48b6fe67081377ee466c3a220b7f69f35c8958baf",
+    "face.dat": "9d8b0b4d081313e2b485748c770472e5a95ed1738146883d84c7030493e82886"
+}
+
+registry_urls = {
+    "ascent.dat": "https://raw.githubusercontent.com/scipy/dataset-ascent/main/ascent.dat",
+    "ecg.dat": "https://raw.githubusercontent.com/scipy/dataset-ecg/main/ecg.dat",
+    "face.dat": "https://raw.githubusercontent.com/scipy/dataset-face/main/face.dat"
+}
+
+# dataset method mapping with their associated filenames
+#  : ["filename1", "filename2", ...]
+method_files_map = {
+    "ascent": ["ascent.dat"],
+    "electrocardiogram": ["ecg.dat"],
+    "face": ["face.dat"]
+}
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_utils.py b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..a78206da9fae576c30cf456f6348708e7e869b1c
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/_utils.py
@@ -0,0 +1,84 @@
+import os
+import shutil
+from ._registry import method_files_map
+
+from scipy._lib._array_api import xp_capabilities
+
+try:
+    import platformdirs
+except ImportError:
+    platformdirs = None  # type: ignore[assignment]
+
+
+def _clear_cache(datasets, cache_dir=None, method_map=None):
+    if method_map is None:
+        # Use SciPy Datasets method map
+        method_map = method_files_map
+    if cache_dir is None:
+        # Use default cache_dir path
+        if platformdirs is None:
+            # platformdirs is pooch dependency
+            raise ImportError("Missing optional dependency 'pooch' required "
+                              "for scipy.datasets module. Please use pip or "
+                              "conda to install 'pooch'.")
+        cache_dir = platformdirs.user_cache_dir("scipy-data")
+
+    if not os.path.exists(cache_dir):
+        print(f"Cache Directory {cache_dir} doesn't exist. Nothing to clear.")
+        return
+
+    if datasets is None:
+        print(f"Cleaning the cache directory {cache_dir}!")
+        shutil.rmtree(cache_dir)
+    else:
+        if not isinstance(datasets, list | tuple):
+            # single dataset method passed should be converted to list
+            datasets = [datasets, ]
+        for dataset in datasets:
+            assert callable(dataset)
+            dataset_name = dataset.__name__  # Name of the dataset method
+            if dataset_name not in method_map:
+                raise ValueError(f"Dataset method {dataset_name} doesn't "
+                                 "exist. Please check if the passed dataset "
+                                 "is a subset of the following dataset "
+                                 f"methods: {list(method_map.keys())}")
+
+            data_files = method_map[dataset_name]
+            data_filepaths = [os.path.join(cache_dir, file)
+                              for file in data_files]
+            for data_filepath in data_filepaths:
+                if os.path.exists(data_filepath):
+                    print("Cleaning the file "
+                          f"{os.path.split(data_filepath)[1]} "
+                          f"for dataset {dataset_name}")
+                    os.remove(data_filepath)
+                else:
+                    print(f"Path {data_filepath} doesn't exist. "
+                          "Nothing to clear.")
+
+
+@xp_capabilities(out_of_scope=True)
+def clear_cache(datasets=None):
+    """
+    Cleans the scipy datasets cache directory.
+
+    If a scipy.datasets method or a list/tuple of the same is
+    provided, then clear_cache removes all the data files
+    associated to the passed dataset method callable(s).
+
+    By default, it removes all the cached data files.
+
+    Parameters
+    ----------
+    datasets : callable or list/tuple of callable or None
+
+    Examples
+    --------
+    >>> from scipy import datasets
+    >>> ascent_array = datasets.ascent()
+    >>> ascent_array.shape
+    (512, 512)
+    >>> datasets.clear_cache([datasets.ascent])
+    Cleaning the file ascent.dat for dataset ascent
+    """
+    _clear_cache(datasets)
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/tests/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/tests/__init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/tests/test_data.py b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/tests/test_data.py
new file mode 100644
index 0000000000000000000000000000000000000000..243176bd89b7b6f16406d66293d1872ac2712252
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/datasets/tests/test_data.py
@@ -0,0 +1,128 @@
+from scipy.datasets._registry import registry
+from scipy.datasets._fetchers import data_fetcher
+from scipy.datasets._utils import _clear_cache
+from scipy.datasets import ascent, face, electrocardiogram, download_all
+from numpy.testing import assert_equal, assert_almost_equal
+import os
+from threading import get_ident
+import pytest
+
+try:
+    import pooch
+except ImportError:
+    raise ImportError("Missing optional dependency 'pooch' required "
+                      "for scipy.datasets module. Please use pip or "
+                      "conda to install 'pooch'.")
+
+
+data_dir = data_fetcher.path  # type: ignore
+
+
+def _has_hash(path, expected_hash):
+    """Check if the provided path has the expected hash."""
+    if not os.path.exists(path):
+        return False
+    return pooch.file_hash(path) == expected_hash
+
+
+class TestDatasets:
+
+    @pytest.fixture(scope='module', autouse=True)
+    def test_download_all(self):
+        # This fixture requires INTERNET CONNECTION
+
+        # test_setup phase
+        download_all()
+
+        yield
+
+    @pytest.mark.fail_slow(10)
+    def test_existence_all(self):
+        assert len(os.listdir(data_dir)) >= len(registry)
+
+    def test_ascent(self):
+        assert_equal(ascent().shape, (512, 512))
+
+        # hash check
+        assert _has_hash(os.path.join(data_dir, "ascent.dat"),
+                         registry["ascent.dat"])
+
+    def test_face(self):
+        assert_equal(face().shape, (768, 1024, 3))
+
+        # hash check
+        assert _has_hash(os.path.join(data_dir, "face.dat"),
+                         registry["face.dat"])
+
+    def test_electrocardiogram(self):
+        # Test shape, dtype and stats of signal
+        ecg = electrocardiogram()
+        assert_equal(ecg.dtype, float)
+        assert_equal(ecg.shape, (108000,))
+        assert_almost_equal(ecg.mean(), -0.16510875)
+        assert_almost_equal(ecg.std(), 0.5992473991177294)
+
+        # hash check
+        assert _has_hash(os.path.join(data_dir, "ecg.dat"),
+                         registry["ecg.dat"])
+
+
+def test_clear_cache(tmp_path):
+    # Note: `tmp_path` is a pytest fixture, it handles cleanup
+    thread_basepath = tmp_path / str(get_ident())
+    thread_basepath.mkdir()
+
+    dummy_basepath = thread_basepath / "dummy_cache_dir"
+    dummy_basepath.mkdir()
+
+    # Create three dummy dataset files for dummy dataset methods
+    dummy_method_map = {}
+    for i in range(4):
+        dummy_method_map[f"data{i}"] = [f"data{i}.dat"]
+        data_filepath = dummy_basepath / f"data{i}.dat"
+        data_filepath.write_text("")
+
+    # clear files associated to single dataset method data0
+    # also test callable argument instead of list of callables
+    def data0():
+        pass
+    _clear_cache(datasets=data0, cache_dir=dummy_basepath,
+                 method_map=dummy_method_map)
+    assert not os.path.exists(dummy_basepath/"data0.dat")
+
+    # clear files associated to multiple dataset methods "data3" and "data4"
+    def data1():
+        pass
+
+    def data2():
+        pass
+    _clear_cache(datasets=[data1, data2], cache_dir=dummy_basepath,
+                 method_map=dummy_method_map)
+    assert not os.path.exists(dummy_basepath/"data1.dat")
+    assert not os.path.exists(dummy_basepath/"data2.dat")
+
+    # clear multiple dataset files "data3_0.dat" and "data3_1.dat"
+    # associated with dataset method "data3"
+    def data4():
+        pass
+    # create files
+    (dummy_basepath / "data4_0.dat").write_text("")
+    (dummy_basepath / "data4_1.dat").write_text("")
+
+    dummy_method_map["data4"] = ["data4_0.dat", "data4_1.dat"]
+    _clear_cache(datasets=[data4], cache_dir=dummy_basepath,
+                 method_map=dummy_method_map)
+    assert not os.path.exists(dummy_basepath/"data4_0.dat")
+    assert not os.path.exists(dummy_basepath/"data4_1.dat")
+
+    # wrong dataset method should raise ValueError since it
+    # doesn't exist in the dummy_method_map
+    def data5():
+        pass
+    with pytest.raises(ValueError):
+        _clear_cache(datasets=[data5], cache_dir=dummy_basepath,
+                     method_map=dummy_method_map)
+
+    # remove all dataset cache
+    _clear_cache(datasets=None, cache_dir=dummy_basepath)
+    assert not os.path.exists(dummy_basepath)
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/differentiate/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/differentiate/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..c3a7ccc4b33f27dbae7958641a89106cf9580326
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/differentiate/__init__.py
@@ -0,0 +1,27 @@
+"""
+==============================================================
+Finite Difference Differentiation (:mod:`scipy.differentiate`)
+==============================================================
+
+.. currentmodule:: scipy.differentiate
+
+SciPy ``differentiate`` provides functions for performing finite difference
+numerical differentiation of black-box functions.
+
+.. autosummary::
+   :toctree: generated/
+
+   derivative
+   jacobian
+   hessian
+
+"""
+
+
+from ._differentiate import *
+
+__all__ = ['derivative', 'jacobian', 'hessian']
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/differentiate/_differentiate.py b/.venv_haddock/lib/python3.12/site-packages/scipy/differentiate/_differentiate.py
new file mode 100644
index 0000000000000000000000000000000000000000..70ea2b1696d73cfd9b8b5dd0a2c5a5cb9aba5f5e
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/differentiate/_differentiate.py
@@ -0,0 +1,1140 @@
+# mypy: disable-error-code="attr-defined"
+import warnings
+import numpy as np
+import scipy._lib._elementwise_iterative_method as eim
+from scipy._lib._util import _RichResult
+from scipy._lib._array_api import array_namespace, xp_copy, xp_promote, xp_capabilities
+import scipy._lib.array_api_extra as xpx
+
+_EERRORINCREASE = -1  # used in derivative
+
+def _derivative_iv(f, x, args, tolerances, maxiter, order, initial_step,
+                   step_factor, step_direction, preserve_shape, callback):
+    # Input validation for `derivative`
+    xp = array_namespace(x)
+
+    if not callable(f):
+        raise ValueError('`f` must be callable.')
+
+    if not np.iterable(args):
+        args = (args,)
+
+    tolerances = {} if tolerances is None else tolerances
+    atol = tolerances.get('atol', None)
+    rtol = tolerances.get('rtol', None)
+
+    # tolerances are floats, not arrays; OK to use NumPy
+    message = 'Tolerances and step parameters must be non-negative scalars.'
+    tols = np.asarray([atol if atol is not None else 1,
+                       rtol if rtol is not None else 1,
+                       step_factor])
+    if (not np.issubdtype(tols.dtype, np.number) or np.any(tols < 0)
+            or np.any(np.isnan(tols)) or tols.shape != (3,)):
+        raise ValueError(message)
+    step_factor = float(tols[2])
+
+    maxiter_int = int(maxiter)
+    if maxiter != maxiter_int or maxiter <= 0:
+        raise ValueError('`maxiter` must be a positive integer.')
+
+    order_int = int(order)
+    if order_int != order or order <= 0:
+        raise ValueError('`order` must be a positive integer.')
+
+    step_direction = xp.asarray(step_direction)
+    initial_step = xp.asarray(initial_step)
+    temp = xp.broadcast_arrays(x, step_direction, initial_step)
+    x, step_direction, initial_step = temp
+
+    message = '`preserve_shape` must be True or False.'
+    if preserve_shape not in {True, False}:
+        raise ValueError(message)
+
+    if callback is not None and not callable(callback):
+        raise ValueError('`callback` must be callable.')
+
+    return (f, x, args, atol, rtol, maxiter_int, order_int, initial_step,
+            step_factor, step_direction, preserve_shape, callback)
+
+
+
+_array_api_strict_skip_reason = 'Array API does not support fancy indexing assignment.'
+_dask_reason = 'boolean indexing assignment'
+
+
+@xp_capabilities(skip_backends=[('array_api_strict', _array_api_strict_skip_reason),
+                                ('dask.array', _dask_reason)], jax_jit=False)
+def derivative(f, x, *, args=(), tolerances=None, maxiter=10,
+               order=8, initial_step=0.5, step_factor=2.0,
+               step_direction=0, preserve_shape=False, callback=None):
+    """Evaluate the derivative of an elementwise, real scalar function numerically.
+
+    For each element of the output of `f`, `derivative` approximates the first
+    derivative of `f` at the corresponding element of `x` using finite difference
+    differentiation.
+
+    This function works elementwise when `x`, `step_direction`, and `args` contain
+    (broadcastable) arrays.
+
+    Parameters
+    ----------
+    f : callable
+        The function whose derivative is desired. The signature must be::
+
+            f(xi: ndarray, *argsi) -> ndarray
+
+        where each element of ``xi`` is a finite real number and ``argsi`` is a tuple,
+        which may contain an arbitrary number of arrays that are broadcastable with
+        ``xi``. `f` must be an elementwise function: each scalar element ``f(xi)[j]``
+        must equal ``f(xi[j])`` for valid indices ``j``. It must not mutate the array
+        ``xi`` or the arrays in ``argsi``.
+    x : float array_like
+        Abscissae at which to evaluate the derivative. Must be broadcastable with
+        `args` and `step_direction`.
+    args : tuple of array_like, optional
+        Additional positional array arguments to be passed to `f`. Arrays
+        must be broadcastable with one another and the arrays of `init`.
+        If the callable for which the root is desired requires arguments that are
+        not broadcastable with `x`, wrap that callable with `f` such that `f`
+        accepts only `x` and broadcastable ``*args``.
+    tolerances : dictionary of floats, optional
+        Absolute and relative tolerances. Valid keys of the dictionary are:
+
+        - ``atol`` - absolute tolerance on the derivative
+        - ``rtol`` - relative tolerance on the derivative
+
+        Iteration will stop when ``res.error < atol + rtol * abs(res.df)``. The default
+        `atol` is the smallest normal number of the appropriate dtype, and
+        the default `rtol` is the square root of the precision of the
+        appropriate dtype.
+    order : int, default: 8
+        The (positive integer) order of the finite difference formula to be
+        used. Odd integers will be rounded up to the next even integer.
+    initial_step : float array_like, default: 0.5
+        The (absolute) initial step size for the finite difference derivative
+        approximation.
+    step_factor : float, default: 2.0
+        The factor by which the step size is *reduced* in each iteration; i.e.
+        the step size in iteration 1 is ``initial_step/step_factor``. If
+        ``step_factor < 1``, subsequent steps will be greater than the initial
+        step; this may be useful if steps smaller than some threshold are
+        undesirable (e.g. due to subtractive cancellation error).
+    maxiter : int, default: 10
+        The maximum number of iterations of the algorithm to perform. See
+        Notes.
+    step_direction : integer array_like
+        An array representing the direction of the finite difference steps (for
+        use when `x` lies near to the boundary of the domain of the function.)
+        Must be broadcastable with `x` and all `args`.
+        Where 0 (default), central differences are used; where negative (e.g.
+        -1), steps are non-positive; and where positive (e.g. 1), all steps are
+        non-negative.
+    preserve_shape : bool, default: False
+        In the following, "arguments of `f`" refers to the array ``xi`` and
+        any arrays within ``argsi``. Let ``shape`` be the broadcasted shape
+        of `x` and all elements of `args` (which is conceptually
+        distinct from ``xi` and ``argsi`` passed into `f`).
+
+        - When ``preserve_shape=False`` (default), `f` must accept arguments
+          of *any* broadcastable shapes.
+
+        - When ``preserve_shape=True``, `f` must accept arguments of shape
+          ``shape`` *or* ``shape + (n,)``, where ``(n,)`` is the number of
+          abscissae at which the function is being evaluated.
+
+        In either case, for each scalar element ``xi[j]`` within ``xi``, the array
+        returned by `f` must include the scalar ``f(xi[j])`` at the same index.
+        Consequently, the shape of the output is always the shape of the input
+        ``xi``.
+
+        See Examples.
+    callback : callable, optional
+        An optional user-supplied function to be called before the first
+        iteration and after each iteration.
+        Called as ``callback(res)``, where ``res`` is a ``_RichResult``
+        similar to that returned by `derivative` (but containing the current
+        iterate's values of all variables). If `callback` raises a
+        ``StopIteration``, the algorithm will terminate immediately and
+        `derivative` will return a result. `callback` must not mutate
+        `res` or its attributes.
+
+    Returns
+    -------
+    res : _RichResult
+        An object similar to an instance of `scipy.optimize.OptimizeResult` with the
+        following attributes. The descriptions are written as though the values will
+        be scalars; however, if `f` returns an array, the outputs will be
+        arrays of the same shape.
+
+        success : bool array
+            ``True`` where the algorithm terminated successfully (status ``0``);
+            ``False`` otherwise.
+        status : int array
+            An integer representing the exit status of the algorithm.
+
+            - ``0`` : The algorithm converged to the specified tolerances.
+            - ``-1`` : The error estimate increased, so iteration was terminated.
+            - ``-2`` : The maximum number of iterations was reached.
+            - ``-3`` : A non-finite value was encountered.
+            - ``-4`` : Iteration was terminated by `callback`.
+            - ``1`` : The algorithm is proceeding normally (in `callback` only).
+
+        df : float array
+            The derivative of `f` at `x`, if the algorithm terminated
+            successfully.
+        error : float array
+            An estimate of the error: the magnitude of the difference between
+            the current estimate of the derivative and the estimate in the
+            previous iteration.
+        nit : int array
+            The number of iterations of the algorithm that were performed.
+        nfev : int array
+            The number of points at which `f` was evaluated.
+        x : float array
+            The value at which the derivative of `f` was evaluated
+            (after broadcasting with `args` and `step_direction`).
+
+    See Also
+    --------
+    jacobian, hessian
+
+    Notes
+    -----
+    The implementation was inspired by jacobi [1]_, numdifftools [2]_, and
+    DERIVEST [3]_, but the implementation follows the theory of Taylor series
+    more straightforwardly (and arguably naively so).
+    In the first iteration, the derivative is estimated using a finite
+    difference formula of order `order` with maximum step size `initial_step`.
+    Each subsequent iteration, the maximum step size is reduced by
+    `step_factor`, and the derivative is estimated again until a termination
+    condition is reached. The error estimate is the magnitude of the difference
+    between the current derivative approximation and that of the previous
+    iteration.
+
+    The stencils of the finite difference formulae are designed such that
+    abscissae are "nested": after `f` is evaluated at ``order + 1``
+    points in the first iteration, `f` is evaluated at only two new points
+    in each subsequent iteration; ``order - 1`` previously evaluated function
+    values required by the finite difference formula are reused, and two
+    function values (evaluations at the points furthest from `x`) are unused.
+
+    Step sizes are absolute. When the step size is small relative to the
+    magnitude of `x`, precision is lost; for example, if `x` is ``1e20``, the
+    default initial step size of ``0.5`` cannot be resolved. Accordingly,
+    consider using larger initial step sizes for large magnitudes of `x`.
+
+    The default tolerances are challenging to satisfy at points where the
+    true derivative is exactly zero. If the derivative may be exactly zero,
+    consider specifying an absolute tolerance (e.g. ``atol=1e-12``) to
+    improve convergence.
+
+    References
+    ----------
+    .. [1] Hans Dembinski (@HDembinski). jacobi.
+           https://github.com/HDembinski/jacobi
+    .. [2] Per A. Brodtkorb and John D'Errico. numdifftools.
+           https://numdifftools.readthedocs.io/en/latest/
+    .. [3] John D'Errico. DERIVEST: Adaptive Robust Numerical Differentiation.
+           https://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation
+    .. [4] Numerical Differentition. Wikipedia.
+           https://en.wikipedia.org/wiki/Numerical_differentiation
+
+    Examples
+    --------
+    Evaluate the derivative of ``np.exp`` at several points ``x``.
+
+    >>> import numpy as np
+    >>> from scipy.differentiate import derivative
+    >>> f = np.exp
+    >>> df = np.exp  # true derivative
+    >>> x = np.linspace(1, 2, 5)
+    >>> res = derivative(f, x)
+    >>> res.df  # approximation of the derivative
+    array([2.71828183, 3.49034296, 4.48168907, 5.75460268, 7.3890561 ])
+    >>> res.error  # estimate of the error
+    array([7.13740178e-12, 9.16600129e-12, 1.17594823e-11, 1.51061386e-11,
+           1.94262384e-11])
+    >>> abs(res.df - df(x))  # true error
+    array([2.53130850e-14, 3.55271368e-14, 5.77315973e-14, 5.59552404e-14,
+           6.92779167e-14])
+
+    Show the convergence of the approximation as the step size is reduced.
+    Each iteration, the step size is reduced by `step_factor`, so for
+    sufficiently small initial step, each iteration reduces the error by a
+    factor of ``1/step_factor**order`` until finite precision arithmetic
+    inhibits further improvement.
+
+    >>> import matplotlib.pyplot as plt
+    >>> iter = list(range(1, 12))  # maximum iterations
+    >>> hfac = 2  # step size reduction per iteration
+    >>> hdir = [-1, 0, 1]  # compare left-, central-, and right- steps
+    >>> order = 4  # order of differentiation formula
+    >>> x = 1
+    >>> ref = df(x)
+    >>> errors = []  # true error
+    >>> for i in iter:
+    ...     res = derivative(f, x, maxiter=i, step_factor=hfac,
+    ...                      step_direction=hdir, order=order,
+    ...                      # prevent early termination
+    ...                      tolerances=dict(atol=0, rtol=0))
+    ...     errors.append(abs(res.df - ref))
+    >>> errors = np.array(errors)
+    >>> plt.semilogy(iter, errors[:, 0], label='left differences')
+    >>> plt.semilogy(iter, errors[:, 1], label='central differences')
+    >>> plt.semilogy(iter, errors[:, 2], label='right differences')
+    >>> plt.xlabel('iteration')
+    >>> plt.ylabel('error')
+    >>> plt.legend()
+    >>> plt.show()
+    >>> (errors[1, 1] / errors[0, 1], 1 / hfac**order)
+    (0.06215223140159822, 0.0625)
+
+    The implementation is vectorized over `x`, `step_direction`, and `args`.
+    The function is evaluated once before the first iteration to perform input
+    validation and standardization, and once per iteration thereafter.
+
+    >>> def f(x, p):
+    ...     f.nit += 1
+    ...     return x**p
+    >>> f.nit = 0
+    >>> def df(x, p):
+    ...     return p*x**(p-1)
+    >>> x = np.arange(1, 5)
+    >>> p = np.arange(1, 6).reshape((-1, 1))
+    >>> hdir = np.arange(-1, 2).reshape((-1, 1, 1))
+    >>> res = derivative(f, x, args=(p,), step_direction=hdir, maxiter=1)
+    >>> np.allclose(res.df, df(x, p))
+    True
+    >>> res.df.shape
+    (3, 5, 4)
+    >>> f.nit
+    2
+
+    By default, `preserve_shape` is False, and therefore the callable
+    `f` may be called with arrays of any broadcastable shapes.
+    For example:
+
+    >>> shapes = []
+    >>> def f(x, c):
+    ...    shape = np.broadcast_shapes(x.shape, c.shape)
+    ...    shapes.append(shape)
+    ...    return np.sin(c*x)
+    >>>
+    >>> c = [1, 5, 10, 20]
+    >>> res = derivative(f, 0, args=(c,))
+    >>> shapes
+    [(4,), (4, 8), (4, 2), (3, 2), (2, 2), (1, 2)]
+
+    To understand where these shapes are coming from - and to better
+    understand how `derivative` computes accurate results - note that
+    higher values of ``c`` correspond with higher frequency sinusoids.
+    The higher frequency sinusoids make the function's derivative change
+    faster, so more function evaluations are required to achieve the target
+    accuracy:
+
+    >>> res.nfev
+    array([11, 13, 15, 17], dtype=int32)
+
+    The initial ``shape``, ``(4,)``, corresponds with evaluating the
+    function at a single abscissa and all four frequencies; this is used
+    for input validation and to determine the size and dtype of the arrays
+    that store results. The next shape corresponds with evaluating the
+    function at an initial grid of abscissae and all four frequencies.
+    Successive calls to the function evaluate the function at two more
+    abscissae, increasing the effective order of the approximation by two.
+    However, in later function evaluations, the function is evaluated at
+    fewer frequencies because the corresponding derivative has already
+    converged to the required tolerance. This saves function evaluations to
+    improve performance, but it requires the function to accept arguments of
+    any shape.
+
+    "Vector-valued" functions are unlikely to satisfy this requirement.
+    For example, consider
+
+    >>> def f(x):
+    ...    return [x, np.sin(3*x), x+np.sin(10*x), np.sin(20*x)*(x-1)**2]
+
+    This integrand is not compatible with `derivative` as written; for instance,
+    the shape of the output will not be the same as the shape of ``x``. Such a
+    function *could* be converted to a compatible form with the introduction of
+    additional parameters, but this would be inconvenient. In such cases,
+    a simpler solution would be to use `preserve_shape`.
+
+    >>> shapes = []
+    >>> def f(x):
+    ...     shapes.append(x.shape)
+    ...     x0, x1, x2, x3 = x
+    ...     return [x0, np.sin(3*x1), x2+np.sin(10*x2), np.sin(20*x3)*(x3-1)**2]
+    >>>
+    >>> x = np.zeros(4)
+    >>> res = derivative(f, x, preserve_shape=True)
+    >>> shapes
+    [(4,), (4, 8), (4, 2), (4, 2), (4, 2), (4, 2)]
+
+    Here, the shape of ``x`` is ``(4,)``. With ``preserve_shape=True``, the
+    function may be called with argument ``x`` of shape ``(4,)`` or ``(4, n)``,
+    and this is what we observe.
+
+    """
+    # TODO (followup):
+    #  - investigate behavior at saddle points
+    #  - multivariate functions?
+    #  - relative steps?
+    #  - show example of `np.vectorize`
+
+    res = _derivative_iv(f, x, args, tolerances, maxiter, order, initial_step,
+                            step_factor, step_direction, preserve_shape, callback)
+    (func, x, args, atol, rtol, maxiter, order,
+     h0, fac, hdir, preserve_shape, callback) = res
+
+    # Initialization
+    # Since f(x) (no step) is not needed for central differences, it may be
+    # possible to eliminate this function evaluation. However, it's useful for
+    # input validation and standardization, and everything else is designed to
+    # reduce function calls, so let's keep it simple.
+    temp = eim._initialize(func, (x,), args, preserve_shape=preserve_shape)
+    func, xs, fs, args, shape, dtype, xp = temp
+
+    finfo = xp.finfo(dtype)
+    atol = finfo.smallest_normal if atol is None else atol
+    rtol = finfo.eps**0.5 if rtol is None else rtol  # keep same as `hessian`
+
+    x, f = xs[0], fs[0]
+    df = xp.full_like(f, xp.nan)
+
+    # Ideally we'd broadcast the shape of `hdir` in `_elementwise_algo_init`, but
+    # it's simpler to do it here than to generalize `_elementwise_algo_init` further.
+    # `hdir` and `x` are already broadcasted in `_derivative_iv`, so we know
+    # that `hdir` can be broadcasted to the final shape. Same with `h0`.
+    hdir = xp.broadcast_to(hdir, shape)
+    hdir = xp.reshape(hdir, (-1,))
+    hdir = xp.astype(xp.sign(hdir), dtype)
+    h0 = xp.broadcast_to(h0, shape)
+    h0 = xp.reshape(h0, (-1,))
+    h0 = xp.astype(h0, dtype)
+    h0 = xpx.at(h0)[h0 <= 0].set(xp.nan)
+
+    status = xp.full_like(x, eim._EINPROGRESS, dtype=xp.int32)  # in progress
+    nit, nfev = 0, 1  # one function evaluations performed above
+    # Boolean indices of left, central, right, and (all) one-sided steps
+    il = hdir < 0
+    ic = hdir == 0
+    ir = hdir > 0
+    io = il | ir
+
+    # Most of these attributes are reasonably obvious, but:
+    # - `fs` holds all the function values of all active `x`. The zeroth
+    #   axis corresponds with active points `x`, the first axis corresponds
+    #   with the different steps (in the order described in
+    #   `_derivative_weights`).
+    # - `terms` (which could probably use a better name) is half the `order`,
+    #   which is always even.
+    work = _RichResult(x=x, df=df, fs=f[:, xp.newaxis], error=xp.nan, h=h0,
+                       df_last=xp.nan, error_last=xp.nan, fac=fac,
+                       atol=atol, rtol=rtol, nit=nit, nfev=nfev,
+                       status=status, dtype=dtype, terms=(order+1)//2,
+                       hdir=hdir, il=il, ic=ic, ir=ir, io=io,
+                       # Store the weights in an object so they can't get compressed
+                       # Using RichResult to allow dot notation, but a dict would work
+                       diff_state=_RichResult(central=[], right=[], fac=None))
+
+    # This is the correspondence between terms in the `work` object and the
+    # final result. In this case, the mapping is trivial. Note that `success`
+    # is prepended automatically.
+    res_work_pairs = [('status', 'status'), ('df', 'df'), ('error', 'error'),
+                      ('nit', 'nit'), ('nfev', 'nfev'), ('x', 'x')]
+
+    def pre_func_eval(work):
+        """Determine the abscissae at which the function needs to be evaluated.
+
+        See `_derivative_weights` for a description of the stencil (pattern
+        of the abscissae).
+
+        In the first iteration, there is only one stored function value in
+        `work.fs`, `f(x)`, so we need to evaluate at `order` new points. In
+        subsequent iterations, we evaluate at two new points. Note that
+        `work.x` is always flattened into a 1D array after broadcasting with
+        all `args`, so we add a new axis at the end and evaluate all point
+        in one call to the function.
+
+        For improvement:
+        - Consider measuring the step size actually taken, since ``(x + h) - x``
+          is not identically equal to `h` with floating point arithmetic.
+        - Adjust the step size automatically if `x` is too big to resolve the
+          step.
+        - We could probably save some work if there are no central difference
+          steps or no one-sided steps.
+        """
+        n = work.terms  # half the order
+        h = work.h[:, xp.newaxis]  # step size
+        c = work.fac  # step reduction factor
+        d = c**0.5  # square root of step reduction factor (one-sided stencil)
+        # Note - no need to be careful about dtypes until we allocate `x_eval`
+
+        if work.nit == 0:
+            hc = h / c**xp.arange(n, dtype=work.dtype)
+            hc = xp.concat((-xp.flip(hc, axis=-1), hc), axis=-1)
+        else:
+            hc = xp.concat((-h, h), axis=-1) / c**(n-1)
+
+        if work.nit == 0:
+            hr = h / d**xp.arange(2*n, dtype=work.dtype)
+        else:
+            hr = xp.concat((h, h/d), axis=-1) / c**(n-1)
+
+        n_new = 2*n if work.nit == 0 else 2  # number of new abscissae
+        x_eval = xp.zeros((work.hdir.shape[0], n_new), dtype=work.dtype)
+        il, ic, ir = work.il, work.ic, work.ir
+        x_eval = xpx.at(x_eval)[ir].set(work.x[ir][:, xp.newaxis] + hr[ir])
+        x_eval = xpx.at(x_eval)[ic].set(work.x[ic][:, xp.newaxis] + hc[ic])
+        x_eval = xpx.at(x_eval)[il].set(work.x[il][:, xp.newaxis] - hr[il])
+        return x_eval
+
+    def post_func_eval(x, f, work):
+        """ Estimate the derivative and error from the function evaluations
+
+        As in `pre_func_eval`: in the first iteration, there is only one stored
+        function value in `work.fs`, `f(x)`, so we need to add the `order` new
+        points. In subsequent iterations, we add two new points. The tricky
+        part is getting the order to match that of the weights, which is
+        described in `_derivative_weights`.
+
+        For improvement:
+        - Change the order of the weights (and steps in `pre_func_eval`) to
+          simplify `work_fc` concatenation and eliminate `fc` concatenation.
+        - It would be simple to do one-step Richardson extrapolation with `df`
+          and `df_last` to increase the order of the estimate and/or improve
+          the error estimate.
+        - Process the function evaluations in a more numerically favorable
+          way. For instance, combining the pairs of central difference evals
+          into a second-order approximation and using Richardson extrapolation
+          to produce a higher order approximation seemed to retain accuracy up
+          to very high order.
+        - Alternatively, we could use `polyfit` like Jacobi. An advantage of
+          fitting polynomial to more points than necessary is improved noise
+          tolerance.
+        """
+        n = work.terms
+        n_new = n if work.nit == 0 else 1
+        il, ic, io = work.il, work.ic, work.io
+
+        # Central difference
+        # `work_fc` is *all* the points at which the function has been evaluated
+        # `fc` is the points we're using *this iteration* to produce the estimate
+        work_fc = (f[ic][:, :n_new], work.fs[ic], f[ic][:, -n_new:])
+        work_fc = xp.concat(work_fc, axis=-1)
+        if work.nit == 0:
+            fc = work_fc
+        else:
+            fc = (work_fc[:, :n], work_fc[:, n:n+1], work_fc[:, -n:])
+            fc = xp.concat(fc, axis=-1)
+
+        # One-sided difference
+        work_fo = xp.concat((work.fs[io], f[io]), axis=-1)
+        if work.nit == 0:
+            fo = work_fo
+        else:
+            fo = xp.concat((work_fo[:, 0:1], work_fo[:, -2*n:]), axis=-1)
+
+        work.fs = xp.zeros((ic.shape[0], work.fs.shape[-1] + 2*n_new), dtype=work.dtype)
+        work.fs = xpx.at(work.fs)[ic].set(work_fc)
+        work.fs = xpx.at(work.fs)[io].set(work_fo)
+
+        wc, wo = _derivative_weights(work, n, xp)
+        work.df_last = xp.asarray(work.df, copy=True)
+        work.df = xpx.at(work.df)[ic].set(fc @ wc / work.h[ic])
+        work.df = xpx.at(work.df)[io].set(fo @ wo / work.h[io])
+        work.df = xpx.at(work.df)[il].multiply(-1)
+
+        work.h /= work.fac
+        work.error_last = work.error
+        # Simple error estimate - the difference in derivative estimates between
+        # this iteration and the last. This is typically conservative because if
+        # convergence has begin, the true error is much closer to the difference
+        # between the current estimate and the *next* error estimate. However,
+        # we could use Richarson extrapolation to produce an error estimate that
+        # is one order higher, and take the difference between that and
+        # `work.df` (which would just be constant factor that depends on `fac`.)
+        work.error = xp.abs(work.df - work.df_last)
+
+    def check_termination(work):
+        """Terminate due to convergence, non-finite values, or error increase"""
+        stop = xp.astype(xp.zeros_like(work.df), xp.bool)
+
+        i = work.error < work.atol + work.rtol*abs(work.df)
+        work.status = xpx.at(work.status)[i].set(eim._ECONVERGED)
+        stop = xpx.at(stop)[i].set(True)
+
+        if work.nit > 0:
+            i = ~((xp.isfinite(work.x) & xp.isfinite(work.df)) | stop)
+            work.df = xpx.at(work.df)[i].set(xp.nan)
+            work.status = xpx.at(work.status)[i].set(eim._EVALUEERR)
+            stop = xpx.at(stop)[i].set(True)
+
+        # With infinite precision, there is a step size below which
+        # all smaller step sizes will reduce the error. But in floating point
+        # arithmetic, catastrophic cancellation will begin to cause the error
+        # to increase again. This heuristic tries to avoid step sizes that are
+        # too small. There may be more theoretically sound approaches for
+        # detecting a step size that minimizes the total error, but this
+        # heuristic seems simple and effective.
+        i = (work.error > work.error_last*10) & ~stop
+        work.status = xpx.at(work.status)[i].set(_EERRORINCREASE)
+        stop = xpx.at(stop)[i].set(True)
+
+        return stop
+
+    def post_termination_check(work):
+        return
+
+    def customize_result(res, shape):
+        return shape
+
+    return eim._loop(work, callback, shape, maxiter, func, args, dtype,
+                     pre_func_eval, post_func_eval, check_termination,
+                     post_termination_check, customize_result, res_work_pairs,
+                     xp, preserve_shape)
+
+
+def _derivative_weights(work, n, xp):
+    # This produces the weights of the finite difference formula for a given
+    # stencil. In experiments, use of a second-order central difference formula
+    # with Richardson extrapolation was more accurate numerically, but it was
+    # more complicated, and it would have become even more complicated when
+    # adding support for one-sided differences. However, now that all the
+    # function evaluation values are stored, they can be processed in whatever
+    # way is desired to produce the derivative estimate. We leave alternative
+    # approaches to future work. To be more self-contained, here is the theory
+    # for deriving the weights below.
+    #
+    # Recall that the Taylor expansion of a univariate, scalar-values function
+    # about a point `x` may be expressed as:
+    #      f(x + h)  =     f(x) + f'(x)*h + f''(x)/2!*h**2  + O(h**3)
+    # Suppose we evaluate f(x), f(x+h), and f(x-h).  We have:
+    #      f(x)      =     f(x)
+    #      f(x + h)  =     f(x) + f'(x)*h + f''(x)/2!*h**2  + O(h**3)
+    #      f(x - h)  =     f(x) - f'(x)*h + f''(x)/2!*h**2  + O(h**3)
+    # We can solve for weights `wi` such that:
+    #   w1*f(x)      = w1*(f(x))
+    # + w2*f(x + h)  = w2*(f(x) + f'(x)*h + f''(x)/2!*h**2) + O(h**3)
+    # + w3*f(x - h)  = w3*(f(x) - f'(x)*h + f''(x)/2!*h**2) + O(h**3)
+    #                =     0    + f'(x)*h + 0               + O(h**3)
+    # Then
+    #     f'(x) ~ (w1*f(x) + w2*f(x+h) + w3*f(x-h))/h
+    # is a finite difference derivative approximation with error O(h**2),
+    # and so it is said to be a "second-order" approximation. Under certain
+    # conditions (e.g. well-behaved function, `h` sufficiently small), the
+    # error in the approximation will decrease with h**2; that is, if `h` is
+    # reduced by a factor of 2, the error is reduced by a factor of 4.
+    #
+    # By default, we use eighth-order formulae. Our central-difference formula
+    # uses abscissae:
+    #   x-h/c**3, x-h/c**2, x-h/c, x-h, x, x+h, x+h/c, x+h/c**2, x+h/c**3
+    # where `c` is the step factor. (Typically, the step factor is greater than
+    # one, so the outermost points - as written above - are actually closest to
+    # `x`.) This "stencil" is chosen so that each iteration, the step can be
+    # reduced by the factor `c`, and most of the function evaluations can be
+    # reused with the new step size. For example, in the next iteration, we
+    # will have:
+    #   x-h/c**4, x-h/c**3, x-h/c**2, x-h/c, x, x+h/c, x+h/c**2, x+h/c**3, x+h/c**4
+    # We do not reuse `x-h` and `x+h` for the new derivative estimate.
+    # While this would increase the order of the formula and thus the
+    # theoretical convergence rate, it is also less stable numerically.
+    # (As noted above, there are other ways of processing the values that are
+    # more stable. Thus, even now we store `f(x-h)` and `f(x+h)` in `work.fs`
+    # to simplify future development of this sort of improvement.)
+    #
+    # The (right) one-sided formula is produced similarly using abscissae
+    #   x, x+h, x+h/d, x+h/d**2, ..., x+h/d**6, x+h/d**7, x+h/d**7
+    # where `d` is the square root of `c`. (The left one-sided formula simply
+    # uses -h.) When the step size is reduced by factor `c = d**2`, we have
+    # abscissae:
+    #   x, x+h/d**2, x+h/d**3..., x+h/d**8, x+h/d**9, x+h/d**9
+    # `d` is chosen as the square root of `c` so that the rate of the step-size
+    # reduction is the same per iteration as in the central difference case.
+    # Note that because the central difference formulas are inherently of even
+    # order, for simplicity, we use only even-order formulas for one-sided
+    # differences, too.
+
+    # It's possible for the user to specify `fac` in, say, double precision but
+    # `x` and `args` in single precision. `fac` gets converted to single
+    # precision, but we should always use double precision for the intermediate
+    # calculations here to avoid additional error in the weights.
+    fac = float(work.fac)
+
+    # Note that if the user switches back to floating point precision with
+    # `x` and `args`, then `fac` will not necessarily equal the (lower
+    # precision) cached `_derivative_weights.fac`, and the weights will
+    # need to be recalculated. This could be fixed, but it's late, and of
+    # low consequence.
+
+    diff_state = work.diff_state
+    if fac != diff_state.fac:
+        diff_state.central = []
+        diff_state.right = []
+        diff_state.fac = fac
+
+    if len(diff_state.central) != 2*n + 1:
+        # Central difference weights. Consider refactoring this; it could
+        # probably be more compact.
+        # Note: Using NumPy here is OK; we convert to xp-type at the end
+        i = np.arange(-n, n + 1)
+        p = np.abs(i) - 1.  # center point has power `p` -1, but sign `s` is 0
+        s = np.sign(i)
+
+        h = s / fac ** p
+        A = np.vander(h, increasing=True).T
+        b = np.zeros(2*n + 1)
+        b[1] = 1
+        weights = np.linalg.solve(A, b)
+
+        # Enforce identities to improve accuracy
+        weights[n] = 0
+        for i in range(n):
+            weights[-i-1] = -weights[i]
+
+        # Cache the weights. We only need to calculate them once unless
+        # the step factor changes.
+        diff_state.central = weights
+
+        # One-sided difference weights. The left one-sided weights (with
+        # negative steps) are simply the negative of the right one-sided
+        # weights, so no need to compute them separately.
+        i = np.arange(2*n + 1)
+        p = i - 1.
+        s = np.sign(i)
+
+        h = s / np.sqrt(fac) ** p
+        A = np.vander(h, increasing=True).T
+        b = np.zeros(2 * n + 1)
+        b[1] = 1
+        weights = np.linalg.solve(A, b)
+
+        diff_state.right = weights
+
+    return (xp.asarray(diff_state.central, dtype=work.dtype),
+            xp.asarray(diff_state.right, dtype=work.dtype))
+
+
+@xp_capabilities(skip_backends=[('array_api_strict', _array_api_strict_skip_reason),
+                                ('dask.array', _dask_reason)], jax_jit=False)
+def jacobian(f, x, *, tolerances=None, maxiter=10, order=8, initial_step=0.5,
+             step_factor=2.0, step_direction=0):
+    r"""Evaluate the Jacobian of a function numerically.
+
+    Parameters
+    ----------
+    f : callable
+        The function whose Jacobian is desired. The signature must be::
+
+            f(xi: ndarray) -> ndarray
+
+        where each element of ``xi`` is a finite real. If the function to be
+        differentiated accepts additional arguments, wrap it (e.g. using
+        `functools.partial` or ``lambda``) and pass the wrapped callable
+        into `jacobian`. `f` must not mutate the array ``xi``. See Notes
+        regarding vectorization and the dimensionality of the input and output.
+    x : float array_like
+        Points at which to evaluate the Jacobian. Must have at least one dimension.
+        See Notes regarding the dimensionality and vectorization.
+    tolerances : dictionary of floats, optional
+        Absolute and relative tolerances. Valid keys of the dictionary are:
+
+        - ``atol`` - absolute tolerance on the derivative
+        - ``rtol`` - relative tolerance on the derivative
+
+        Iteration will stop when ``res.error < atol + rtol * abs(res.df)``. The default
+        `atol` is the smallest normal number of the appropriate dtype, and
+        the default `rtol` is the square root of the precision of the
+        appropriate dtype.
+    maxiter : int, default: 10
+        The maximum number of iterations of the algorithm to perform. See
+        Notes.
+    order : int, default: 8
+        The (positive integer) order of the finite difference formula to be
+        used. Odd integers will be rounded up to the next even integer.
+    initial_step : float array_like, default: 0.5
+        The (absolute) initial step size for the finite difference derivative
+        approximation. Must be broadcastable with `x` and `step_direction`.
+    step_factor : float, default: 2.0
+        The factor by which the step size is *reduced* in each iteration; i.e.
+        the step size in iteration 1 is ``initial_step/step_factor``. If
+        ``step_factor < 1``, subsequent steps will be greater than the initial
+        step; this may be useful if steps smaller than some threshold are
+        undesirable (e.g. due to subtractive cancellation error).
+    step_direction : integer array_like
+        An array representing the direction of the finite difference steps (e.g.
+        for use when `x` lies near to the boundary of the domain of the function.)
+        Must be broadcastable with `x` and `initial_step`.
+        Where 0 (default), central differences are used; where negative (e.g.
+        -1), steps are non-positive; and where positive (e.g. 1), all steps are
+        non-negative.
+
+    Returns
+    -------
+    res : _RichResult
+        An object similar to an instance of `scipy.optimize.OptimizeResult` with the
+        following attributes. The descriptions are written as though the values will
+        be scalars; however, if `f` returns an array, the outputs will be
+        arrays of the same shape.
+
+        success : bool array
+            ``True`` where the algorithm terminated successfully (status ``0``);
+            ``False`` otherwise.
+        status : int array
+            An integer representing the exit status of the algorithm.
+
+            - ``0`` : The algorithm converged to the specified tolerances.
+            - ``-1`` : The error estimate increased, so iteration was terminated.
+            - ``-2`` : The maximum number of iterations was reached.
+            - ``-3`` : A non-finite value was encountered.
+
+        df : float array
+            The Jacobian of `f` at `x`, if the algorithm terminated
+            successfully.
+        error : float array
+            An estimate of the error: the magnitude of the difference between
+            the current estimate of the Jacobian and the estimate in the
+            previous iteration.
+        nit : int array
+            The number of iterations of the algorithm that were performed.
+        nfev : int array
+            The number of points at which `f` was evaluated.
+
+        Each element of an attribute is associated with the corresponding
+        element of `df`. For instance, element ``i`` of `nfev` is the
+        number of points at which `f` was evaluated for the sake of
+        computing element ``i`` of `df`.
+
+    See Also
+    --------
+    derivative, hessian
+
+    Notes
+    -----
+    Suppose we wish to evaluate the Jacobian of a function
+    :math:`f: \mathbf{R}^m \rightarrow \mathbf{R}^n`. Assign to variables
+    ``m`` and ``n`` the positive integer values of :math:`m` and :math:`n`,
+    respectively, and let ``...`` represent an arbitrary tuple of integers.
+    If we wish to evaluate the Jacobian at a single point, then:
+
+    - argument `x` must be an array of shape ``(m,)``
+    - argument `f` must be vectorized to accept an array of shape ``(m, ...)``.
+      The first axis represents the :math:`m` inputs of :math:`f`; the remainder
+      are for evaluating the function at multiple points in a single call.
+    - argument `f` must return an array of shape ``(n, ...)``. The first
+      axis represents the :math:`n` outputs of :math:`f`; the remainder
+      are for the result of evaluating the function at multiple points.
+    - attribute ``df`` of the result object will be an array of shape ``(n, m)``,
+      the Jacobian.
+
+    This function is also vectorized in the sense that the Jacobian can be
+    evaluated at ``k`` points in a single call. In this case, `x` would be an
+    array of shape ``(m, k)``, `f` would accept an array of shape
+    ``(m, k, ...)`` and return an array of shape ``(n, k, ...)``, and the ``df``
+    attribute of the result would have shape ``(n, m, k)``.
+
+    Suppose the desired callable ``f_not_vectorized`` is not vectorized; it can
+    only accept an array of shape ``(m,)``. A simple solution to satisfy the required
+    interface is to wrap ``f_not_vectorized`` as follows::
+
+        def f(x):
+            return np.apply_along_axis(f_not_vectorized, axis=0, arr=x)
+
+    Alternatively, suppose the desired callable ``f_vec_q`` is vectorized, but
+    only for 2-D arrays of shape ``(m, q)``. To satisfy the required interface,
+    consider::
+
+        def f(x):
+            m, batch = x.shape[0], x.shape[1:]  # x.shape is (m, ...)
+            x = np.reshape(x, (m, -1))  # `-1` is short for q = prod(batch)
+            res = f_vec_q(x)  # pass shape (m, q) to function
+            n = res.shape[0]
+            return np.reshape(res, (n,) + batch)  # return shape (n, ...)
+
+    Then pass the wrapped callable ``f`` as the first argument of `jacobian`.
+
+    References
+    ----------
+    .. [1] Jacobian matrix and determinant, *Wikipedia*,
+           https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant
+
+    Examples
+    --------
+    The Rosenbrock function maps from :math:`\mathbf{R}^m \rightarrow \mathbf{R}`;
+    the SciPy implementation `scipy.optimize.rosen` is vectorized to accept an
+    array of shape ``(m, p)`` and return an array of shape ``p``. Suppose we wish
+    to evaluate the Jacobian (AKA the gradient because the function returns a scalar)
+    at ``[0.5, 0.5, 0.5]``.
+
+    >>> import numpy as np
+    >>> from scipy.differentiate import jacobian
+    >>> from scipy.optimize import rosen, rosen_der
+    >>> m = 3
+    >>> x = np.full(m, 0.5)
+    >>> res = jacobian(rosen, x)
+    >>> ref = rosen_der(x)  # reference value of the gradient
+    >>> res.df, ref
+    (array([-51.,  -1.,  50.]), array([-51.,  -1.,  50.]))
+
+    As an example of a function with multiple outputs, consider Example 4
+    from [1]_.
+
+    >>> def f(x):
+    ...     x1, x2, x3 = x
+    ...     return [x1, 5*x3, 4*x2**2 - 2*x3, x3*np.sin(x1)]
+
+    The true Jacobian is given by:
+
+    >>> def df(x):
+    ...         x1, x2, x3 = x
+    ...         one = np.ones_like(x1)
+    ...         return [[one, 0*one, 0*one],
+    ...                 [0*one, 0*one, 5*one],
+    ...                 [0*one, 8*x2, -2*one],
+    ...                 [x3*np.cos(x1), 0*one, np.sin(x1)]]
+
+    Evaluate the Jacobian at an arbitrary point.
+
+    >>> rng = np.random.default_rng(389252938452)
+    >>> x = rng.random(size=3)
+    >>> res = jacobian(f, x)
+    >>> ref = df(x)
+    >>> res.df.shape == (4, 3)
+    True
+    >>> np.allclose(res.df, ref)
+    True
+
+    Evaluate the Jacobian at 10 arbitrary points in a single call.
+
+    >>> x = rng.random(size=(3, 10))
+    >>> res = jacobian(f, x)
+    >>> ref = df(x)
+    >>> res.df.shape == (4, 3, 10)
+    True
+    >>> np.allclose(res.df, ref)
+    True
+
+    """
+    xp = array_namespace(x)
+    x0 = xp_promote(x, force_floating=True, xp=xp)
+
+    if x0.ndim < 1:
+        message = "Argument `x` must be at least 1-D."
+        raise ValueError(message)
+
+    m = x0.shape[0]
+    i = xp.arange(m)
+
+    def wrapped(x):
+        p = () if x.ndim == x0.ndim else (x.shape[-1],)  # number of abscissae
+
+        new_shape = (m, m) + x0.shape[1:] + p
+        xph = xp.expand_dims(x0, axis=1)
+        if x.ndim != x0.ndim:
+            xph = xp.expand_dims(xph, axis=-1)
+        xph = xp_copy(xp.broadcast_to(xph, new_shape), xp=xp)
+        xph = xpx.at(xph)[i, i].set(x)
+        return f(xph)
+
+    res = derivative(wrapped, x, tolerances=tolerances,
+                     maxiter=maxiter, order=order, initial_step=initial_step,
+                     step_factor=step_factor, preserve_shape=True,
+                     step_direction=step_direction)
+
+    del res.x  # the user knows `x`, and the way it gets broadcasted is meaningless here
+    return res
+
+
+@xp_capabilities(skip_backends=[('array_api_strict', _array_api_strict_skip_reason),
+                                ('dask.array', _dask_reason)], jax_jit=False)
+def hessian(f, x, *, tolerances=None, maxiter=10,
+            order=8, initial_step=0.5, step_factor=2.0):
+    r"""Evaluate the Hessian of a function numerically.
+
+    Parameters
+    ----------
+    f : callable
+        The function whose Hessian is desired. The signature must be::
+
+            f(xi: ndarray) -> ndarray
+
+        where each element of ``xi`` is a finite real. If the function to be
+        differentiated accepts additional arguments, wrap it (e.g. using
+        `functools.partial` or ``lambda``) and pass the wrapped callable
+        into `hessian`. `f` must not mutate the array ``xi``. See Notes
+        regarding vectorization and the dimensionality of the input and output.
+    x : float array_like
+        Points at which to evaluate the Hessian. Must have at least one dimension.
+        See Notes regarding the dimensionality and vectorization.
+    tolerances : dictionary of floats, optional
+        Absolute and relative tolerances. Valid keys of the dictionary are:
+
+        - ``atol`` - absolute tolerance on the derivative
+        - ``rtol`` - relative tolerance on the derivative
+
+        Iteration will stop when ``res.error < atol + rtol * abs(res.df)``. The default
+        `atol` is the smallest normal number of the appropriate dtype, and
+        the default `rtol` is the square root of the precision of the
+        appropriate dtype.
+    order : int, default: 8
+        The (positive integer) order of the finite difference formula to be
+        used. Odd integers will be rounded up to the next even integer.
+    initial_step : float, default: 0.5
+        The (absolute) initial step size for the finite difference derivative
+        approximation.
+    step_factor : float, default: 2.0
+        The factor by which the step size is *reduced* in each iteration; i.e.
+        the step size in iteration 1 is ``initial_step/step_factor``. If
+        ``step_factor < 1``, subsequent steps will be greater than the initial
+        step; this may be useful if steps smaller than some threshold are
+        undesirable (e.g. due to subtractive cancellation error).
+    maxiter : int, default: 10
+        The maximum number of iterations of the algorithm to perform. See
+        Notes.
+
+    Returns
+    -------
+    res : _RichResult
+        An object similar to an instance of `scipy.optimize.OptimizeResult` with the
+        following attributes. The descriptions are written as though the values will
+        be scalars; however, if `f` returns an array, the outputs will be
+        arrays of the same shape.
+
+        success : bool array
+            ``True`` where the algorithm terminated successfully (status ``0``);
+            ``False`` otherwise.
+        status : int array
+            An integer representing the exit status of the algorithm.
+
+            - ``0`` : The algorithm converged to the specified tolerances.
+            - ``-1`` : The error estimate increased, so iteration was terminated.
+            - ``-2`` : The maximum number of iterations was reached.
+            - ``-3`` : A non-finite value was encountered.
+
+        ddf : float array
+            The Hessian of `f` at `x`, if the algorithm terminated
+            successfully.
+        error : float array
+            An estimate of the error: the magnitude of the difference between
+            the current estimate of the Hessian and the estimate in the
+            previous iteration.
+        nfev : int array
+            The number of points at which `f` was evaluated.
+
+        Each element of an attribute is associated with the corresponding
+        element of `ddf`. For instance, element ``[i, j]`` of `nfev` is the
+        number of points at which `f` was evaluated for the sake of
+        computing element ``[i, j]`` of `ddf`.
+
+    See Also
+    --------
+    derivative, jacobian
+
+    Notes
+    -----
+    Suppose we wish to evaluate the Hessian of a function
+    :math:`f: \mathbf{R}^m \rightarrow \mathbf{R}`, and we assign to variable
+    ``m`` the positive integer value of :math:`m`. If we wish to evaluate
+    the Hessian at a single point, then:
+
+    - argument `x` must be an array of shape ``(m,)``
+    - argument `f` must be vectorized to accept an array of shape
+      ``(m, ...)``. The first axis represents the :math:`m` inputs of
+      :math:`f`; the remaining axes indicated by ellipses are for evaluating
+      the function at several abscissae in a single call.
+    - argument `f` must return an array of shape ``(...)``.
+    - attribute ``dff`` of the result object will be an array of shape ``(m, m)``,
+      the Hessian.
+
+    This function is also vectorized in the sense that the Hessian can be
+    evaluated at ``k`` points in a single call. In this case, `x` would be an
+    array of shape ``(m, k)``, `f` would accept an array of shape
+    ``(m, ...)`` and return an array of shape ``(...)``, and the ``ddf``
+    attribute of the result would have shape ``(m, m, k)``. Note that the
+    axis associated with the ``k`` points is included within the axes
+    denoted by ``(...)``.
+
+    Currently, `hessian` is implemented by nesting calls to `jacobian`.
+    All options passed to `hessian` are used for both the inner and outer
+    calls with one exception: the `rtol` used in the inner `jacobian` call
+    is tightened by a factor of 100 with the expectation that the inner
+    error can be ignored. A consequence is that `rtol` should not be set
+    less than 100 times the precision of the dtype of `x`; a warning is
+    emitted otherwise.
+
+    References
+    ----------
+    .. [1] Hessian matrix, *Wikipedia*,
+           https://en.wikipedia.org/wiki/Hessian_matrix
+
+    Examples
+    --------
+    The Rosenbrock function maps from :math:`\mathbf{R}^m \rightarrow \mathbf{R}`;
+    the SciPy implementation `scipy.optimize.rosen` is vectorized to accept an
+    array of shape ``(m, ...)`` and return an array of shape ``...``. Suppose we
+    wish to evaluate the Hessian at ``[0.5, 0.5, 0.5]``.
+
+    >>> import numpy as np
+    >>> from scipy.differentiate import hessian
+    >>> from scipy.optimize import rosen, rosen_hess
+    >>> m = 3
+    >>> x = np.full(m, 0.5)
+    >>> res = hessian(rosen, x)
+    >>> ref = rosen_hess(x)  # reference value of the Hessian
+    >>> np.allclose(res.ddf, ref)
+    True
+
+    `hessian` is vectorized to evaluate the Hessian at multiple points
+    in a single call.
+
+    >>> rng = np.random.default_rng(4589245925010)
+    >>> x = rng.random((m, 10))
+    >>> res = hessian(rosen, x)
+    >>> ref = [rosen_hess(xi) for xi in x.T]
+    >>> ref = np.moveaxis(ref, 0, -1)
+    >>> np.allclose(res.ddf, ref)
+    True
+
+    """
+    # todo:
+    # - add ability to vectorize over additional parameters (*args?)
+    # - error estimate stack with inner jacobian (or use legit 2D stencil)
+
+    kwargs = dict(maxiter=maxiter, order=order, initial_step=initial_step,
+                  step_factor=step_factor)
+    tolerances = {} if tolerances is None else tolerances
+    atol = tolerances.get('atol', None)
+    rtol = tolerances.get('rtol', None)
+
+    xp = array_namespace(x)
+    x0 = xp_promote(x, force_floating=True, xp=xp)
+
+    finfo = xp.finfo(x0.dtype)
+    rtol = finfo.eps**0.5 if rtol is None else rtol  # keep same as `derivative`
+
+    # tighten the inner tolerance to make the inner error negligible
+    rtol_min = finfo.eps * 100
+    message = (f"The specified `{rtol=}`, but error estimates are likely to be "
+               f"unreliable when `rtol < {rtol_min}`.")
+    if 0 < rtol < rtol_min:  # rtol <= 0 is an error
+        warnings.warn(message, RuntimeWarning, stacklevel=2)
+        rtol = rtol_min
+
+    def df(x):
+        tolerances = dict(rtol=rtol/100, atol=atol)
+        temp = jacobian(f, x, tolerances=tolerances, **kwargs)
+        nfev.append(temp.nfev if len(nfev) == 0 else temp.nfev.sum(axis=-1))
+        return temp.df
+
+    nfev = []  # track inner function evaluations
+    res = jacobian(df, x, tolerances=tolerances, **kwargs)  # jacobian of jacobian
+
+    nfev = xp.cumulative_sum(xp.stack(nfev), axis=0)
+    res_nit = xp.astype(res.nit[xp.newaxis, ...], xp.int64)  # appease torch
+    res.nfev = xp.take_along_axis(nfev, res_nit, axis=0)[0]
+    res.ddf = res.df
+    del res.df  # this is renamed to ddf
+    del res.nit  # this is only the outer-jacobian nit
+
+    return res
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--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/differentiate/tests/test_differentiate.py
@@ -0,0 +1,690 @@
+import math
+import pytest
+
+import numpy as np
+
+import scipy._lib._elementwise_iterative_method as eim
+import scipy._lib.array_api_extra as xpx
+from scipy._lib._array_api_no_0d import xp_assert_close, xp_assert_equal, xp_assert_less
+from scipy._lib._array_api import is_numpy, is_torch, make_xp_test_case
+
+from scipy import stats, optimize, special
+from scipy.differentiate import derivative, jacobian, hessian
+from scipy.differentiate._differentiate import _EERRORINCREASE
+
+
+
+@make_xp_test_case(derivative)
+class TestDerivative:
+
+    def f(self, x):
+        return special.ndtr(x)
+
+    @pytest.mark.parametrize('x', [0.6, np.linspace(-0.05, 1.05, 10)])
+    def test_basic(self, x, xp):
+        # Invert distribution CDF and compare against distribution `ppf`
+        default_dtype = xp.asarray(1.).dtype
+        res = derivative(self.f, xp.asarray(x, dtype=default_dtype))
+        ref = xp.asarray(stats.norm().pdf(x), dtype=default_dtype)
+        xp_assert_close(res.df, ref)
+        # This would be nice, but doesn't always work out. `error` is an
+        # estimate, not a bound.
+        if not is_torch(xp):
+            xp_assert_less(xp.abs(res.df - ref), res.error)
+
+    @pytest.mark.parametrize('case', stats._distr_params.distcont)
+    def test_accuracy(self, case):
+        distname, params = case
+        dist = getattr(stats, distname)(*params)
+        x = dist.median() + 0.1
+        res = derivative(dist.cdf, x)
+        ref = dist.pdf(x)
+        xp_assert_close(res.df, ref, atol=1e-10)
+
+    @pytest.mark.parametrize('order', [1, 6])
+    @pytest.mark.parametrize('shape', [tuple(), (12,), (3, 4), (3, 2, 2)])
+    def test_vectorization(self, order, shape, xp):
+        # Test for correct functionality, output shapes, and dtypes for various
+        # input shapes.
+        x = np.linspace(-0.05, 1.05, 12).reshape(shape) if shape else 0.6
+        n = np.size(x)
+        state = {}
+
+        @np.vectorize
+        def _derivative_single(x):
+            return derivative(self.f, x, order=order)
+
+        def f(x, *args, **kwargs):
+            state['nit'] += 1
+            state['feval'] += 1 if (x.size == n or x.ndim <=1) else x.shape[-1]
+            return self.f(x, *args, **kwargs)
+
+        state['nit'] = -1
+        state['feval'] = 0
+
+        res = derivative(f, xp.asarray(x, dtype=xp.float64), order=order)
+        refs = _derivative_single(x).ravel()
+
+        ref_x = [ref.x for ref in refs]
+        xp_assert_close(xp.reshape(res.x, (-1,)), xp.asarray(ref_x))
+
+        ref_df = [ref.df for ref in refs]
+        xp_assert_close(xp.reshape(res.df, (-1,)), xp.asarray(ref_df))
+
+        ref_error = [ref.error for ref in refs]
+        xp_assert_close(xp.reshape(res.error, (-1,)), xp.asarray(ref_error),
+                        atol=1e-12)
+
+        ref_success = [bool(ref.success) for ref in refs]
+        xp_assert_equal(xp.reshape(res.success, (-1,)), xp.asarray(ref_success))
+
+        ref_flag = [np.int32(ref.status) for ref in refs]
+        xp_assert_equal(xp.reshape(res.status, (-1,)), xp.asarray(ref_flag))
+
+        ref_nfev = [np.int32(ref.nfev) for ref in refs]
+        xp_assert_equal(xp.reshape(res.nfev, (-1,)), xp.asarray(ref_nfev))
+        if is_numpy(xp):  # can't expect other backends to be exactly the same
+            assert xp.max(res.nfev) == state['feval']
+
+        ref_nit = [np.int32(ref.nit) for ref in refs]
+        xp_assert_equal(xp.reshape(res.nit, (-1,)), xp.asarray(ref_nit))
+        if is_numpy(xp):  # can't expect other backends to be exactly the same
+            assert xp.max(res.nit) == state['nit']
+
+    def test_flags(self, xp):
+        # Test cases that should produce different status flags; show that all
+        # can be produced simultaneously.
+        rng = np.random.default_rng(5651219684984213)
+        def f(xs, js):
+            f.nit += 1
+            funcs = [lambda x: x - 2.5,  # converges
+                     lambda x: xp.exp(x)*rng.random(),  # error increases
+                     lambda x: xp.exp(x),  # reaches maxiter due to order=2
+                     lambda x: xp.full_like(x, xp.nan)]  # stops due to NaN
+            res = [funcs[int(j)](x) for x, j in zip(xs, xp.reshape(js, (-1,)))]
+            return xp.stack(res)
+        f.nit = 0
+
+        args = (xp.arange(4, dtype=xp.int64),)
+        res = derivative(f, xp.ones(4, dtype=xp.float64),
+                         tolerances=dict(rtol=1e-14),
+                         order=2, args=args)
+
+        ref_flags = xp.asarray([eim._ECONVERGED,
+                                _EERRORINCREASE,
+                                eim._ECONVERR,
+                                eim._EVALUEERR], dtype=xp.int32)
+        xp_assert_equal(res.status, ref_flags)
+
+    def test_flags_preserve_shape(self, xp):
+        # Same test as above but using `preserve_shape` option to simplify.
+        rng = np.random.default_rng(5651219684984213)
+        def f(x):
+            out = [x - 2.5,  # converges
+                   xp.exp(x)*rng.random(),  # error increases
+                   xp.exp(x),  # reaches maxiter due to order=2
+                   xp.full_like(x, xp.nan)]  # stops due to NaN
+            return xp.stack(out)
+
+        res = derivative(f, xp.asarray(1, dtype=xp.float64),
+                         tolerances=dict(rtol=1e-14),
+                         order=2, preserve_shape=True)
+
+        ref_flags = xp.asarray([eim._ECONVERGED,
+                                _EERRORINCREASE,
+                                eim._ECONVERR,
+                                eim._EVALUEERR], dtype=xp.int32)
+        xp_assert_equal(res.status, ref_flags)
+
+    def test_preserve_shape(self, xp):
+        # Test `preserve_shape` option
+        def f(x):
+            out = [x, xp.sin(3*x), x+xp.sin(10*x), xp.sin(20*x)*(x-1)**2]
+            return xp.stack(out)
+
+        x = xp.asarray(0.)
+        ref = xp.asarray([xp.asarray(1), 3*xp.cos(3*x), 1+10*xp.cos(10*x),
+                          20*xp.cos(20*x)*(x-1)**2 + 2*xp.sin(20*x)*(x-1)])
+        res = derivative(f, x, preserve_shape=True)
+        xp_assert_close(res.df, ref)
+
+    def test_convergence(self, xp):
+        # Test that the convergence tolerances behave as expected
+        x = xp.asarray(1., dtype=xp.float64)
+        f = special.ndtr
+        ref = float(stats.norm.pdf(1.))
+        tolerances0 = dict(atol=0, rtol=0)
+
+        tolerances = tolerances0.copy()
+        tolerances['atol'] = 1e-3
+        res1 = derivative(f, x, tolerances=tolerances, order=4)
+        assert abs(res1.df - ref) < 1e-3
+        tolerances['atol'] = 1e-6
+        res2 = derivative(f, x, tolerances=tolerances, order=4)
+        assert abs(res2.df - ref) < 1e-6
+        assert abs(res2.df - ref) < abs(res1.df - ref)
+
+        tolerances = tolerances0.copy()
+        tolerances['rtol'] = 1e-3
+        res1 = derivative(f, x, tolerances=tolerances, order=4)
+        assert abs(res1.df - ref) < 1e-3 * ref
+        tolerances['rtol'] = 1e-6
+        res2 = derivative(f, x, tolerances=tolerances, order=4)
+        assert abs(res2.df - ref) < 1e-6 * ref
+        assert abs(res2.df - ref) < abs(res1.df - ref)
+
+    def test_step_parameters(self, xp):
+        # Test that step factors have the expected effect on accuracy
+        x = xp.asarray(1., dtype=xp.float64)
+        f = special.ndtr
+        ref = float(stats.norm.pdf(1.))
+
+        res1 = derivative(f, x, initial_step=0.5, maxiter=1)
+        res2 = derivative(f, x, initial_step=0.05, maxiter=1)
+        assert abs(res2.df - ref) < abs(res1.df - ref)
+
+        res1 = derivative(f, x, step_factor=2, maxiter=1)
+        res2 = derivative(f, x, step_factor=20, maxiter=1)
+        assert abs(res2.df - ref) < abs(res1.df - ref)
+
+        # `step_factor` can be less than 1: `initial_step` is the minimum step
+        kwargs = dict(order=4, maxiter=1, step_direction=0)
+        res = derivative(f, x, initial_step=0.5, step_factor=0.5, **kwargs)
+        ref = derivative(f, x, initial_step=1, step_factor=2, **kwargs)
+        xp_assert_close(res.df, ref.df, rtol=5e-15)
+
+        # This is a similar test for one-sided difference
+        kwargs = dict(order=2, maxiter=1, step_direction=1)
+        res = derivative(f, x, initial_step=1, step_factor=2, **kwargs)
+        ref = derivative(f, x, initial_step=1/np.sqrt(2), step_factor=0.5, **kwargs)
+        xp_assert_close(res.df, ref.df, rtol=5e-15)
+
+        kwargs['step_direction'] = -1
+        res = derivative(f, x, initial_step=1, step_factor=2, **kwargs)
+        ref = derivative(f, x, initial_step=1/np.sqrt(2), step_factor=0.5, **kwargs)
+        xp_assert_close(res.df, ref.df, rtol=5e-15)
+
+    def test_step_direction(self, xp):
+        # test that `step_direction` works as expected
+        def f(x):
+            y = xp.exp(x)
+            y = xpx.at(y)[(x < 0) + (x > 2)].set(xp.nan)
+            return y
+
+        x = xp.linspace(0, 2, 10)
+        step_direction = xp.zeros_like(x)
+        step_direction = xpx.at(step_direction)[x < 0.6].set(1)
+        step_direction = xpx.at(step_direction)[x > 1.4].set(-1)
+        res = derivative(f, x, step_direction=step_direction)
+        xp_assert_close(res.df, xp.exp(x))
+        assert xp.all(res.success)
+
+    def test_vectorized_step_direction_args(self, xp):
+        # test that `step_direction` and `args` are vectorized properly
+        def f(x, p):
+            return x ** p
+
+        def df(x, p):
+            return p * x ** (p - 1)
+
+        x = xp.reshape(xp.asarray([1, 2, 3, 4]), (-1, 1, 1))
+        hdir = xp.reshape(xp.asarray([-1, 0, 1]), (1, -1, 1))
+        p = xp.reshape(xp.asarray([2, 3]), (1, 1, -1))
+        res = derivative(f, x, step_direction=hdir, args=(p,))
+        ref = xp.broadcast_to(df(x, p), res.df.shape)
+        ref = xp.asarray(ref, dtype=xp.asarray(1.).dtype)
+        xp_assert_close(res.df, ref)
+
+    def test_initial_step(self, xp):
+        # Test that `initial_step` works as expected and is vectorized
+        def f(x):
+            return xp.exp(x)
+
+        x = xp.asarray(0., dtype=xp.float64)
+        step_direction = xp.asarray([-1, 0, 1])
+        h0 = xp.reshape(xp.logspace(-3, 0, 10), (-1, 1))
+        res = derivative(f, x, initial_step=h0, order=2, maxiter=1,
+                         step_direction=step_direction)
+        err = xp.abs(res.df - f(x))
+
+        # error should be smaller for smaller step sizes
+        assert xp.all(err[:-1, ...] < err[1:, ...])
+
+        # results of vectorized call should match results with
+        # initial_step taken one at a time
+        for i in range(h0.shape[0]):
+            ref = derivative(f, x, initial_step=h0[i, 0], order=2, maxiter=1,
+                             step_direction=step_direction)
+            xp_assert_close(res.df[i, :], ref.df, rtol=1e-14)
+
+    def test_maxiter_callback(self, xp):
+        # Test behavior of `maxiter` parameter and `callback` interface
+        x = xp.asarray(0.612814, dtype=xp.float64)
+        maxiter = 3
+
+        def f(x):
+            res = special.ndtr(x)
+            return res
+
+        default_order = 8
+        res = derivative(f, x, maxiter=maxiter, tolerances=dict(rtol=1e-15))
+        assert not xp.any(res.success)
+        assert xp.all(res.nfev == default_order + 1 + (maxiter - 1)*2)
+        assert xp.all(res.nit == maxiter)
+
+        def callback(res):
+            callback.iter += 1
+            callback.res = res
+            assert hasattr(res, 'x')
+            assert float(res.df) not in callback.dfs
+            callback.dfs.add(float(res.df))
+            assert res.status == eim._EINPROGRESS
+            if callback.iter == maxiter:
+                raise StopIteration
+        callback.iter = -1  # callback called once before first iteration
+        callback.res = None
+        callback.dfs = set()
+
+        res2 = derivative(f, x, callback=callback, tolerances=dict(rtol=1e-15))
+        # terminating with callback is identical to terminating due to maxiter
+        # (except for `status`)
+        for key in res.keys():
+            if key == 'status':
+                assert res[key] == eim._ECONVERR
+                assert res2[key] == eim._ECALLBACK
+            elif key == 'error':
+                # switched from equality check to accommodate
+                # macosx-x86_64/Accelerate
+                xp_assert_close(res2[key], res[key], atol=1e-14)
+                xp_assert_close(callback.res[key], res[key], atol=1e-14)
+            else:
+                assert res2[key] == callback.res[key] == res[key]
+
+    @pytest.mark.parametrize("hdir", (-1, 0, 1))
+    @pytest.mark.parametrize("x", (0.65, [0.65, 0.7]))
+    @pytest.mark.parametrize("dtype", ('float32', 'float64'))
+    def test_dtype(self, hdir, x, dtype, xp):
+        # Test that dtypes are preserved
+        dtype = getattr(xp, dtype)
+        x = xp.asarray(x, dtype=dtype)
+
+        def f(x):
+            assert x.dtype == dtype
+            return xp.exp(x)
+
+        def callback(res):
+            assert res.x.dtype == dtype
+            assert res.df.dtype == dtype
+            assert res.error.dtype == dtype
+
+        res = derivative(f, x, order=4, step_direction=hdir, callback=callback)
+        assert res.x.dtype == dtype
+        assert res.df.dtype == dtype
+        assert res.error.dtype == dtype
+        eps = xp.finfo(dtype).eps
+        # not sure why torch is less accurate here; might be worth investigating
+        rtol = eps**0.5 * 50 if is_torch(xp) else eps**0.5
+        xp_assert_close(res.df, xp.exp(res.x), rtol=rtol)
+
+    def test_input_validation(self, xp):
+        # Test input validation for appropriate error messages
+        one = xp.asarray(1)
+
+        message = '`f` must be callable.'
+        with pytest.raises(ValueError, match=message):
+            derivative(None, one)
+
+        message = 'Abscissae and function output must be real numbers.'
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, xp.asarray(-4+1j))
+
+        message = "When `preserve_shape=False`, the shape of the array..."
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: [1, 2, 3], xp.asarray([-2, -3]))
+
+        message = 'Tolerances and step parameters must be non-negative...'
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, one, tolerances=dict(atol=-1))
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, one, tolerances=dict(rtol='ekki'))
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, one, step_factor=object())
+
+        message = '`maxiter` must be a positive integer.'
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, one, maxiter=1.5)
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, one, maxiter=0)
+
+        message = '`order` must be a positive integer'
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, one, order=1.5)
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, one, order=0)
+
+        message = '`preserve_shape` must be True or False.'
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, one, preserve_shape='herring')
+
+        message = '`callback` must be callable.'
+        with pytest.raises(ValueError, match=message):
+            derivative(lambda x: x, one, callback='shrubbery')
+
+    def test_special_cases(self, xp):
+        # Test edge cases and other special cases
+
+        # Test that integers are not passed to `f`
+        # (otherwise this would overflow)
+        def f(x):
+            assert xp.isdtype(x.dtype, 'real floating')
+            return x ** 99 - 1
+
+        if not is_torch(xp):  # torch defaults to float32
+            res = derivative(f, xp.asarray(7), tolerances=dict(rtol=1e-10))
+            assert res.success
+            xp_assert_close(res.df, xp.asarray(99*7.**98))
+
+        # Test invalid step size and direction
+        res = derivative(xp.exp, xp.asarray(1), step_direction=xp.nan)
+        xp_assert_equal(res.df, xp.asarray(xp.nan))
+        xp_assert_equal(res.status, xp.asarray(-3, dtype=xp.int32))
+
+        res = derivative(xp.exp, xp.asarray(1), initial_step=0)
+        xp_assert_equal(res.df, xp.asarray(xp.nan))
+        xp_assert_equal(res.status, xp.asarray(-3, dtype=xp.int32))
+
+        # Test that if success is achieved in the correct number
+        # of iterations if function is a polynomial. Ideally, all polynomials
+        # of order 0-2 would get exact result with 0 refinement iterations,
+        # all polynomials of order 3-4 would be differentiated exactly after
+        # 1 iteration, etc. However, it seems that `derivative` needs an
+        # extra iteration to detect convergence based on the error estimate.
+
+        for n in range(6):
+            x = xp.asarray(1.5, dtype=xp.float64)
+            def f(x):
+                return 2*x**n
+
+            ref = 2*n*x**(n-1)
+
+            res = derivative(f, x, maxiter=1, order=max(1, n))
+            xp_assert_close(res.df, ref, rtol=1e-15)
+            xp_assert_equal(res.error, xp.asarray(xp.nan, dtype=xp.float64))
+
+            res = derivative(f, x, order=max(1, n))
+            assert res.success
+            assert res.nit == 2
+            xp_assert_close(res.df, ref, rtol=1e-15)
+
+        # Test scalar `args` (not in tuple)
+        def f(x, c):
+            return c*x - 1
+
+        res = derivative(f, xp.asarray(2), args=xp.asarray(3))
+        xp_assert_close(res.df, xp.asarray(3.))
+
+    # no need to run a test on multiple backends if it's xfailed
+    @pytest.mark.skip_xp_backends(np_only=True)
+    @pytest.mark.xfail
+    @pytest.mark.parametrize("case", (  # function, evaluation point
+        (lambda x: (x - 1) ** 3, 1),
+        (lambda x: np.where(x > 1, (x - 1) ** 5, (x - 1) ** 3), 1)
+    ))
+    def test_saddle_gh18811(self, case, xp):
+        # With default settings, `derivative` will not always converge when
+        # the true derivative is exactly zero. This tests that specifying a
+        # (tight) `atol` alleviates the problem. See discussion in gh-18811.
+        atol = 1e-16
+        res = derivative(*case, step_direction=[-1, 0, 1], atol=atol)
+        assert np.all(res.success)
+        xp_assert_close(res.df, 0, atol=atol)
+
+
+class JacobianHessianTest:
+    def test_iv(self, xp):
+        jh_func = self.jh_func.__func__
+
+        # Test input validation
+        message = "Argument `x` must be at least 1-D."
+        with pytest.raises(ValueError, match=message):
+            jh_func(xp.sin, 1, tolerances=dict(atol=-1))
+
+        # Confirm that other parameters are being passed to `derivative`,
+        # which raises an appropriate error message.
+        x = xp.ones(3)
+        func = optimize.rosen
+        message = 'Tolerances and step parameters must be non-negative scalars.'
+        with pytest.raises(ValueError, match=message):
+            jh_func(func, x, tolerances=dict(atol=-1))
+        with pytest.raises(ValueError, match=message):
+            jh_func(func, x, tolerances=dict(rtol=-1))
+        with pytest.raises(ValueError, match=message):
+            jh_func(func, x, step_factor=-1)
+
+        message = '`order` must be a positive integer.'
+        with pytest.raises(ValueError, match=message):
+            jh_func(func, x, order=-1)
+
+        message = '`maxiter` must be a positive integer.'
+        with pytest.raises(ValueError, match=message):
+            jh_func(func, x, maxiter=-1)
+
+
+@make_xp_test_case(jacobian)
+class TestJacobian(JacobianHessianTest):
+    jh_func = jacobian
+
+    # Example functions and Jacobians from Wikipedia:
+    # https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant#Examples
+
+    def f1(z, xp):
+        x, y = z
+        return xp.stack([x ** 2 * y, 5 * x + xp.sin(y)])
+
+    def df1(z):
+        x, y = z
+        return [[2 * x * y, x ** 2], [np.full_like(x, 5), np.cos(y)]]
+
+    f1.mn = 2, 2  # type: ignore[attr-defined]
+    f1.ref = df1  # type: ignore[attr-defined]
+
+    def f2(z, xp):
+        r, phi = z
+        return xp.stack([r * xp.cos(phi), r * xp.sin(phi)])
+
+    def df2(z):
+        r, phi = z
+        return [[np.cos(phi), -r * np.sin(phi)],
+                [np.sin(phi), r * np.cos(phi)]]
+
+    f2.mn = 2, 2  # type: ignore[attr-defined]
+    f2.ref = df2  # type: ignore[attr-defined]
+
+    def f3(z, xp):
+        r, phi, th = z
+        return xp.stack([r * xp.sin(phi) * xp.cos(th), r * xp.sin(phi) * xp.sin(th),
+                         r * xp.cos(phi)])
+
+    def df3(z):
+        r, phi, th = z
+        return [[np.sin(phi) * np.cos(th), r * np.cos(phi) * np.cos(th),
+                 -r * np.sin(phi) * np.sin(th)],
+                [np.sin(phi) * np.sin(th), r * np.cos(phi) * np.sin(th),
+                 r * np.sin(phi) * np.cos(th)],
+                [np.cos(phi), -r * np.sin(phi), np.zeros_like(r)]]
+
+    f3.mn = 3, 3  # type: ignore[attr-defined]
+    f3.ref = df3  # type: ignore[attr-defined]
+
+    def f4(x, xp):
+        x1, x2, x3 = x
+        return xp.stack([x1, 5 * x3, 4 * x2 ** 2 - 2 * x3, x3 * xp.sin(x1)])
+
+    def df4(x):
+        x1, x2, x3 = x
+        one = np.ones_like(x1)
+        return [[one, 0 * one, 0 * one],
+                [0 * one, 0 * one, 5 * one],
+                [0 * one, 8 * x2, -2 * one],
+                [x3 * np.cos(x1), 0 * one, np.sin(x1)]]
+
+    f4.mn = 3, 4  # type: ignore[attr-defined]
+    f4.ref = df4  # type: ignore[attr-defined]
+
+    def f5(x, xp):
+        x1, x2, x3 = x
+        return xp.stack([5 * x2, 4 * x1 ** 2 - 2 * xp.sin(x2 * x3), x2 * x3])
+
+    def df5(x):
+        x1, x2, x3 = x
+        one = np.ones_like(x1)
+        return [[0 * one, 5 * one, 0 * one],
+                [8 * x1, -2 * x3 * np.cos(x2 * x3), -2 * x2 * np.cos(x2 * x3)],
+                [0 * one, x3, x2]]
+
+    f5.mn = 3, 3  # type: ignore[attr-defined]
+    f5.ref = df5  # type: ignore[attr-defined]
+
+    def rosen(x, _): return optimize.rosen(x)
+    rosen.mn = 5, 1  # type: ignore[attr-defined]
+    rosen.ref = optimize.rosen_der  # type: ignore[attr-defined]
+
+    @pytest.mark.parametrize('dtype', ('float32', 'float64'))
+    @pytest.mark.parametrize('size', [(), (6,), (2, 3)])
+    @pytest.mark.parametrize('func', [f1, f2, f3, f4, f5, rosen])
+    def test_examples(self, dtype, size, func, xp):
+        atol = 1e-10 if dtype == 'float64' else 1.99e-3
+        dtype = getattr(xp, dtype)
+        rng = np.random.default_rng(458912319542)
+        m, n = func.mn
+        x = rng.random(size=(m,) + size)
+        res = jacobian(lambda x: func(x , xp), xp.asarray(x, dtype=dtype))
+        # convert list of arrays to single array before converting to xp array
+        ref = xp.asarray(np.asarray(func.ref(x)), dtype=dtype)
+        xp_assert_close(res.df, ref, atol=atol)
+
+    def test_attrs(self, xp):
+        # Test attributes of result object
+        z = xp.asarray([0.5, 0.25])
+
+        # case in which some elements of the Jacobian are harder
+        # to calculate than others
+        def df1(z):
+            x, y = z
+            return xp.stack([xp.cos(0.5*x) * xp.cos(y), xp.sin(2*x) * y**2])
+
+        def df1_0xy(x, y):
+            return xp.cos(0.5*x) * xp.cos(y)
+
+        def df1_1xy(x, y):
+            return xp.sin(2*x) * y**2
+
+        res = jacobian(df1, z, initial_step=10)
+        # FIXME https://github.com/scipy/scipy/pull/22320#discussion_r1914898175
+        if not is_torch(xp):
+            assert xpx.nunique(res.nit) == 4
+            assert xpx.nunique(res.nfev) == 4
+
+        res00 = jacobian(lambda x: df1_0xy(x, z[1]), z[0:1], initial_step=10)
+        res01 = jacobian(lambda y: df1_0xy(z[0], y), z[1:2], initial_step=10)
+        res10 = jacobian(lambda x: df1_1xy(x, z[1]), z[0:1], initial_step=10)
+        res11 = jacobian(lambda y: df1_1xy(z[0], y), z[1:2], initial_step=10)
+        ref = optimize.OptimizeResult()
+        for attr in ['success', 'status', 'df', 'nit', 'nfev']:
+            ref_attr = xp.asarray([[getattr(res00, attr), getattr(res01, attr)],
+                                   [getattr(res10, attr), getattr(res11, attr)]])
+            ref[attr] = xp.squeeze(
+                ref_attr,
+                axis=tuple(ax for ax, size in enumerate(ref_attr.shape) if size == 1)
+            )
+            rtol = 1.5e-5 if res[attr].dtype == xp.float32 else 1.5e-14
+            xp_assert_close(res[attr], ref[attr], rtol=rtol)
+
+    def test_step_direction_size(self, xp):
+        # Check that `step_direction` and `initial_step` can be used to ensure that
+        # the usable domain of a function is respected.
+        rng = np.random.default_rng(23892589425245)
+        b = rng.random(3)
+        eps = 1e-7  # torch needs wiggle room?
+
+        def f(x):
+            x = xpx.at(x)[0, x[0] < b[0]].set(xp.nan)
+            x = xpx.at(x)[0, x[0] > b[0] + 0.25].set(xp.nan)
+            x = xpx.at(x)[1, x[1] > b[1]].set(xp.nan)
+            x = xpx.at(x)[1, x[1] < b[1] - 0.1-eps].set(xp.nan)
+            return TestJacobian.f5(x, xp)
+
+        dir = [1, -1, 0]
+        h0 = [0.25, 0.1, 0.5]
+        atol = {'atol': 1e-8}
+        res = jacobian(f, xp.asarray(b, dtype=xp.float64), initial_step=h0,
+                       step_direction=dir, tolerances=atol)
+        ref = xp.asarray(TestJacobian.df5(b), dtype=xp.float64)
+        xp_assert_close(res.df, ref, atol=1e-8)
+        assert xp.all(xp.isfinite(ref))
+
+
+@make_xp_test_case(hessian)
+class TestHessian(JacobianHessianTest):
+    jh_func = hessian
+
+    @pytest.mark.parametrize('shape', [(), (4,), (2, 4)])
+    def test_example(self, shape, xp):
+        rng = np.random.default_rng(458912319542)
+        m = 3
+        x = xp.asarray(rng.random((m,) + shape), dtype=xp.float64)
+        res = hessian(optimize.rosen, x)
+        if shape:
+            x = xp.reshape(x, (m, -1))
+            ref = xp.stack([optimize.rosen_hess(xi) for xi in x.T])
+            ref = xp.moveaxis(ref, 0, -1)
+            ref = xp.reshape(ref, (m, m,) + shape)
+        else:
+            ref = optimize.rosen_hess(x)
+        xp_assert_close(res.ddf, ref, atol=1e-8)
+
+        # # Removed symmetry enforcement; consider adding back in as a feature
+        # # check symmetry
+        # for key in ['ddf', 'error', 'nfev', 'success', 'status']:
+        #     assert_equal(res[key], np.swapaxes(res[key], 0, 1))
+
+    def test_float32(self, xp):
+        rng = np.random.default_rng(458912319542)
+        x = xp.asarray(rng.random(3), dtype=xp.float32)
+        res = hessian(optimize.rosen, x)
+        ref = optimize.rosen_hess(x)
+        mask = (ref != 0)
+        xp_assert_close(res.ddf[mask], ref[mask])
+        atol = 1e-2 * xp.abs(xp.min(ref[mask]))
+        xp_assert_close(res.ddf[~mask], ref[~mask], atol=atol)
+
+    def test_nfev(self, xp):
+        z = xp.asarray([0.5, 0.25])
+
+        def f1(z):
+            x, y = xp.broadcast_arrays(*z)
+            f1.nfev = f1.nfev + (math.prod(x.shape[2:]) if x.ndim > 2 else 1)
+            return xp.sin(x) * y ** 3
+        f1.nfev = 0
+
+
+        res = hessian(f1, z, initial_step=10)
+        f1.nfev = 0
+        res00 = hessian(lambda x: f1([x[0], z[1]]), z[0:1], initial_step=10)
+        assert res.nfev[0, 0] == f1.nfev == res00.nfev[0, 0]
+
+        f1.nfev = 0
+        res11 = hessian(lambda y: f1([z[0], y[0]]), z[1:2], initial_step=10)
+        assert res.nfev[1, 1] == f1.nfev == res11.nfev[0, 0]
+
+        # Removed symmetry enforcement; consider adding back in as a feature
+        # assert_equal(res.nfev, res.nfev.T)  # check symmetry
+        # assert np.unique(res.nfev).size == 3
+
+
+    @pytest.mark.skip_xp_backends(np_only=True,
+                                  reason='Python list input uses NumPy backend')
+    def test_small_rtol_warning(self, xp):
+        message = 'The specified `rtol=1e-15`, but...'
+        with pytest.warns(RuntimeWarning, match=message):
+            hessian(xp.sin, [1.], tolerances=dict(rtol=1e-15))
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@@ -0,0 +1,114 @@
+"""
+==============================================
+Discrete Fourier transforms (:mod:`scipy.fft`)
+==============================================
+
+.. currentmodule:: scipy.fft
+
+Fast Fourier Transforms (FFTs)
+==============================
+
+.. autosummary::
+   :toctree: generated/
+
+   fft - Fast (discrete) Fourier Transform (FFT)
+   ifft - Inverse FFT
+   fft2 - 2-D FFT
+   ifft2 - 2-D inverse FFT
+   fftn - N-D FFT
+   ifftn - N-D inverse FFT
+   rfft - FFT of strictly real-valued sequence
+   irfft - Inverse of rfft
+   rfft2 - 2-D FFT of real sequence
+   irfft2 - Inverse of rfft2
+   rfftn - N-D FFT of real sequence
+   irfftn - Inverse of rfftn
+   hfft - FFT of a Hermitian sequence (real spectrum)
+   ihfft - Inverse of hfft
+   hfft2 - 2-D FFT of a Hermitian sequence
+   ihfft2 - Inverse of hfft2
+   hfftn - N-D FFT of a Hermitian sequence
+   ihfftn - Inverse of hfftn
+
+Discrete Sin and Cosine Transforms (DST and DCT)
+================================================
+
+.. autosummary::
+   :toctree: generated/
+
+   dct - Discrete cosine transform
+   idct - Inverse discrete cosine transform
+   dctn - N-D Discrete cosine transform
+   idctn - N-D Inverse discrete cosine transform
+   dst - Discrete sine transform
+   idst - Inverse discrete sine transform
+   dstn - N-D Discrete sine transform
+   idstn - N-D Inverse discrete sine transform
+
+Fast Hankel Transforms
+======================
+
+.. autosummary::
+   :toctree: generated/
+
+   fht - Fast Hankel transform
+   ifht - Inverse of fht
+
+Helper functions
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   fftshift - Shift the zero-frequency component to the center of the spectrum
+   ifftshift - The inverse of `fftshift`
+   fftfreq - Return the Discrete Fourier Transform sample frequencies
+   rfftfreq - DFT sample frequencies (for usage with rfft, irfft)
+   fhtoffset - Compute an optimal offset for the Fast Hankel Transform
+   next_fast_len - Find the optimal length to zero-pad an FFT for speed
+   prev_fast_len - Find the maximum slice length that results in a fast FFT
+   set_workers - Context manager to set default number of workers
+   get_workers - Get the current default number of workers
+
+Backend control
+===============
+
+.. autosummary::
+   :toctree: generated/
+
+   set_backend - Context manager to set the backend within a fixed scope
+   skip_backend - Context manager to skip a backend within a fixed scope
+   set_global_backend - Sets the global fft backend
+   register_backend - Register a backend for permanent use
+
+"""
+
+from ._basic import (
+    fft, ifft, fft2, ifft2, fftn, ifftn,
+    rfft, irfft, rfft2, irfft2, rfftn, irfftn,
+    hfft, ihfft, hfft2, ihfft2, hfftn, ihfftn)
+from ._realtransforms import dct, idct, dst, idst, dctn, idctn, dstn, idstn
+from ._fftlog import fht, ifht, fhtoffset
+from ._helper import (
+    next_fast_len, prev_fast_len, fftfreq,
+    rfftfreq, fftshift, ifftshift)
+from ._backend import (set_backend, skip_backend, set_global_backend,
+                       register_backend)
+from ._pocketfft.helper import set_workers, get_workers
+
+__all__ = [
+    'fft', 'ifft', 'fft2', 'ifft2', 'fftn', 'ifftn',
+    'rfft', 'irfft', 'rfft2', 'irfft2', 'rfftn', 'irfftn',
+    'hfft', 'ihfft', 'hfft2', 'ihfft2', 'hfftn', 'ihfftn',
+    'fftfreq', 'rfftfreq', 'fftshift', 'ifftshift',
+    'next_fast_len', 'prev_fast_len',
+    'dct', 'idct', 'dst', 'idst', 'dctn', 'idctn', 'dstn', 'idstn',
+    'fht', 'ifht',
+    'fhtoffset',
+    'set_backend', 'skip_backend', 'set_global_backend', 'register_backend',
+    'get_workers', 'set_workers']
+
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_backend.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_backend.py
new file mode 100644
index 0000000000000000000000000000000000000000..db044fef38d696bb63f3800be8cbfc69ace1303b
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_backend.py
@@ -0,0 +1,201 @@
+import scipy._lib.uarray as ua
+from scipy._lib._array_api import xp_capabilities
+from . import _basic_backend
+from . import _realtransforms_backend
+from . import _fftlog_backend
+
+
+class _ScipyBackend:
+    """The default backend for fft calculations
+
+    Notes
+    -----
+    We use the domain ``numpy.scipy`` rather than ``scipy`` because ``uarray``
+    treats the domain as a hierarchy. This means the user can install a single
+    backend for ``numpy`` and have it implement ``numpy.scipy.fft`` as well.
+    """
+    __ua_domain__ = "numpy.scipy.fft"
+
+    @staticmethod
+    def __ua_function__(method, args, kwargs):
+
+        fn = getattr(_basic_backend, method.__name__, None)
+        if fn is None:
+            fn = getattr(_realtransforms_backend, method.__name__, None)
+        if fn is None:
+            fn = getattr(_fftlog_backend, method.__name__, None)
+        if fn is None:
+            return NotImplemented
+        return fn(*args, **kwargs)
+
+
+_named_backends = {
+    'scipy': _ScipyBackend,
+}
+
+
+def _backend_from_arg(backend):
+    """Maps strings to known backends and validates the backend"""
+
+    if isinstance(backend, str):
+        try:
+            backend = _named_backends[backend]
+        except KeyError as e:
+            raise ValueError(f'Unknown backend {backend}') from e
+
+    if backend.__ua_domain__ != 'numpy.scipy.fft':
+        raise ValueError('Backend does not implement "numpy.scipy.fft"')
+
+    return backend
+
+
+@xp_capabilities(out_of_scope=True)
+def set_global_backend(backend, coerce=False, only=False, try_last=False):
+    """Sets the global fft backend
+
+    This utility method replaces the default backend for permanent use. It
+    will be tried in the list of backends automatically, unless the
+    ``only`` flag is set on a backend. This will be the first tried
+    backend outside the :obj:`set_backend` context manager.
+
+    Parameters
+    ----------
+    backend : {object, 'scipy'}
+        The backend to use.
+        Can either be a ``str`` containing the name of a known backend
+        {'scipy'} or an object that implements the uarray protocol.
+    coerce : bool
+        Whether to coerce input types when trying this backend.
+    only : bool
+        If ``True``, no more backends will be tried if this fails.
+        Implied by ``coerce=True``.
+    try_last : bool
+        If ``True``, the global backend is tried after registered backends.
+
+    Raises
+    ------
+    ValueError: If the backend does not implement ``numpy.scipy.fft``.
+
+    Notes
+    -----
+    This will overwrite the previously set global backend, which, by default, is
+    the SciPy implementation.
+
+    Examples
+    --------
+    We can set the global fft backend:
+
+    >>> from scipy.fft import fft, set_global_backend
+    >>> set_global_backend("scipy")  # Sets global backend (default is "scipy").
+    >>> fft([1])  # Calls the global backend
+    array([1.+0.j])
+    """
+    backend = _backend_from_arg(backend)
+    ua.set_global_backend(backend, coerce=coerce, only=only, try_last=try_last)
+
+
+@xp_capabilities(out_of_scope=True)
+def register_backend(backend):
+    """
+    Register a backend for permanent use.
+
+    Registered backends have the lowest priority and will be tried after the
+    global backend.
+
+    Parameters
+    ----------
+    backend : {object, 'scipy'}
+        The backend to use.
+        Can either be a ``str`` containing the name of a known backend
+        {'scipy'} or an object that implements the uarray protocol.
+
+    Raises
+    ------
+    ValueError: If the backend does not implement ``numpy.scipy.fft``.
+
+    Examples
+    --------
+    We can register a new fft backend:
+
+    >>> from scipy.fft import fft, register_backend, set_global_backend
+    >>> class NoopBackend:  # Define an invalid Backend
+    ...     __ua_domain__ = "numpy.scipy.fft"
+    ...     def __ua_function__(self, func, args, kwargs):
+    ...          return NotImplemented
+    >>> set_global_backend(NoopBackend())  # Set the invalid backend as global
+    >>> register_backend("scipy")  # Register a new backend
+    # The registered backend is called because
+    # the global backend returns `NotImplemented`
+    >>> fft([1])
+    array([1.+0.j])
+    >>> set_global_backend("scipy")  # Restore global backend to default
+
+    """
+    backend = _backend_from_arg(backend)
+    ua.register_backend(backend)
+
+
+@xp_capabilities(out_of_scope=True)
+def set_backend(backend, coerce=False, only=False):
+    """Context manager to set the backend within a fixed scope.
+
+    Upon entering the ``with`` statement, the given backend will be added to
+    the list of available backends with the highest priority. Upon exit, the
+    backend is reset to the state before entering the scope.
+
+    Parameters
+    ----------
+    backend : {object, 'scipy'}
+        The backend to use.
+        Can either be a ``str`` containing the name of a known backend
+        {'scipy'} or an object that implements the uarray protocol.
+    coerce : bool, optional
+        Whether to allow expensive conversions for the ``x`` parameter. e.g.,
+        copying a NumPy array to the GPU for a CuPy backend. Implies ``only``.
+    only : bool, optional
+        If only is ``True`` and this backend returns ``NotImplemented``, then a
+        BackendNotImplemented error will be raised immediately. Ignoring any
+        lower priority backends.
+
+    Examples
+    --------
+    >>> import scipy.fft as fft
+    >>> with fft.set_backend('scipy', only=True):
+    ...     fft.fft([1])  # Always calls the scipy implementation
+    array([1.+0.j])
+    """
+    backend = _backend_from_arg(backend)
+    return ua.set_backend(backend, coerce=coerce, only=only)
+
+
+@xp_capabilities(out_of_scope=True)
+def skip_backend(backend):
+    """Context manager to skip a backend within a fixed scope.
+
+    Within the context of a ``with`` statement, the given backend will not be
+    called. This covers backends registered both locally and globally. Upon
+    exit, the backend will again be considered.
+
+    Parameters
+    ----------
+    backend : {object, 'scipy'}
+        The backend to skip.
+        Can either be a ``str`` containing the name of a known backend
+        {'scipy'} or an object that implements the uarray protocol.
+
+    Examples
+    --------
+    >>> import scipy.fft as fft
+    >>> fft.fft([1])  # Calls default SciPy backend
+    array([1.+0.j])
+    >>> with fft.skip_backend('scipy'):  # We explicitly skip the SciPy backend
+    ...     fft.fft([1])                 # leaving no implementation available
+    Traceback (most recent call last):
+        ...
+    BackendNotImplementedError: No selected backends had an implementation ...
+    """
+    backend = _backend_from_arg(backend)
+    return ua.skip_backend(backend)
+
+
+set_global_backend('scipy', try_last=True)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..eb15e40e6562090f5e0e02a13982bc7247ed7380
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_basic.py
@@ -0,0 +1,1670 @@
+from scipy._lib.uarray import generate_multimethod, Dispatchable
+from scipy._lib._array_api import xp_capabilities
+
+import numpy as np
+
+
+def _x_replacer(args, kwargs, dispatchables):
+    """
+    uarray argument replacer to replace the transform input array (``x``)
+    """
+    if len(args) > 0:
+        return (dispatchables[0],) + args[1:], kwargs
+    kw = kwargs.copy()
+    kw['x'] = dispatchables[0]
+    return args, kw
+
+
+def _dispatch(func):
+    """
+    Function annotation that creates a uarray multimethod from the function
+    """
+    return generate_multimethod(func, _x_replacer, domain="numpy.scipy.fft")
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def fft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+        plan=None):
+    """
+    Compute the 1-D discrete Fourier Transform.
+
+    This function computes the 1-D *n*-point discrete Fourier
+    Transform (DFT) with the efficient Fast Fourier Transform (FFT)
+    algorithm [1]_.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    n : int, optional
+        Length of the transformed axis of the output.
+        If `n` is smaller than the length of the input, the input is cropped.
+        If it is larger, the input is padded with zeros. If `n` is not given,
+        the length of the input along the axis specified by `axis` is used.
+    axis : int, optional
+        Axis over which to compute the FFT. If not given, the last axis is
+        used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode. Default is "backward", meaning no normalization on
+        the forward transforms and scaling by ``1/n`` on the `ifft`.
+        "forward" instead applies the ``1/n`` factor on the forward transform.
+        For ``norm="ortho"``, both directions are scaled by ``1/sqrt(n)``.
+
+        .. versionadded:: 1.6.0
+           ``norm={"forward", "backward"}`` options were added
+
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See the notes below for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``. See below for more
+        details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+
+    Raises
+    ------
+    IndexError
+        if `axes` is larger than the last axis of `x`.
+
+    See Also
+    --------
+    ifft : The inverse of `fft`.
+    fft2 : The 2-D FFT.
+    fftn : The N-D FFT.
+    rfftn : The N-D FFT of real input.
+    fftfreq : Frequency bins for given FFT parameters.
+    next_fast_len : Size to pad input to for most efficient transforms
+
+    Notes
+    -----
+    FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform
+    (DFT) can be calculated efficiently, by using symmetries in the calculated
+    terms. The symmetry is highest when `n` is a power of 2, and the transform
+    is therefore most efficient for these sizes. For poorly factorizable sizes,
+    `scipy.fft` uses Bluestein's algorithm [2]_ and so is never worse than
+    O(`n` log `n`). Further performance improvements may be seen by zero-padding
+    the input using `next_fast_len`.
+
+    If ``x`` is a 1d array, then the `fft` is equivalent to ::
+
+        y[k] = np.sum(x * np.exp(-2j * np.pi * k * np.arange(n)/n))
+
+    The frequency term ``f=k/n`` is found at ``y[k]``. At ``y[n/2]`` we reach
+    the Nyquist frequency and wrap around to the negative-frequency terms. So,
+    for an 8-point transform, the frequencies of the result are
+    [0, 1, 2, 3, -4, -3, -2, -1]. To rearrange the fft output so that the
+    zero-frequency component is centered, like [-4, -3, -2, -1, 0, 1, 2, 3],
+    use `fftshift`.
+
+    Transforms can be done in single, double, or extended precision (long
+    double) floating point. Half precision inputs will be converted to single
+    precision and non-floating-point inputs will be converted to double
+    precision.
+
+    If the data type of ``x`` is real, a "real FFT" algorithm is automatically
+    used, which roughly halves the computation time. To increase efficiency
+    a little further, use `rfft`, which does the same calculation, but only
+    outputs half of the symmetrical spectrum. If the data are both real and
+    symmetrical, the `dct` can again double the efficiency, by generating
+    half of the spectrum from half of the signal.
+
+    When ``overwrite_x=True`` is specified, the memory referenced by ``x`` may
+    be used by the implementation in any way. This may include reusing the
+    memory for the result, but this is in no way guaranteed. You should not
+    rely on the contents of ``x`` after the transform as this may change in
+    future without warning.
+
+    The ``workers`` argument specifies the maximum number of parallel jobs to
+    split the FFT computation into. This will execute independent 1-D
+    FFTs within ``x``. So, ``x`` must be at least 2-D and the
+    non-transformed axes must be large enough to split into chunks. If ``x`` is
+    too small, fewer jobs may be used than requested.
+
+    References
+    ----------
+    .. [1] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the
+           machine calculation of complex Fourier series," *Math. Comput.*
+           19: 297-301.
+    .. [2] Bluestein, L., 1970, "A linear filtering approach to the
+           computation of discrete Fourier transform". *IEEE Transactions on
+           Audio and Electroacoustics.* 18 (4): 451-455.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> scipy.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8))
+    array([-2.33486982e-16+1.14423775e-17j,  8.00000000e+00-1.25557246e-15j,
+            2.33486982e-16+2.33486982e-16j,  0.00000000e+00+1.22464680e-16j,
+           -1.14423775e-17+2.33486982e-16j,  0.00000000e+00+5.20784380e-16j,
+            1.14423775e-17+1.14423775e-17j,  0.00000000e+00+1.22464680e-16j])
+
+    In this example, real input has an FFT which is Hermitian, i.e., symmetric
+    in the real part and anti-symmetric in the imaginary part:
+
+    >>> from scipy.fft import fft, fftfreq, fftshift
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.arange(256)
+    >>> sp = fftshift(fft(np.sin(t)))
+    >>> freq = fftshift(fftfreq(t.shape[-1]))
+    >>> plt.plot(freq, sp.real, freq, sp.imag)
+    [,
+     ]
+    >>> plt.show()
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def ifft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the 1-D inverse discrete Fourier Transform.
+
+    This function computes the inverse of the 1-D *n*-point
+    discrete Fourier transform computed by `fft`.  In other words,
+    ``ifft(fft(x)) == x`` to within numerical accuracy.
+
+    The input should be ordered in the same way as is returned by `fft`,
+    i.e.,
+
+    * ``x[0]`` should contain the zero frequency term,
+    * ``x[1:n//2]`` should contain the positive-frequency terms,
+    * ``x[n//2 + 1:]`` should contain the negative-frequency terms, in
+      increasing order starting from the most negative frequency.
+
+    For an even number of input points, ``x[n//2]`` represents the sum of
+    the values at the positive and negative Nyquist frequencies, as the two
+    are aliased together. See `fft` for details.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    n : int, optional
+        Length of the transformed axis of the output.
+        If `n` is smaller than the length of the input, the input is cropped.
+        If it is larger, the input is padded with zeros. If `n` is not given,
+        the length of the input along the axis specified by `axis` is used.
+        See notes about padding issues.
+    axis : int, optional
+        Axis over which to compute the inverse DFT. If not given, the last
+        axis is used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+
+    Raises
+    ------
+    IndexError
+        If `axes` is larger than the last axis of `x`.
+
+    See Also
+    --------
+    fft : The 1-D (forward) FFT, of which `ifft` is the inverse.
+    ifft2 : The 2-D inverse FFT.
+    ifftn : The N-D inverse FFT.
+
+    Notes
+    -----
+    If the input parameter `n` is larger than the size of the input, the input
+    is padded by appending zeros at the end. Even though this is the common
+    approach, it might lead to surprising results. If a different padding is
+    desired, it must be performed before calling `ifft`.
+
+    If ``x`` is a 1-D array, then the `ifft` is equivalent to ::
+
+        y[k] = np.sum(x * np.exp(2j * np.pi * k * np.arange(n)/n)) / len(x)
+
+    As with `fft`, `ifft` has support for all floating point types and is
+    optimized for real input.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> scipy.fft.ifft([0, 4, 0, 0])
+    array([ 1.+0.j,  0.+1.j, -1.+0.j,  0.-1.j]) # may vary
+
+    Create and plot a band-limited signal with random phases:
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> t = np.arange(400)
+    >>> n = np.zeros((400,), dtype=complex)
+    >>> n[40:60] = np.exp(1j*rng.uniform(0, 2*np.pi, (20,)))
+    >>> s = scipy.fft.ifft(n)
+    >>> plt.plot(t, s.real, 'b-', t, s.imag, 'r--')
+    [, ]
+    >>> plt.legend(('real', 'imaginary'))
+    
+    >>> plt.show()
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def rfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the 1-D discrete Fourier Transform for real input.
+
+    This function computes the 1-D *n*-point discrete Fourier
+    Transform (DFT) of a real-valued array by means of an efficient algorithm
+    called the Fast Fourier Transform (FFT).
+
+    Parameters
+    ----------
+    x : array_like
+        Input array
+    n : int, optional
+        Number of points along transformation axis in the input to use.
+        If `n` is smaller than the length of the input, the input is cropped.
+        If it is larger, the input is padded with zeros. If `n` is not given,
+        the length of the input along the axis specified by `axis` is used.
+    axis : int, optional
+        Axis over which to compute the FFT. If not given, the last axis is
+        used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+        If `n` is even, the length of the transformed axis is ``(n/2)+1``.
+        If `n` is odd, the length is ``(n+1)/2``.
+
+    Raises
+    ------
+    IndexError
+        If `axis` is larger than the last axis of `a`.
+
+    See Also
+    --------
+    irfft : The inverse of `rfft`.
+    fft : The 1-D FFT of general (complex) input.
+    fftn : The N-D FFT.
+    rfft2 : The 2-D FFT of real input.
+    rfftn : The N-D FFT of real input.
+
+    Notes
+    -----
+    When the DFT is computed for purely real input, the output is
+    Hermitian-symmetric, i.e., the negative frequency terms are just the complex
+    conjugates of the corresponding positive-frequency terms, and the
+    negative-frequency terms are therefore redundant. This function does not
+    compute the negative frequency terms, and the length of the transformed
+    axis of the output is therefore ``n//2 + 1``.
+
+    When ``X = rfft(x)`` and fs is the sampling frequency, ``X[0]`` contains
+    the zero-frequency term 0*fs, which is real due to Hermitian symmetry.
+
+    If `n` is even, ``A[-1]`` contains the term representing both positive
+    and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely
+    real. If `n` is odd, there is no term at fs/2; ``A[-1]`` contains
+    the largest positive frequency (fs/2*(n-1)/n), and is complex in the
+    general case.
+
+    If the input `a` contains an imaginary part, it is silently discarded.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> scipy.fft.fft([0, 1, 0, 0])
+    array([ 1.+0.j,  0.-1.j, -1.+0.j,  0.+1.j]) # may vary
+    >>> scipy.fft.rfft([0, 1, 0, 0])
+    array([ 1.+0.j,  0.-1.j, -1.+0.j]) # may vary
+
+    Notice how the final element of the `fft` output is the complex conjugate
+    of the second element, for real input. For `rfft`, this symmetry is
+    exploited to compute only the non-negative frequency terms.
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def irfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Computes the inverse of `rfft`.
+
+    This function computes the inverse of the 1-D *n*-point
+    discrete Fourier Transform of real input computed by `rfft`.
+    In other words, ``irfft(rfft(x), len(x)) == x`` to within numerical
+    accuracy. (See Notes below for why ``len(a)`` is necessary here.)
+
+    The input is expected to be in the form returned by `rfft`, i.e., the
+    real zero-frequency term followed by the complex positive frequency terms
+    in order of increasing frequency. Since the discrete Fourier Transform of
+    real input is Hermitian-symmetric, the negative frequency terms are taken
+    to be the complex conjugates of the corresponding positive frequency terms.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    n : int, optional
+        Length of the transformed axis of the output.
+        For `n` output points, ``n//2+1`` input points are necessary. If the
+        input is longer than this, it is cropped. If it is shorter than this,
+        it is padded with zeros. If `n` is not given, it is taken to be
+        ``2*(m-1)``, where ``m`` is the length of the input along the axis
+        specified by `axis`.
+    axis : int, optional
+        Axis over which to compute the inverse FFT. If not given, the last
+        axis is used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+        The length of the transformed axis is `n`, or, if `n` is not given,
+        ``2*(m-1)`` where ``m`` is the length of the transformed axis of the
+        input. To get an odd number of output points, `n` must be specified.
+
+    Raises
+    ------
+    IndexError
+        If `axis` is larger than the last axis of `x`.
+
+    See Also
+    --------
+    rfft : The 1-D FFT of real input, of which `irfft` is inverse.
+    fft : The 1-D FFT.
+    irfft2 : The inverse of the 2-D FFT of real input.
+    irfftn : The inverse of the N-D FFT of real input.
+
+    Notes
+    -----
+    Returns the real valued `n`-point inverse discrete Fourier transform
+    of `x`, where `x` contains the non-negative frequency terms of a
+    Hermitian-symmetric sequence. `n` is the length of the result, not the
+    input.
+
+    If you specify an `n` such that `a` must be zero-padded or truncated, the
+    extra/removed values will be added/removed at high frequencies. One can
+    thus resample a series to `m` points via Fourier interpolation by:
+    ``a_resamp = irfft(rfft(a), m)``.
+
+    The default value of `n` assumes an even output length. By the Hermitian
+    symmetry, the last imaginary component must be 0 and so is ignored. To
+    avoid losing information, the correct length of the real input *must* be
+    given.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> scipy.fft.ifft([1, -1j, -1, 1j])
+    array([0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]) # may vary
+    >>> scipy.fft.irfft([1, -1j, -1])
+    array([0.,  1.,  0.,  0.])
+
+    Notice how the last term in the input to the ordinary `ifft` is the
+    complex conjugate of the second term, and the output has zero imaginary
+    part everywhere. When calling `irfft`, the negative frequencies are not
+    specified, and the output array is purely real.
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def hfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the FFT of a signal that has Hermitian symmetry, i.e., a real
+    spectrum.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    n : int, optional
+        Length of the transformed axis of the output. For `n` output
+        points, ``n//2 + 1`` input points are necessary. If the input is
+        longer than this, it is cropped. If it is shorter than this, it is
+        padded with zeros. If `n` is not given, it is taken to be ``2*(m-1)``,
+        where ``m`` is the length of the input along the axis specified by
+        `axis`.
+    axis : int, optional
+        Axis over which to compute the FFT. If not given, the last
+        axis is used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See `fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+        The length of the transformed axis is `n`, or, if `n` is not given,
+        ``2*m - 2``, where ``m`` is the length of the transformed axis of
+        the input. To get an odd number of output points, `n` must be
+        specified, for instance, as ``2*m - 1`` in the typical case,
+
+    Raises
+    ------
+    IndexError
+        If `axis` is larger than the last axis of `a`.
+
+    See Also
+    --------
+    rfft : Compute the 1-D FFT for real input.
+    ihfft : The inverse of `hfft`.
+    hfftn : Compute the N-D FFT of a Hermitian signal.
+
+    Notes
+    -----
+    `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the
+    opposite case: here the signal has Hermitian symmetry in the time
+    domain and is real in the frequency domain. So, here, it's `hfft`, for
+    which you must supply the length of the result if it is to be odd.
+    * even: ``ihfft(hfft(a, 2*len(a) - 2) == a``, within roundoff error,
+    * odd: ``ihfft(hfft(a, 2*len(a) - 1) == a``, within roundoff error.
+
+    Examples
+    --------
+    >>> from scipy.fft import fft, hfft
+    >>> import numpy as np
+    >>> a = 2 * np.pi * np.arange(10) / 10
+    >>> signal = np.cos(a) + 3j * np.sin(3 * a)
+    >>> fft(signal).round(10)
+    array([ -0.+0.j,   5.+0.j,  -0.+0.j,  15.-0.j,   0.+0.j,   0.+0.j,
+            -0.+0.j, -15.-0.j,   0.+0.j,   5.+0.j])
+    >>> hfft(signal[:6]).round(10) # Input first half of signal
+    array([  0.,   5.,   0.,  15.,  -0.,   0.,   0., -15.,  -0.,   5.])
+    >>> hfft(signal, 10)  # Input entire signal and truncate
+    array([  0.,   5.,   0.,  15.,  -0.,   0.,   0., -15.,  -0.,   5.])
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def ihfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the inverse FFT of a signal that has Hermitian symmetry.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    n : int, optional
+        Length of the inverse FFT, the number of points along
+        transformation axis in the input to use.  If `n` is smaller than
+        the length of the input, the input is cropped. If it is larger,
+        the input is padded with zeros. If `n` is not given, the length of
+        the input along the axis specified by `axis` is used.
+    axis : int, optional
+        Axis over which to compute the inverse FFT. If not given, the last
+        axis is used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See `fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axis
+        indicated by `axis`, or the last one if `axis` is not specified.
+        The length of the transformed axis is ``n//2 + 1``.
+
+    See Also
+    --------
+    hfft, irfft
+
+    Notes
+    -----
+    `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the
+    opposite case: here, the signal has Hermitian symmetry in the time
+    domain and is real in the frequency domain. So, here, it's `hfft`, for
+    which you must supply the length of the result if it is to be odd:
+    * even: ``ihfft(hfft(a, 2*len(a) - 2) == a``, within roundoff error,
+    * odd: ``ihfft(hfft(a, 2*len(a) - 1) == a``, within roundoff error.
+
+    Examples
+    --------
+    >>> from scipy.fft import ifft, ihfft
+    >>> import numpy as np
+    >>> spectrum = np.array([ 15, -4, 0, -1, 0, -4])
+    >>> ifft(spectrum)
+    array([1.+0.j,  2.+0.j,  3.+0.j,  4.+0.j,  3.+0.j,  2.+0.j]) # may vary
+    >>> ihfft(spectrum)
+    array([ 1.-0.j,  2.-0.j,  3.-0.j,  4.-0.j]) # may vary
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def fftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the N-D discrete Fourier Transform.
+
+    This function computes the N-D discrete Fourier Transform over
+    any number of axes in an M-D array by means of the Fast Fourier
+    Transform (FFT).
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        This corresponds to ``n`` for ``fft(x, n)``.
+        Along any axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` and `x`,
+        as explained in the parameters section above.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    ifftn : The inverse of `fftn`, the inverse N-D FFT.
+    fft : The 1-D FFT, with definitions and conventions used.
+    rfftn : The N-D FFT of real input.
+    fft2 : The 2-D FFT.
+    fftshift : Shifts zero-frequency terms to centre of array.
+
+    Notes
+    -----
+    The output, analogously to `fft`, contains the term for zero frequency in
+    the low-order corner of all axes, the positive frequency terms in the
+    first half of all axes, the term for the Nyquist frequency in the middle
+    of all axes and the negative frequency terms in the second half of all
+    axes, in order of decreasingly negative frequency.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.mgrid[:3, :3, :3][0]
+    >>> scipy.fft.fftn(x, axes=(1, 2))
+    array([[[ 0.+0.j,   0.+0.j,   0.+0.j], # may vary
+            [ 0.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j]],
+           [[ 9.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j]],
+           [[18.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j],
+            [ 0.+0.j,   0.+0.j,   0.+0.j]]])
+    >>> scipy.fft.fftn(x, (2, 2), axes=(0, 1))
+    array([[[ 2.+0.j,  2.+0.j,  2.+0.j], # may vary
+            [ 0.+0.j,  0.+0.j,  0.+0.j]],
+           [[-2.+0.j, -2.+0.j, -2.+0.j],
+            [ 0.+0.j,  0.+0.j,  0.+0.j]]])
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> [X, Y] = np.meshgrid(2 * np.pi * np.arange(200) / 12,
+    ...                      2 * np.pi * np.arange(200) / 34)
+    >>> S = np.sin(X) + np.cos(Y) + rng.uniform(0, 1, X.shape)
+    >>> FS = scipy.fft.fftn(S)
+    >>> plt.imshow(np.log(np.abs(scipy.fft.fftshift(FS))**2))
+    
+    >>> plt.show()
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def ifftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the N-D inverse discrete Fourier Transform.
+
+    This function computes the inverse of the N-D discrete
+    Fourier Transform over any number of axes in an M-D array by
+    means of the Fast Fourier Transform (FFT).  In other words,
+    ``ifftn(fftn(x)) == x`` to within numerical accuracy.
+
+    The input, analogously to `ifft`, should be ordered in the same way as is
+    returned by `fftn`, i.e., it should have the term for zero frequency
+    in all axes in the low-order corner, the positive frequency terms in the
+    first half of all axes, the term for the Nyquist frequency in the middle
+    of all axes and the negative frequency terms in the second half of all
+    axes, in order of decreasingly negative frequency.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        This corresponds to ``n`` for ``ifft(x, n)``.
+        Along any axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used. See notes for issue on `ifft` zero padding.
+    axes : sequence of ints, optional
+        Axes over which to compute the IFFT.  If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` or `x`,
+        as explained in the parameters section above.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    fftn : The forward N-D FFT, of which `ifftn` is the inverse.
+    ifft : The 1-D inverse FFT.
+    ifft2 : The 2-D inverse FFT.
+    ifftshift : Undoes `fftshift`, shifts zero-frequency terms to beginning
+        of array.
+
+    Notes
+    -----
+    Zero-padding, analogously with `ifft`, is performed by appending zeros to
+    the input along the specified dimension. Although this is the common
+    approach, it might lead to surprising results. If another form of zero
+    padding is desired, it must be performed before `ifftn` is called.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.eye(4)
+    >>> scipy.fft.ifftn(scipy.fft.fftn(x, axes=(0,)), axes=(1,))
+    array([[1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j], # may vary
+           [0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],
+           [0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
+           [0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j]])
+
+
+    Create and plot an image with band-limited frequency content:
+
+    >>> import matplotlib.pyplot as plt
+    >>> rng = np.random.default_rng()
+    >>> n = np.zeros((200,200), dtype=complex)
+    >>> n[60:80, 20:40] = np.exp(1j*rng.uniform(0, 2*np.pi, (20, 20)))
+    >>> im = scipy.fft.ifftn(n).real
+    >>> plt.imshow(im)
+    
+    >>> plt.show()
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def fft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    """
+    Compute the 2-D discrete Fourier Transform
+
+    This function computes the N-D discrete Fourier Transform
+    over any axes in an M-D array by means of the
+    Fast Fourier Transform (FFT). By default, the transform is computed over
+    the last two axes of the input array, i.e., a 2-dimensional FFT.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        This corresponds to ``n`` for ``fft(x, n)``.
+        Along each axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last two axes are
+        used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or the last two axes if `axes` is not given.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length, or `axes` not given and
+        ``len(s) != 2``.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    ifft2 : The inverse 2-D FFT.
+    fft : The 1-D FFT.
+    fftn : The N-D FFT.
+    fftshift : Shifts zero-frequency terms to the center of the array.
+        For 2-D input, swaps first and third quadrants, and second
+        and fourth quadrants.
+
+    Notes
+    -----
+    `fft2` is just `fftn` with a different default for `axes`.
+
+    The output, analogously to `fft`, contains the term for zero frequency in
+    the low-order corner of the transformed axes, the positive frequency terms
+    in the first half of these axes, the term for the Nyquist frequency in the
+    middle of the axes and the negative frequency terms in the second half of
+    the axes, in order of decreasingly negative frequency.
+
+    See `fftn` for details and a plotting example, and `fft` for
+    definitions and conventions used.
+
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.mgrid[:5, :5][0]
+    >>> scipy.fft.fft2(x)
+    array([[ 50.  +0.j        ,   0.  +0.j        ,   0.  +0.j        , # may vary
+              0.  +0.j        ,   0.  +0.j        ],
+           [-12.5+17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
+              0.  +0.j        ,   0.  +0.j        ],
+           [-12.5 +4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
+              0.  +0.j        ,   0.  +0.j        ],
+           [-12.5 -4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
+              0.  +0.j        ,   0.  +0.j        ],
+           [-12.5-17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
+              0.  +0.j        ,   0.  +0.j        ]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def ifft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the 2-D inverse discrete Fourier Transform.
+
+    This function computes the inverse of the 2-D discrete Fourier
+    Transform over any number of axes in an M-D array by means of
+    the Fast Fourier Transform (FFT). In other words, ``ifft2(fft2(x)) == x``
+    to within numerical accuracy. By default, the inverse transform is
+    computed over the last two axes of the input array.
+
+    The input, analogously to `ifft`, should be ordered in the same way as is
+    returned by `fft2`, i.e., it should have the term for zero frequency
+    in the low-order corner of the two axes, the positive frequency terms in
+    the first half of these axes, the term for the Nyquist frequency in the
+    middle of the axes and the negative frequency terms in the second half of
+    both axes, in order of decreasingly negative frequency.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, can be complex.
+    s : sequence of ints, optional
+        Shape (length of each axis) of the output (``s[0]`` refers to axis 0,
+        ``s[1]`` to axis 1, etc.). This corresponds to `n` for ``ifft(x, n)``.
+        Along each axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.  See notes for issue on `ifft` zero padding.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last two
+        axes are used.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or the last two axes if `axes` is not given.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length, or `axes` not given and
+        ``len(s) != 2``.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    fft2 : The forward 2-D FFT, of which `ifft2` is the inverse.
+    ifftn : The inverse of the N-D FFT.
+    fft : The 1-D FFT.
+    ifft : The 1-D inverse FFT.
+
+    Notes
+    -----
+    `ifft2` is just `ifftn` with a different default for `axes`.
+
+    See `ifftn` for details and a plotting example, and `fft` for
+    definition and conventions used.
+
+    Zero-padding, analogously with `ifft`, is performed by appending zeros to
+    the input along the specified dimension. Although this is the common
+    approach, it might lead to surprising results. If another form of zero
+    padding is desired, it must be performed before `ifft2` is called.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = 4 * np.eye(4)
+    >>> scipy.fft.ifft2(x)
+    array([[1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j], # may vary
+           [0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],
+           [0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],
+           [0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def rfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the N-D discrete Fourier Transform for real input.
+
+    This function computes the N-D discrete Fourier Transform over
+    any number of axes in an M-D real array by means of the Fast
+    Fourier Transform (FFT). By default, all axes are transformed, with the
+    real transform performed over the last axis, while the remaining
+    transforms are complex.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, taken to be real.
+    s : sequence of ints, optional
+        Shape (length along each transformed axis) to use from the input.
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        The final element of `s` corresponds to `n` for ``rfft(x, n)``, while
+        for the remaining axes, it corresponds to `n` for ``fft(x, n)``.
+        Along any axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` and `x`,
+        as explained in the parameters section above.
+        The length of the last axis transformed will be ``s[-1]//2+1``,
+        while the remaining transformed axes will have lengths according to
+        `s`, or unchanged from the input.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    irfftn : The inverse of `rfftn`, i.e., the inverse of the N-D FFT
+         of real input.
+    fft : The 1-D FFT, with definitions and conventions used.
+    rfft : The 1-D FFT of real input.
+    fftn : The N-D FFT.
+    rfft2 : The 2-D FFT of real input.
+
+    Notes
+    -----
+    The transform for real input is performed over the last transformation
+    axis, as by `rfft`, then the transform over the remaining axes is
+    performed as by `fftn`. The order of the output is as for `rfft` for the
+    final transformation axis, and as for `fftn` for the remaining
+    transformation axes.
+
+    See `fft` for details, definitions and conventions used.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.ones((2, 2, 2))
+    >>> scipy.fft.rfftn(x)
+    array([[[8.+0.j,  0.+0.j], # may vary
+            [0.+0.j,  0.+0.j]],
+           [[0.+0.j,  0.+0.j],
+            [0.+0.j,  0.+0.j]]])
+
+    >>> scipy.fft.rfftn(x, axes=(2, 0))
+    array([[[4.+0.j,  0.+0.j], # may vary
+            [4.+0.j,  0.+0.j]],
+           [[0.+0.j,  0.+0.j],
+            [0.+0.j,  0.+0.j]]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def rfft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the 2-D FFT of a real array.
+
+    Parameters
+    ----------
+    x : array
+        Input array, taken to be real.
+    s : sequence of ints, optional
+        Shape of the FFT.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The result of the real 2-D FFT.
+
+    See Also
+    --------
+    irfft2 : The inverse of the 2-D FFT of real input.
+    rfft : The 1-D FFT of real input.
+    rfftn : Compute the N-D discrete Fourier Transform for real
+            input.
+
+    Notes
+    -----
+    This is really just `rfftn` with different default behavior.
+    For more details see `rfftn`.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.broadcast_to([1, 0, -1, 0], (4, 4))
+    >>> scipy.fft.rfft2(x)
+    array([[0.+0.j, 8.+0.j, 0.+0.j],
+           [0.+0.j, 0.+0.j, 0.+0.j],
+           [0.+0.j, 0.+0.j, 0.+0.j],
+           [0.+0.j, 0.+0.j, 0.+0.j]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def irfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+           plan=None):
+    """
+    Computes the inverse of `rfftn`
+
+    This function computes the inverse of the N-D discrete
+    Fourier Transform for real input over any number of axes in an
+    M-D array by means of the Fast Fourier Transform (FFT). In
+    other words, ``irfftn(rfftn(x), x.shape) == x`` to within numerical
+    accuracy. (The ``a.shape`` is necessary like ``len(a)`` is for `irfft`,
+    and for the same reason.)
+
+    The input should be ordered in the same way as is returned by `rfftn`,
+    i.e., as for `irfft` for the final transformation axis, and as for `ifftn`
+    along all the other axes.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the
+        number of input points used along this axis, except for the last axis,
+        where ``s[-1]//2+1`` points of the input are used.
+        Along any axis, if the shape indicated by `s` is smaller than that of
+        the input, the input is cropped. If it is larger, the input is padded
+        with zeros. If `s` is not given, the shape of the input along the axes
+        specified by axes is used. Except for the last axis which is taken to be
+        ``2*(m-1)``, where ``m`` is the length of the input along that axis.
+    axes : sequence of ints, optional
+        Axes over which to compute the inverse FFT. If not given, the last
+        `len(s)` axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` or `x`,
+        as explained in the parameters section above.
+        The length of each transformed axis is as given by the corresponding
+        element of `s`, or the length of the input in every axis except for the
+        last one if `s` is not given. In the final transformed axis the length
+        of the output when `s` is not given is ``2*(m-1)``, where ``m`` is the
+        length of the final transformed axis of the input. To get an odd
+        number of output points in the final axis, `s` must be specified.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    rfftn : The forward N-D FFT of real input,
+            of which `ifftn` is the inverse.
+    fft : The 1-D FFT, with definitions and conventions used.
+    irfft : The inverse of the 1-D FFT of real input.
+    irfft2 : The inverse of the 2-D FFT of real input.
+
+    Notes
+    -----
+    See `fft` for definitions and conventions used.
+
+    See `rfft` for definitions and conventions used for real input.
+
+    The default value of `s` assumes an even output length in the final
+    transformation axis. When performing the final complex to real
+    transformation, the Hermitian symmetry requires that the last imaginary
+    component along that axis must be 0 and so it is ignored. To avoid losing
+    information, the correct length of the real input *must* be given.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.zeros((3, 2, 2))
+    >>> x[0, 0, 0] = 3 * 2 * 2
+    >>> scipy.fft.irfftn(x)
+    array([[[1.,  1.],
+            [1.,  1.]],
+           [[1.,  1.],
+            [1.,  1.]],
+           [[1.,  1.],
+            [1.,  1.]]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def irfft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+           plan=None):
+    """
+    Computes the inverse of `rfft2`
+
+    Parameters
+    ----------
+    x : array_like
+        The input array
+    s : sequence of ints, optional
+        Shape of the real output to the inverse FFT.
+    axes : sequence of ints, optional
+        The axes over which to compute the inverse fft.
+        Default is the last two axes.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The result of the inverse real 2-D FFT.
+
+    See Also
+    --------
+    rfft2 : The 2-D FFT of real input.
+    irfft : The inverse of the 1-D FFT of real input.
+    irfftn : The inverse of the N-D FFT of real input.
+
+    Notes
+    -----
+    This is really `irfftn` with different defaults.
+    For more details see `irfftn`.
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def hfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the N-D FFT of Hermitian symmetric complex input, i.e., a
+    signal with a real spectrum.
+
+    This function computes the N-D discrete Fourier Transform for a
+    Hermitian symmetric complex input over any number of axes in an
+    M-D array by means of the Fast Fourier Transform (FFT). In other
+    words, ``ihfftn(hfftn(x, s)) == x`` to within numerical accuracy. (``s``
+    here is ``x.shape`` with ``s[-1] = x.shape[-1] * 2 - 1``, this is necessary
+    for the same reason ``x.shape`` would be necessary for `irfft`.)
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    s : sequence of ints, optional
+        Shape (length of each transformed axis) of the output
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the
+        number of input points used along this axis, except for the last axis,
+        where ``s[-1]//2+1`` points of the input are used.
+        Along any axis, if the shape indicated by `s` is smaller than that of
+        the input, the input is cropped. If it is larger, the input is padded
+        with zeros. If `s` is not given, the shape of the input along the axes
+        specified by axes is used. Except for the last axis which is taken to be
+        ``2*(m-1)`` where ``m`` is the length of the input along that axis.
+    axes : sequence of ints, optional
+        Axes over which to compute the inverse FFT. If not given, the last
+        `len(s)` axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` or `x`,
+        as explained in the parameters section above.
+        The length of each transformed axis is as given by the corresponding
+        element of `s`, or the length of the input in every axis except for the
+        last one if `s` is not given.  In the final transformed axis the length
+        of the output when `s` is not given is ``2*(m-1)`` where ``m`` is the
+        length of the final transformed axis of the input.  To get an odd
+        number of output points in the final axis, `s` must be specified.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    ihfftn : The inverse N-D FFT with real spectrum. Inverse of `hfftn`.
+    fft : The 1-D FFT, with definitions and conventions used.
+    rfft : Forward FFT of real input.
+
+    Notes
+    -----
+    For a 1-D signal ``x`` to have a real spectrum, it must satisfy
+    the Hermitian property::
+
+        x[i] == np.conj(x[-i]) for all i
+
+    This generalizes into higher dimensions by reflecting over each axis in
+    turn::
+
+        x[i, j, k, ...] == np.conj(x[-i, -j, -k, ...]) for all i, j, k, ...
+
+    This should not be confused with a Hermitian matrix, for which the
+    transpose is its own conjugate::
+
+        x[i, j] == np.conj(x[j, i]) for all i, j
+
+
+    The default value of `s` assumes an even output length in the final
+    transformation axis. When performing the final complex to real
+    transformation, the Hermitian symmetry requires that the last imaginary
+    component along that axis must be 0 and so it is ignored. To avoid losing
+    information, the correct length of the real input *must* be given.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.ones((3, 2, 2))
+    >>> scipy.fft.hfftn(x)
+    array([[[12.,  0.],
+            [ 0.,  0.]],
+           [[ 0.,  0.],
+            [ 0.,  0.]],
+           [[ 0.,  0.],
+            [ 0.,  0.]]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def hfft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+          plan=None):
+    """
+    Compute the 2-D FFT of a Hermitian complex array.
+
+    Parameters
+    ----------
+    x : array
+        Input array, taken to be Hermitian complex.
+    s : sequence of ints, optional
+        Shape of the real output.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See `fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The real result of the 2-D Hermitian complex real FFT.
+
+    See Also
+    --------
+    hfftn : Compute the N-D discrete Fourier Transform for Hermitian
+            complex input.
+
+    Notes
+    -----
+    This is really just `hfftn` with different default behavior.
+    For more details see `hfftn`.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.array([[1+0j, 2+0j], [2+0j, 1+0j]])  # Hermitian-symmetric input
+    >>> scipy.fft.hfft2(x, s=(2, 2))
+    array([[ 6.,  0.],
+           [ 0., -2.]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def ihfftn(x, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *,
+           plan=None):
+    """
+    Compute the N-D inverse discrete Fourier Transform for a real
+    spectrum.
+
+    This function computes the N-D inverse discrete Fourier Transform
+    over any number of axes in an M-D real array by means of the Fast
+    Fourier Transform (FFT). By default, all axes are transformed, with the
+    real transform performed over the last axis, while the remaining transforms
+    are complex.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array, taken to be real.
+    s : sequence of ints, optional
+        Shape (length along each transformed axis) to use from the input.
+        (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
+        Along any axis, if the given shape is smaller than that of the input,
+        the input is cropped. If it is larger, the input is padded with zeros.
+        if `s` is not given, the shape of the input along the axes specified
+        by `axes` is used.
+    axes : sequence of ints, optional
+        Axes over which to compute the FFT. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : complex ndarray
+        The truncated or zero-padded input, transformed along the axes
+        indicated by `axes`, or by a combination of `s` and `x`,
+        as explained in the parameters section above.
+        The length of the last axis transformed will be ``s[-1]//2+1``,
+        while the remaining transformed axes will have lengths according to
+        `s`, or unchanged from the input.
+
+    Raises
+    ------
+    ValueError
+        If `s` and `axes` have different length.
+    IndexError
+        If an element of `axes` is larger than the number of axes of `x`.
+
+    See Also
+    --------
+    hfftn : The forward N-D FFT of Hermitian input.
+    hfft : The 1-D FFT of Hermitian input.
+    fft : The 1-D FFT, with definitions and conventions used.
+    fftn : The N-D FFT.
+    hfft2 : The 2-D FFT of Hermitian input.
+
+    Notes
+    -----
+    The transform for real input is performed over the last transformation
+    axis, as by `ihfft`, then the transform over the remaining axes is
+    performed as by `ifftn`. The order of the output is the positive part of
+    the Hermitian output signal, in the same format as `rfft`.
+
+    Examples
+    --------
+    >>> import scipy.fft
+    >>> import numpy as np
+    >>> x = np.ones((2, 2, 2))
+    >>> scipy.fft.ihfftn(x)
+    array([[[1.+0.j,  0.+0.j], # may vary
+            [0.+0.j,  0.+0.j]],
+           [[0.+0.j,  0.+0.j],
+            [0.+0.j,  0.+0.j]]])
+    >>> scipy.fft.ihfftn(x, axes=(2, 0))
+    array([[[1.+0.j,  0.+0.j], # may vary
+            [1.+0.j,  0.+0.j]],
+           [[0.+0.j,  0.+0.j],
+            [0.+0.j,  0.+0.j]]])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def ihfft2(x, s=None, axes=(-2, -1), norm=None, overwrite_x=False, workers=None, *,
+           plan=None):
+    """
+    Compute the 2-D inverse FFT of a real spectrum.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array
+    s : sequence of ints, optional
+        Shape of the real input to the inverse FFT.
+    axes : sequence of ints, optional
+        The axes over which to compute the inverse fft.
+        Default is the last two axes.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see `fft`). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+        See :func:`fft` for more details.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    plan : object, optional
+        This argument is reserved for passing in a precomputed plan provided
+        by downstream FFT vendors. It is currently not used in SciPy.
+
+        .. versionadded:: 1.5.0
+
+    Returns
+    -------
+    out : ndarray
+        The result of the inverse real 2-D FFT.
+
+    See Also
+    --------
+    ihfftn : Compute the inverse of the N-D FFT of Hermitian input.
+
+    Notes
+    -----
+    This is really `ihfftn` with different defaults.
+    For more details see `ihfftn`.
+
+    """
+    return (Dispatchable(x, np.ndarray),)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_basic_backend.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_basic_backend.py
new file mode 100644
index 0000000000000000000000000000000000000000..9ca20dd6470934cdd064b4ee02c623f01cfac8be
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_basic_backend.py
@@ -0,0 +1,197 @@
+from scipy._lib._array_api import (
+    array_namespace, is_numpy, xp_unsupported_param_msg, is_complex, xp_float_to_complex
+)
+from . import _pocketfft
+import numpy as np
+
+
+def _validate_fft_args(workers, plan, norm):
+    if workers is not None:
+        raise ValueError(xp_unsupported_param_msg("workers"))
+    if plan is not None:
+        raise ValueError(xp_unsupported_param_msg("plan"))
+    if norm is None:
+        norm = 'backward'
+    return norm
+
+
+# these functions expect complex input in the fft standard extension
+complex_funcs = {'fft', 'ifft', 'fftn', 'ifftn', 'hfft', 'irfft', 'irfftn'}
+
+# pocketfft is used whenever SCIPY_ARRAY_API is not set,
+# or x is a NumPy array or array-like.
+# When SCIPY_ARRAY_API is set, we try to use xp.fft for CuPy arrays,
+# PyTorch arrays and other array API standard supporting objects.
+# If xp.fft does not exist, we attempt to convert to np and back to use pocketfft.
+
+def _execute_1D(func_str, pocketfft_func, x, n, axis, norm, overwrite_x, workers, plan):
+    xp = array_namespace(x)
+
+    if is_numpy(xp):
+        x = np.asarray(x)
+        return pocketfft_func(x, n=n, axis=axis, norm=norm,
+                              overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+    norm = _validate_fft_args(workers, plan, norm)
+    if hasattr(xp, 'fft'):
+        xp_func = getattr(xp.fft, func_str)
+        if func_str in complex_funcs:
+            try:
+                res = xp_func(x, n=n, axis=axis, norm=norm)
+            except: # backends may require complex input  # noqa: E722
+                x = xp_float_to_complex(x, xp)
+                res = xp_func(x, n=n, axis=axis, norm=norm)
+            return res
+        return xp_func(x, n=n, axis=axis, norm=norm)
+
+    x = np.asarray(x)
+    y = pocketfft_func(x, n=n, axis=axis, norm=norm)
+    return xp.asarray(y)
+
+
+def _execute_nD(func_str, pocketfft_func, x, s, axes, norm, overwrite_x, workers, plan):
+    xp = array_namespace(x)
+
+    if is_numpy(xp):
+        x = np.asarray(x)
+        return pocketfft_func(x, s=s, axes=axes, norm=norm,
+                              overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+    norm = _validate_fft_args(workers, plan, norm)
+    if hasattr(xp, 'fft'):
+        xp_func = getattr(xp.fft, func_str)
+        if func_str in complex_funcs:
+            try:
+                res = xp_func(x, s=s, axes=axes, norm=norm)
+            except: # backends may require complex input  # noqa: E722
+                x = xp_float_to_complex(x, xp)
+                res = xp_func(x, s=s, axes=axes, norm=norm)
+            return res
+        return xp_func(x, s=s, axes=axes, norm=norm)
+
+    x = np.asarray(x)
+    y = pocketfft_func(x, s=s, axes=axes, norm=norm)
+    return xp.asarray(y)
+
+
+def fft(x, n=None, axis=-1, norm=None,
+        overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('fft', _pocketfft.fft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def ifft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *,
+         plan=None):
+    return _execute_1D('ifft', _pocketfft.ifft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def rfft(x, n=None, axis=-1, norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('rfft', _pocketfft.rfft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def irfft(x, n=None, axis=-1, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('irfft', _pocketfft.irfft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def hfft(x, n=None, axis=-1, norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('hfft', _pocketfft.hfft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def ihfft(x, n=None, axis=-1, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return _execute_1D('ihfft', _pocketfft.ihfft, x, n=n, axis=axis, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def fftn(x, s=None, axes=None, norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return _execute_nD('fftn', _pocketfft.fftn, x, s=s, axes=axes, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+
+def ifftn(x, s=None, axes=None, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return _execute_nD('ifftn', _pocketfft.ifftn, x, s=s, axes=axes, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def fft2(x, s=None, axes=(-2, -1), norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return fftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def ifft2(x, s=None, axes=(-2, -1), norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return ifftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def rfftn(x, s=None, axes=None, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return _execute_nD('rfftn', _pocketfft.rfftn, x, s=s, axes=axes, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def rfft2(x, s=None, axes=(-2, -1), norm=None,
+         overwrite_x=False, workers=None, *, plan=None):
+    return rfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def irfftn(x, s=None, axes=None, norm=None,
+           overwrite_x=False, workers=None, *, plan=None):
+    return _execute_nD('irfftn', _pocketfft.irfftn, x, s=s, axes=axes, norm=norm,
+                       overwrite_x=overwrite_x, workers=workers, plan=plan)
+
+
+def irfft2(x, s=None, axes=(-2, -1), norm=None,
+           overwrite_x=False, workers=None, *, plan=None):
+    return irfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def _swap_direction(norm):
+    if norm in (None, 'backward'):
+        norm = 'forward'
+    elif norm == 'forward':
+        norm = 'backward'
+    elif norm != 'ortho':
+        raise ValueError(f'Invalid norm value {norm}; should be "backward", '
+                         '"ortho", or "forward".')
+    return norm
+
+
+def hfftn(x, s=None, axes=None, norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    xp = array_namespace(x)
+    if is_numpy(xp):
+        x = np.asarray(x)
+        return _pocketfft.hfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+    if is_complex(x, xp):
+        x = xp.conj(x)
+    return irfftn(x, s, axes, _swap_direction(norm),
+                  overwrite_x, workers, plan=plan)
+
+
+def hfft2(x, s=None, axes=(-2, -1), norm=None,
+          overwrite_x=False, workers=None, *, plan=None):
+    return hfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+
+
+def ihfftn(x, s=None, axes=None, norm=None,
+           overwrite_x=False, workers=None, *, plan=None):
+    xp = array_namespace(x)
+    if is_numpy(xp):
+        x = np.asarray(x)
+        return _pocketfft.ihfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
+    return xp.conj(rfftn(x, s, axes, _swap_direction(norm),
+                         overwrite_x, workers, plan=plan))
+
+def ihfft2(x, s=None, axes=(-2, -1), norm=None,
+           overwrite_x=False, workers=None, *, plan=None):
+    return ihfftn(x, s, axes, norm, overwrite_x, workers, plan=plan)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_debug_backends.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_debug_backends.py
new file mode 100644
index 0000000000000000000000000000000000000000..c9647c5d6ceddc73b97d95f562662ada02c1ae74
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_debug_backends.py
@@ -0,0 +1,22 @@
+import numpy as np
+
+class NumPyBackend:
+    """Backend that uses numpy.fft"""
+    __ua_domain__ = "numpy.scipy.fft"
+
+    @staticmethod
+    def __ua_function__(method, args, kwargs):
+        kwargs.pop("overwrite_x", None)
+
+        fn = getattr(np.fft, method.__name__, None)
+        return (NotImplemented if fn is None
+                else fn(*args, **kwargs))
+
+
+class EchoBackend:
+    """Backend that just prints the __ua_function__ arguments"""
+    __ua_domain__ = "numpy.scipy.fft"
+
+    @staticmethod
+    def __ua_function__(method, args, kwargs):
+        print(method, args, kwargs, sep='\n')
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_fftlog.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_fftlog.py
new file mode 100644
index 0000000000000000000000000000000000000000..7a01e2cc4a2734fdf9c11e33faf5bdd8bbfd8367
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_fftlog.py
@@ -0,0 +1,227 @@
+"""Fast Hankel transforms using the FFTLog algorithm.
+
+The implementation closely follows the Fortran code of Hamilton (2000).
+
+added: 14/11/2020 Nicolas Tessore 
+"""
+
+from ._basic import _dispatch
+from scipy._lib.uarray import Dispatchable
+from ._fftlog_backend import fhtoffset
+from scipy._lib._array_api import xp_capabilities
+
+import numpy as np
+
+__all__ = ['fht', 'ifht', 'fhtoffset']
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def fht(a, dln, mu, offset=0.0, bias=0.0):
+    r'''Compute the fast Hankel transform.
+
+    Computes the discrete Hankel transform of a logarithmically spaced periodic
+    sequence using the FFTLog algorithm [1]_, [2]_.
+
+    Parameters
+    ----------
+    a : array_like (..., n)
+        Real periodic input array, uniformly logarithmically spaced.  For
+        multidimensional input, the transform is performed over the last axis.
+    dln : float
+        Uniform logarithmic spacing of the input array.
+    mu : float
+        Order of the Hankel transform, any positive or negative real number.
+    offset : float, optional
+        Offset of the uniform logarithmic spacing of the output array.
+    bias : float, optional
+        Exponent of power law bias, any positive or negative real number.
+
+    Returns
+    -------
+    A : array_like (..., n)
+        The transformed output array, which is real, periodic, uniformly
+        logarithmically spaced, and of the same shape as the input array.
+
+    See Also
+    --------
+    ifht : The inverse of `fht`.
+    fhtoffset : Return an optimal offset for `fht`.
+
+    Notes
+    -----
+    This function computes a discrete version of the Hankel transform
+
+    .. math::
+
+        A(k) = \int_{0}^{\infty} \! a(r) \, J_\mu(kr) \, k \, dr \;,
+
+    where :math:`J_\mu` is the Bessel function of order :math:`\mu`.  The index
+    :math:`\mu` may be any real number, positive or negative.  Note that the
+    numerical Hankel transform uses an integrand of :math:`k \, dr`, while the
+    mathematical Hankel transform is commonly defined using :math:`r \, dr`.
+
+    The input array `a` is a periodic sequence of length :math:`n`, uniformly
+    logarithmically spaced with spacing `dln`,
+
+    .. math::
+
+        a_j = a(r_j) \;, \quad
+        r_j = r_c \exp[(j-j_c) \, \mathtt{dln}]
+
+    centred about the point :math:`r_c`.  Note that the central index
+    :math:`j_c = (n-1)/2` is half-integral if :math:`n` is even, so that
+    :math:`r_c` falls between two input elements.  Similarly, the output
+    array `A` is a periodic sequence of length :math:`n`, also uniformly
+    logarithmically spaced with spacing `dln`
+
+    .. math::
+
+       A_j = A(k_j) \;, \quad
+       k_j = k_c \exp[(j-j_c) \, \mathtt{dln}]
+
+    centred about the point :math:`k_c`.
+
+    The centre points :math:`r_c` and :math:`k_c` of the periodic intervals may
+    be chosen arbitrarily, but it would be usual to choose the product
+    :math:`k_c r_c = k_j r_{n-1-j} = k_{n-1-j} r_j` to be unity.  This can be
+    changed using the `offset` parameter, which controls the logarithmic offset
+    :math:`\log(k_c) = \mathtt{offset} - \log(r_c)` of the output array.
+    Choosing an optimal value for `offset` may reduce ringing of the discrete
+    Hankel transform.
+
+    If the `bias` parameter is nonzero, this function computes a discrete
+    version of the biased Hankel transform
+
+    .. math::
+
+        A(k) = \int_{0}^{\infty} \! a_q(r) \, (kr)^q \, J_\mu(kr) \, k \, dr
+
+    where :math:`q` is the value of `bias`, and a power law bias
+    :math:`a_q(r) = a(r) \, (kr)^{-q}` is applied to the input sequence.
+    Biasing the transform can help approximate the continuous transform of
+    :math:`a(r)` if there is a value :math:`q` such that :math:`a_q(r)` is
+    close to a periodic sequence, in which case the resulting :math:`A(k)` will
+    be close to the continuous transform.
+
+    References
+    ----------
+    .. [1] Talman J. D., 1978, J. Comp. Phys., 29, 35
+    .. [2] Hamilton A. J. S., 2000, MNRAS, 312, 257 (astro-ph/9905191)
+
+    Examples
+    --------
+
+    This example is the adapted version of ``fftlogtest.f`` which is provided
+    in [2]_. It evaluates the integral
+
+    .. math::
+
+        \int^\infty_0 r^{\mu+1} \exp(-r^2/2) J_\mu(kr) k dr
+        = k^{\mu+1} \exp(-k^2/2) .
+
+    >>> import numpy as np
+    >>> from scipy import fft
+    >>> import matplotlib.pyplot as plt
+
+    Parameters for the transform.
+
+    >>> mu = 0.0                     # Order mu of Bessel function
+    >>> r = np.logspace(-7, 1, 128)  # Input evaluation points
+    >>> dln = np.log(r[1]/r[0])      # Step size
+    >>> offset = fft.fhtoffset(dln, initial=-6*np.log(10), mu=mu)
+    >>> k = np.exp(offset)/r[::-1]   # Output evaluation points
+
+    Define the analytical function.
+
+    >>> def f(x, mu):
+    ...     """Analytical function: x^(mu+1) exp(-x^2/2)."""
+    ...     return x**(mu + 1)*np.exp(-x**2/2)
+
+    Evaluate the function at ``r`` and compute the corresponding values at
+    ``k`` using FFTLog.
+
+    >>> a_r = f(r, mu)
+    >>> fht = fft.fht(a_r, dln, mu=mu, offset=offset)
+
+    For this example we can actually compute the analytical response (which in
+    this case is the same as the input function) for comparison and compute the
+    relative error.
+
+    >>> a_k = f(k, mu)
+    >>> rel_err = abs((fht-a_k)/a_k)
+
+    Plot the result.
+
+    >>> figargs = {'sharex': True, 'sharey': True, 'constrained_layout': True}
+    >>> fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4), **figargs)
+    >>> ax1.set_title(r'$r^{\mu+1}\ \exp(-r^2/2)$')
+    >>> ax1.loglog(r, a_r, 'k', lw=2)
+    >>> ax1.set_xlabel('r')
+    >>> ax2.set_title(r'$k^{\mu+1} \exp(-k^2/2)$')
+    >>> ax2.loglog(k, a_k, 'k', lw=2, label='Analytical')
+    >>> ax2.loglog(k, fht, 'C3--', lw=2, label='FFTLog')
+    >>> ax2.set_xlabel('k')
+    >>> ax2.legend(loc=3, framealpha=1)
+    >>> ax2.set_ylim([1e-10, 1e1])
+    >>> ax2b = ax2.twinx()
+    >>> ax2b.loglog(k, rel_err, 'C0', label='Rel. Error (-)')
+    >>> ax2b.set_ylabel('Rel. Error (-)', color='C0')
+    >>> ax2b.tick_params(axis='y', labelcolor='C0')
+    >>> ax2b.legend(loc=4, framealpha=1)
+    >>> ax2b.set_ylim([1e-9, 1e-3])
+    >>> plt.show()
+
+    '''
+    return (Dispatchable(a, np.ndarray),)
+
+
+@xp_capabilities(allow_dask_compute=True)
+@_dispatch
+def ifht(A, dln, mu, offset=0.0, bias=0.0):
+    r"""Compute the inverse fast Hankel transform.
+
+    Computes the discrete inverse Hankel transform of a logarithmically spaced
+    periodic sequence. This is the inverse operation to `fht`.
+
+    Parameters
+    ----------
+    A : array_like (..., n)
+        Real periodic input array, uniformly logarithmically spaced.  For
+        multidimensional input, the transform is performed over the last axis.
+    dln : float
+        Uniform logarithmic spacing of the input array.
+    mu : float
+        Order of the Hankel transform, any positive or negative real number.
+    offset : float, optional
+        Offset of the uniform logarithmic spacing of the output array.
+    bias : float, optional
+        Exponent of power law bias, any positive or negative real number.
+
+    Returns
+    -------
+    a : array_like (..., n)
+        The transformed output array, which is real, periodic, uniformly
+        logarithmically spaced, and of the same shape as the input array.
+
+    See Also
+    --------
+    fht : Definition of the fast Hankel transform.
+    fhtoffset : Return an optimal offset for `ifht`.
+
+    Notes
+    -----
+    This function computes a discrete version of the Hankel transform
+
+    .. math::
+
+        a(r) = \int_{0}^{\infty} \! A(k) \, J_\mu(kr) \, r \, dk \;,
+
+    where :math:`J_\mu` is the Bessel function of order :math:`\mu`.  The index
+    :math:`\mu` may be any real number, positive or negative. Note that the
+    numerical inverse Hankel transform uses an integrand of :math:`r \, dk`, while the
+    mathematical inverse Hankel transform is commonly defined using :math:`k \, dk`.
+
+    See `fht` for further details.
+    """
+    return (Dispatchable(A, np.ndarray),)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_fftlog_backend.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_fftlog_backend.py
new file mode 100644
index 0000000000000000000000000000000000000000..d361708ea96c0bb590ec023e775e9bcfdad71a16
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_fftlog_backend.py
@@ -0,0 +1,201 @@
+import numpy as np
+from warnings import warn
+from ._basic import rfft, irfft
+from ..special import loggamma, poch
+
+from scipy._lib._array_api import array_namespace, xp_capabilities
+
+__all__ = ['fht', 'ifht', 'fhtoffset']
+
+# constants
+LN_2 = np.log(2)
+
+
+def fht(a, dln, mu, offset=0.0, bias=0.0):
+    xp = array_namespace(a)
+    a = xp.asarray(a)
+
+    # size of transform
+    n = a.shape[-1]
+
+    # bias input array
+    if bias != 0:
+        # a_q(r) = a(r) (r/r_c)^{-q}
+        j_c = (n-1)/2
+        j = xp.arange(n, dtype=xp.float64)
+        a = a * xp.exp(-bias*(j - j_c)*dln)
+
+    # compute FHT coefficients
+    u = xp.asarray(fhtcoeff(n, dln, mu, offset=offset, bias=bias))
+
+    # transform
+    A = _fhtq(a, u, xp=xp)
+
+    # bias output array
+    if bias != 0:
+        # A(k) = A_q(k) (k/k_c)^{-q} (k_c r_c)^{-q}
+        A *= xp.exp(-bias*((j - j_c)*dln + offset))
+
+    return A
+
+
+def ifht(A, dln, mu, offset=0.0, bias=0.0):
+    xp = array_namespace(A)
+    A = xp.asarray(A)
+
+    # size of transform
+    n = A.shape[-1]
+
+    # bias input array
+    if bias != 0:
+        # A_q(k) = A(k) (k/k_c)^{q} (k_c r_c)^{q}
+        j_c = (n-1)/2
+        j = xp.arange(n, dtype=xp.float64)
+        A = A * xp.exp(bias*((j - j_c)*dln + offset))
+
+    # compute FHT coefficients
+    u = xp.asarray(fhtcoeff(n, dln, mu, offset=offset, bias=bias, inverse=True))
+
+    # transform
+    a = _fhtq(A, u, inverse=True, xp=xp)
+
+    # bias output array
+    if bias != 0:
+        # a(r) = a_q(r) (r/r_c)^{q}
+        a /= xp.exp(-bias*(j - j_c)*dln)
+
+    return a
+
+
+def fhtcoeff(n, dln, mu, offset=0.0, bias=0.0, inverse=False):
+    """Compute the coefficient array for a fast Hankel transform."""
+    lnkr, q = offset, bias
+
+    # Hankel transform coefficients
+    # u_m = (kr)^{-i 2m pi/(n dlnr)} U_mu(q + i 2m pi/(n dlnr))
+    # with U_mu(x) = 2^x Gamma((mu+1+x)/2)/Gamma((mu+1-x)/2)
+    xp = (mu+1+q)/2
+    xm = (mu+1-q)/2
+    y = np.linspace(0, np.pi*(n//2)/(n*dln), n//2+1)
+    u = np.empty(n//2+1, dtype=complex)
+    v = np.empty(n//2+1, dtype=complex)
+    u.imag[:] = y
+    u.real[:] = xm
+    loggamma(u, out=v)
+    u.real[:] = xp
+    loggamma(u, out=u)
+    y *= 2*(LN_2 - lnkr)
+    u.real -= v.real
+    u.real += LN_2*q
+    u.imag += v.imag
+    u.imag += y
+    np.exp(u, out=u)
+
+    # fix last coefficient to be real
+    if n % 2 == 0:
+        u.imag[-1] = 0
+
+    # deal with special cases
+    if not np.isfinite(u[0]):
+        # write u_0 = 2^q Gamma(xp)/Gamma(xm) = 2^q poch(xm, xp-xm)
+        # poch() handles special cases for negative integers correctly
+        u[0] = 2**q * poch(xm, xp-xm)
+        # the coefficient may be inf or 0, meaning the transform or the
+        # inverse transform, respectively, is singular
+
+    # check for singular transform or singular inverse transform
+    if np.isinf(u[0]) and not inverse:
+        warn('singular transform; consider changing the bias', stacklevel=3)
+        # fix coefficient to obtain (potentially correct) transform anyway
+        u = np.copy(u)
+        u[0] = 0
+    elif u[0] == 0 and inverse:
+        warn('singular inverse transform; consider changing the bias', stacklevel=3)
+        # fix coefficient to obtain (potentially correct) inverse anyway
+        u = np.copy(u)
+        u[0] = np.inf
+
+    return u
+
+
+@xp_capabilities(out_of_scope=True)
+def fhtoffset(dln, mu, initial=0.0, bias=0.0):
+    """Return optimal offset for a fast Hankel transform.
+
+    Returns an offset close to `initial` that fulfils the low-ringing
+    condition of [1]_ for the fast Hankel transform `fht` with logarithmic
+    spacing `dln`, order `mu` and bias `bias`.
+
+    Parameters
+    ----------
+    dln : float
+        Uniform logarithmic spacing of the transform.
+    mu : float
+        Order of the Hankel transform, any positive or negative real number.
+    initial : float, optional
+        Initial value for the offset. Returns the closest value that fulfils
+        the low-ringing condition.
+    bias : float, optional
+        Exponent of power law bias, any positive or negative real number.
+
+    Returns
+    -------
+    offset : float
+        Optimal offset of the uniform logarithmic spacing of the transform that
+        fulfils a low-ringing condition.
+
+    Examples
+    --------
+    >>> from scipy.fft import fhtoffset
+    >>> dln = 0.1
+    >>> mu = 2.0
+    >>> initial = 0.5
+    >>> bias = 0.0
+    >>> offset = fhtoffset(dln, mu, initial, bias)
+    >>> offset
+    0.5454581477676637
+
+    See Also
+    --------
+    fht : Definition of the fast Hankel transform.
+
+    References
+    ----------
+    .. [1] Hamilton A. J. S., 2000, MNRAS, 312, 257 (astro-ph/9905191)
+
+    """
+
+    lnkr, q = initial, bias
+
+    xp = (mu+1+q)/2
+    xm = (mu+1-q)/2
+    y = np.pi/(2*dln)
+    zp = loggamma(xp + 1j*y)
+    zm = loggamma(xm + 1j*y)
+    arg = (LN_2 - lnkr)/dln + (zp.imag + zm.imag)/np.pi
+    return lnkr + (arg - np.round(arg))*dln
+
+
+def _fhtq(a, u, inverse=False, *, xp=None):
+    """Compute the biased fast Hankel transform.
+
+    This is the basic FFTLog routine.
+    """
+    if xp is None:
+        xp = np
+
+    # size of transform
+    n = a.shape[-1]
+
+    # biased fast Hankel transform via real FFT
+    A = rfft(a, axis=-1)
+    if not inverse:
+        # forward transform
+        A *= u
+    else:
+        # backward transform
+        A /= xp.conj(u)
+    A = irfft(A, n, axis=-1)
+    A = xp.flip(A, axis=-1)
+
+    return A
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_helper.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_helper.py
new file mode 100644
index 0000000000000000000000000000000000000000..29896a30520ed7ce3e3b6eb080ee50a656194734
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_helper.py
@@ -0,0 +1,355 @@
+from functools import update_wrapper, lru_cache
+import inspect
+
+from ._pocketfft import helper as _helper
+
+import numpy as np
+from scipy._lib._array_api import array_namespace
+from scipy._lib._array_api import xp_capabilities
+
+
+_init_nd_shape_and_axes = _helper._init_nd_shape_and_axes
+
+
+def next_fast_len(target, real=False):
+    """Find the next fast size of input data to ``fft``, for zero-padding, etc.
+
+    SciPy's FFT algorithms gain their speed by a recursive divide and conquer
+    strategy. This relies on efficient functions for small prime factors of the
+    input length. Thus, the transforms are fastest when using composites of the
+    prime factors handled by the fft implementation. If there are efficient
+    functions for all radices <= `n`, then the result will be a number `x`
+    >= ``target`` with only prime factors < `n`. (Also known as `n`-smooth
+    numbers)
+
+    Parameters
+    ----------
+    target : int
+        Length to start searching from. Must be a positive integer.
+    real : bool, optional
+        True if the FFT involves real input or output (e.g., `rfft` or `hfft`
+        but not `fft`). Defaults to False.
+
+    Returns
+    -------
+    out : int
+        The smallest fast length greater than or equal to ``target``.
+
+    Notes
+    -----
+    The result of this function may change in future as performance
+    considerations change, for example, if new prime factors are added.
+
+    Calling `fft` or `ifft` with real input data performs an ``'R2C'``
+    transform internally.
+
+    Examples
+    --------
+    On a particular machine, an FFT of prime length takes 11.4 ms:
+
+    >>> from scipy import fft
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> min_len = 93059  # prime length is worst case for speed
+    >>> a = rng.standard_normal(min_len)
+    >>> b = fft.fft(a)
+
+    Zero-padding to the next regular length reduces computation time to
+    1.6 ms, a speedup of 7.3 times:
+
+    >>> fft.next_fast_len(min_len, real=True)
+    93312
+    >>> b = fft.fft(a, 93312)
+
+    Rounding up to the next power of 2 is not optimal, taking 3.0 ms to
+    compute; 1.9 times longer than the size given by ``next_fast_len``:
+
+    >>> b = fft.fft(a, 131072)
+
+    """
+    pass
+
+
+# Directly wrap the c-function good_size but take the docstring etc., from the
+# next_fast_len function above
+_sig = inspect.signature(next_fast_len)
+next_fast_len = update_wrapper(lru_cache(_helper.good_size), next_fast_len)
+next_fast_len = xp_capabilities(out_of_scope=True)(next_fast_len)
+next_fast_len.__wrapped__ = _helper.good_size
+next_fast_len.__signature__ = _sig
+
+
+def prev_fast_len(target, real=False):
+    """Find the previous fast size of input data to ``fft``.
+    Useful for discarding a minimal number of samples before FFT.
+
+    SciPy's FFT algorithms gain their speed by a recursive divide and conquer
+    strategy. This relies on efficient functions for small prime factors of the
+    input length. Thus, the transforms are fastest when using composites of the
+    prime factors handled by the fft implementation. If there are efficient
+    functions for all radices <= `n`, then the result will be a number `x`
+    <= ``target`` with only prime factors <= `n`. (Also known as `n`-smooth
+    numbers)
+
+    Parameters
+    ----------
+    target : int
+        Maximum length to search until. Must be a positive integer.
+    real : bool, optional
+        True if the FFT involves real input or output (e.g., `rfft` or `hfft`
+        but not `fft`). Defaults to False.
+
+    Returns
+    -------
+    out : int
+        The largest fast length less than or equal to ``target``.
+
+    Notes
+    -----
+    The result of this function may change in future as performance
+    considerations change, for example, if new prime factors are added.
+
+    Calling `fft` or `ifft` with real input data performs an ``'R2C'``
+    transform internally.
+
+    In the current implementation, prev_fast_len assumes radices of
+    2,3,5,7,11 for complex FFT and 2,3,5 for real FFT.
+
+    Examples
+    --------
+    On a particular machine, an FFT of prime length takes 16.2 ms:
+
+    >>> from scipy import fft
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> max_len = 93059  # prime length is worst case for speed
+    >>> a = rng.standard_normal(max_len)
+    >>> b = fft.fft(a)
+
+    Performing FFT on the maximum fast length less than max_len
+    reduces the computation time to 1.5 ms, a speedup of 10.5 times:
+
+    >>> fft.prev_fast_len(max_len, real=True)
+    92160
+    >>> c = fft.fft(a[:92160]) # discard last 899 samples
+
+    """
+    pass
+
+
+# Directly wrap the c-function prev_good_size but take the docstring etc.,
+# from the prev_fast_len function above
+_sig_prev_fast_len = inspect.signature(prev_fast_len)
+prev_fast_len = update_wrapper(lru_cache()(_helper.prev_good_size), prev_fast_len)
+prev_fast_len = xp_capabilities(out_of_scope=True)(prev_fast_len)
+prev_fast_len.__wrapped__ = _helper.prev_good_size
+prev_fast_len.__signature__ = _sig_prev_fast_len
+
+
+@xp_capabilities()
+def fftfreq(n, d=1.0, *, xp=None, device=None):
+    """Return the Discrete Fourier Transform sample frequencies.
+
+    The returned float array `f` contains the frequency bin centers in cycles
+    per unit of the sample spacing (with zero at the start).  For instance, if
+    the sample spacing is in seconds, then the frequency unit is cycles/second.
+
+    Given a window length `n` and a sample spacing `d`::
+
+      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
+      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd
+
+    Parameters
+    ----------
+    n : int
+        Window length.
+    d : scalar, optional
+        Sample spacing (inverse of the sampling rate). Defaults to 1.
+    xp : array_namespace, optional
+        The namespace for the return array. Default is None, where NumPy is used.
+    device : device, optional
+        The device for the return array.
+        Only valid when `xp.fft.fftfreq` implements the device parameter.
+
+    Returns
+    -------
+    f : ndarray
+        Array of length `n` containing the sample frequencies.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.fft
+    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
+    >>> fourier = scipy.fft.fft(signal)
+    >>> n = signal.size
+    >>> timestep = 0.1
+    >>> freq = scipy.fft.fftfreq(n, d=timestep)
+    >>> freq
+    array([ 0.  ,  1.25,  2.5 , ..., -3.75, -2.5 , -1.25])
+
+    """
+    xp = np if xp is None else xp
+    # numpy does not yet support the `device` keyword
+    # `xp.__name__ != 'numpy'` should be removed when numpy is compatible
+    if hasattr(xp, 'fft') and xp.__name__ != 'numpy':
+        return xp.fft.fftfreq(n, d=d, device=device)
+    if device is not None:
+        raise ValueError('device parameter is not supported for input array type')
+    return np.fft.fftfreq(n, d=d)
+
+
+@xp_capabilities()
+def rfftfreq(n, d=1.0, *, xp=None, device=None):
+    """Return the Discrete Fourier Transform sample frequencies
+    (for usage with rfft, irfft).
+
+    The returned float array `f` contains the frequency bin centers in cycles
+    per unit of the sample spacing (with zero at the start).  For instance, if
+    the sample spacing is in seconds, then the frequency unit is cycles/second.
+
+    Given a window length `n` and a sample spacing `d`::
+
+      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
+      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd
+
+    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
+    the Nyquist frequency component is considered to be positive.
+
+    Parameters
+    ----------
+    n : int
+        Window length.
+    d : scalar, optional
+        Sample spacing (inverse of the sampling rate). Defaults to 1.
+    xp : array_namespace, optional
+        The namespace for the return array. Default is None, where NumPy is used.
+    device : device, optional
+        The device for the return array.
+        Only valid when `xp.fft.rfftfreq` implements the device parameter.
+
+    Returns
+    -------
+    f : ndarray
+        Array of length ``n//2 + 1`` containing the sample frequencies.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import scipy.fft
+    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
+    >>> fourier = scipy.fft.rfft(signal)
+    >>> n = signal.size
+    >>> sample_rate = 100
+    >>> freq = scipy.fft.fftfreq(n, d=1./sample_rate)
+    >>> freq
+    array([  0.,  10.,  20., ..., -30., -20., -10.])
+    >>> freq = scipy.fft.rfftfreq(n, d=1./sample_rate)
+    >>> freq
+    array([  0.,  10.,  20.,  30.,  40.,  50.])
+
+    """
+    xp = np if xp is None else xp
+    # numpy does not yet support the `device` keyword
+    # `xp.__name__ != 'numpy'` should be removed when numpy is compatible
+    if hasattr(xp, 'fft') and xp.__name__ != 'numpy':
+        return xp.fft.rfftfreq(n, d=d, device=device)
+    if device is not None:
+        raise ValueError('device parameter is not supported for input array type')
+    return np.fft.rfftfreq(n, d=d)
+
+
+@xp_capabilities()
+def fftshift(x, axes=None):
+    """Shift the zero-frequency component to the center of the spectrum.
+
+    This function swaps half-spaces for all axes listed (defaults to all).
+    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    axes : int or shape tuple, optional
+        Axes over which to shift.  Default is None, which shifts all axes.
+
+    Returns
+    -------
+    y : ndarray
+        The shifted array.
+
+    See Also
+    --------
+    ifftshift : The inverse of `fftshift`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> freqs = np.fft.fftfreq(10, 0.1)
+    >>> freqs
+    array([ 0.,  1.,  2., ..., -3., -2., -1.])
+    >>> np.fft.fftshift(freqs)
+    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])
+
+    Shift the zero-frequency component only along the second axis:
+
+    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
+    >>> freqs
+    array([[ 0.,  1.,  2.],
+           [ 3.,  4., -4.],
+           [-3., -2., -1.]])
+    >>> np.fft.fftshift(freqs, axes=(1,))
+    array([[ 2.,  0.,  1.],
+           [-4.,  3.,  4.],
+           [-1., -3., -2.]])
+
+    """
+    xp = array_namespace(x)
+    if hasattr(xp, 'fft'):
+        return xp.fft.fftshift(x, axes=axes)
+    x = np.asarray(x)
+    y = np.fft.fftshift(x, axes=axes)
+    return xp.asarray(y)
+
+
+@xp_capabilities()
+def ifftshift(x, axes=None):
+    """The inverse of `fftshift`. Although identical for even-length `x`, the
+    functions differ by one sample for odd-length `x`.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    axes : int or shape tuple, optional
+        Axes over which to calculate.  Defaults to None, which shifts all axes.
+
+    Returns
+    -------
+    y : ndarray
+        The shifted array.
+
+    See Also
+    --------
+    fftshift : Shift zero-frequency component to the center of the spectrum.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
+    >>> freqs
+    array([[ 0.,  1.,  2.],
+           [ 3.,  4., -4.],
+           [-3., -2., -1.]])
+    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
+    array([[ 0.,  1.,  2.],
+           [ 3.,  4., -4.],
+           [-3., -2., -1.]])
+
+    """
+    xp = array_namespace(x)
+    if hasattr(xp, 'fft'):
+        return xp.fft.ifftshift(x, axes=axes)
+    x = np.asarray(x)
+    y = np.fft.ifftshift(x, axes=axes)
+    return xp.asarray(y)
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/._tests b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/._tests
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/LICENSE.md b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/LICENSE.md
new file mode 100644
index 0000000000000000000000000000000000000000..1b5163d8435976c24988afbd39ded304947178cb
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/LICENSE.md
@@ -0,0 +1,25 @@
+Copyright (C) 2010-2019 Max-Planck-Society
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without modification,
+are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+* Redistributions in binary form must reproduce the above copyright notice, this
+  list of conditions and the following disclaimer in the documentation and/or
+  other materials provided with the distribution.
+* Neither the name of the copyright holder nor the names of its contributors may
+  be used to endorse or promote products derived from this software without
+  specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..0671484c9a0780df353b9b783813b6fa7492d38d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/__init__.py
@@ -0,0 +1,9 @@
+""" FFT backend using pypocketfft """
+
+from .basic import *
+from .realtransforms import *
+from .helper import *
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..bd2d0d33958021c431171b72f72c37363ac98e03
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/basic.py
@@ -0,0 +1,251 @@
+"""
+Discrete Fourier Transforms - basic.py
+"""
+import numpy as np
+import functools
+from . import pypocketfft as pfft
+from .helper import (_asfarray, _init_nd_shape_and_axes, _datacopied,
+                     _fix_shape, _fix_shape_1d, _normalization,
+                     _workers)
+
+def c2c(forward, x, n=None, axis=-1, norm=None, overwrite_x=False,
+        workers=None, *, plan=None):
+    """ Return discrete Fourier transform of real or complex sequence. """
+    if plan is not None:
+        raise NotImplementedError('Passing a precomputed plan is not yet '
+                                  'supported by scipy.fft functions')
+    tmp = _asfarray(x)
+    overwrite_x = overwrite_x or _datacopied(tmp, x)
+    norm = _normalization(norm, forward)
+    workers = _workers(workers)
+
+    if n is not None:
+        tmp, copied = _fix_shape_1d(tmp, n, axis)
+        overwrite_x = overwrite_x or copied
+    elif tmp.shape[axis] < 1:
+        message = f"invalid number of data points ({tmp.shape[axis]}) specified"
+        raise ValueError(message)
+
+    out = (tmp if overwrite_x and tmp.dtype.kind == 'c' else None)
+
+    return pfft.c2c(tmp, (axis,), forward, norm, out, workers)
+
+
+fft = functools.partial(c2c, True)
+fft.__name__ = 'fft'
+ifft = functools.partial(c2c, False)
+ifft.__name__ = 'ifft'
+
+
+def r2c(forward, x, n=None, axis=-1, norm=None, overwrite_x=False,
+        workers=None, *, plan=None):
+    """
+    Discrete Fourier transform of a real sequence.
+    """
+    if plan is not None:
+        raise NotImplementedError('Passing a precomputed plan is not yet '
+                                  'supported by scipy.fft functions')
+    tmp = _asfarray(x)
+    norm = _normalization(norm, forward)
+    workers = _workers(workers)
+
+    if not np.isrealobj(tmp):
+        raise TypeError("x must be a real sequence")
+
+    if n is not None:
+        tmp, _ = _fix_shape_1d(tmp, n, axis)
+    elif tmp.shape[axis] < 1:
+        raise ValueError(f"invalid number of data points ({tmp.shape[axis]}) specified")
+
+    # Note: overwrite_x is not utilised
+    return pfft.r2c(tmp, (axis,), forward, norm, None, workers)
+
+
+rfft = functools.partial(r2c, True)
+rfft.__name__ = 'rfft'
+ihfft = functools.partial(r2c, False)
+ihfft.__name__ = 'ihfft'
+
+
+def c2r(forward, x, n=None, axis=-1, norm=None, overwrite_x=False,
+        workers=None, *, plan=None):
+    """
+    Return inverse discrete Fourier transform of real sequence x.
+    """
+    if plan is not None:
+        raise NotImplementedError('Passing a precomputed plan is not yet '
+                                  'supported by scipy.fft functions')
+    tmp = _asfarray(x)
+    norm = _normalization(norm, forward)
+    workers = _workers(workers)
+
+    # TODO: Optimize for hermitian and real?
+    if np.isrealobj(tmp):
+        tmp = tmp + 0.j
+
+    # Last axis utilizes hermitian symmetry
+    if n is None:
+        n = (tmp.shape[axis] - 1) * 2
+        if n < 1:
+            raise ValueError(f"Invalid number of data points ({n}) specified")
+    else:
+        tmp, _ = _fix_shape_1d(tmp, (n//2) + 1, axis)
+
+    # Note: overwrite_x is not utilized
+    return pfft.c2r(tmp, (axis,), n, forward, norm, None, workers)
+
+
+hfft = functools.partial(c2r, True)
+hfft.__name__ = 'hfft'
+irfft = functools.partial(c2r, False)
+irfft.__name__ = 'irfft'
+
+
+def hfft2(x, s=None, axes=(-2,-1), norm=None, overwrite_x=False, workers=None,
+          *, plan=None):
+    """
+    2-D discrete Fourier transform of a Hermitian sequence
+    """
+    if plan is not None:
+        raise NotImplementedError('Passing a precomputed plan is not yet '
+                                  'supported by scipy.fft functions')
+    return hfftn(x, s, axes, norm, overwrite_x, workers)
+
+
+def ihfft2(x, s=None, axes=(-2,-1), norm=None, overwrite_x=False, workers=None,
+           *, plan=None):
+    """
+    2-D discrete inverse Fourier transform of a Hermitian sequence
+    """
+    if plan is not None:
+        raise NotImplementedError('Passing a precomputed plan is not yet '
+                                  'supported by scipy.fft functions')
+    return ihfftn(x, s, axes, norm, overwrite_x, workers)
+
+
+def c2cn(forward, x, s=None, axes=None, norm=None, overwrite_x=False,
+         workers=None, *, plan=None):
+    """
+    Return multidimensional discrete Fourier transform.
+    """
+    if plan is not None:
+        raise NotImplementedError('Passing a precomputed plan is not yet '
+                                  'supported by scipy.fft functions')
+    tmp = _asfarray(x)
+
+    shape, axes = _init_nd_shape_and_axes(tmp, s, axes)
+    overwrite_x = overwrite_x or _datacopied(tmp, x)
+    workers = _workers(workers)
+
+    if len(axes) == 0:
+        return x
+
+    tmp, copied = _fix_shape(tmp, shape, axes)
+    overwrite_x = overwrite_x or copied
+
+    norm = _normalization(norm, forward)
+    out = (tmp if overwrite_x and tmp.dtype.kind == 'c' else None)
+
+    return pfft.c2c(tmp, axes, forward, norm, out, workers)
+
+
+fftn = functools.partial(c2cn, True)
+fftn.__name__ = 'fftn'
+ifftn = functools.partial(c2cn, False)
+ifftn.__name__ = 'ifftn'
+
+def r2cn(forward, x, s=None, axes=None, norm=None, overwrite_x=False,
+         workers=None, *, plan=None):
+    """Return multidimensional discrete Fourier transform of real input"""
+    if plan is not None:
+        raise NotImplementedError('Passing a precomputed plan is not yet '
+                                  'supported by scipy.fft functions')
+    tmp = _asfarray(x)
+
+    if not np.isrealobj(tmp):
+        raise TypeError("x must be a real sequence")
+
+    shape, axes = _init_nd_shape_and_axes(tmp, s, axes)
+    tmp, _ = _fix_shape(tmp, shape, axes)
+    norm = _normalization(norm, forward)
+    workers = _workers(workers)
+
+    if len(axes) == 0:
+        raise ValueError("at least 1 axis must be transformed")
+
+    # Note: overwrite_x is not utilized
+    return pfft.r2c(tmp, axes, forward, norm, None, workers)
+
+
+rfftn = functools.partial(r2cn, True)
+rfftn.__name__ = 'rfftn'
+ihfftn = functools.partial(r2cn, False)
+ihfftn.__name__ = 'ihfftn'
+
+
+def c2rn(forward, x, s=None, axes=None, norm=None, overwrite_x=False,
+         workers=None, *, plan=None):
+    """Multidimensional inverse discrete fourier transform with real output"""
+    if plan is not None:
+        raise NotImplementedError('Passing a precomputed plan is not yet '
+                                  'supported by scipy.fft functions')
+    tmp = _asfarray(x)
+
+    # TODO: Optimize for hermitian and real?
+    if np.isrealobj(tmp):
+        tmp = tmp + 0.j
+
+    noshape = s is None
+    shape, axes = _init_nd_shape_and_axes(tmp, s, axes)
+
+    if len(axes) == 0:
+        raise ValueError("at least 1 axis must be transformed")
+
+    shape = list(shape)
+    if noshape:
+        shape[-1] = (x.shape[axes[-1]] - 1) * 2
+
+    norm = _normalization(norm, forward)
+    workers = _workers(workers)
+
+    # Last axis utilizes hermitian symmetry
+    lastsize = shape[-1]
+    shape[-1] = (shape[-1] // 2) + 1
+
+    tmp, _ = tuple(_fix_shape(tmp, shape, axes))
+
+    # Note: overwrite_x is not utilized
+    return pfft.c2r(tmp, axes, lastsize, forward, norm, None, workers)
+
+
+hfftn = functools.partial(c2rn, True)
+hfftn.__name__ = 'hfftn'
+irfftn = functools.partial(c2rn, False)
+irfftn.__name__ = 'irfftn'
+
+
+def r2r_fftpack(forward, x, n=None, axis=-1, norm=None, overwrite_x=False):
+    """FFT of a real sequence, returning fftpack half complex format"""
+    tmp = _asfarray(x)
+    overwrite_x = overwrite_x or _datacopied(tmp, x)
+    norm = _normalization(norm, forward)
+    workers = _workers(None)
+
+    if tmp.dtype.kind == 'c':
+        raise TypeError('x must be a real sequence')
+
+    if n is not None:
+        tmp, copied = _fix_shape_1d(tmp, n, axis)
+        overwrite_x = overwrite_x or copied
+    elif tmp.shape[axis] < 1:
+        raise ValueError(f"invalid number of data points ({tmp.shape[axis]}) specified")
+
+    out = (tmp if overwrite_x else None)
+
+    return pfft.r2r_fftpack(tmp, (axis,), forward, forward, norm, out, workers)
+
+
+rfft_fftpack = functools.partial(r2r_fftpack, True)
+rfft_fftpack.__name__ = 'rfft_fftpack'
+irfft_fftpack = functools.partial(r2r_fftpack, False)
+irfft_fftpack.__name__ = 'irfft_fftpack'
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/helper.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/helper.py
new file mode 100644
index 0000000000000000000000000000000000000000..81e4827a88bf8162ca6fe830f1df1ad1bcfd30d6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/helper.py
@@ -0,0 +1,252 @@
+from numbers import Number
+import operator
+import os
+import threading
+import contextlib
+
+import numpy as np
+
+from scipy._lib._util import copy_if_needed
+from scipy._lib._array_api import xp_capabilities
+
+# good_size is exposed (and used) from this import
+from .pypocketfft import good_size, prev_good_size
+
+
+__all__ = ['good_size', 'prev_good_size', 'set_workers', 'get_workers']
+
+_config = threading.local()
+_cpu_count = os.cpu_count()
+
+
+def _iterable_of_int(x, name=None):
+    """Convert ``x`` to an iterable sequence of int
+
+    Parameters
+    ----------
+    x : value, or sequence of values, convertible to int
+    name : str, optional
+        Name of the argument being converted, only used in the error message
+
+    Returns
+    -------
+    y : ``List[int]``
+    """
+    if isinstance(x, Number):
+        x = (x,)
+
+    try:
+        x = [operator.index(a) for a in x]
+    except TypeError as e:
+        name = name or "value"
+        raise ValueError(f"{name} must be a scalar or iterable of integers") from e
+
+    return x
+
+
+def _init_nd_shape_and_axes(x, shape, axes):
+    """
+    Handle shape and axes arguments for N-D transforms.
+
+    Returns the shape and axes in a standard form, taking into account negative
+    values and checking for various potential errors.
+
+    Parameters
+    ----------
+    x : ndarray
+        The input array.
+    shape : int or array_like of ints or None
+        The shape of the result. If both `shape` and `axes` (see below) are
+        None, `shape` is ``x.shape``; if `shape` is None but `axes` is
+        not None, then `shape` is ``numpy.take(x.shape, axes, axis=0)``.
+        If `shape` is -1, the size of the corresponding dimension of `x` is
+        used.
+    axes : int or array_like of ints or None
+        Axes along which the calculation is computed.
+        The default is over all axes.
+        Negative indices are automatically converted to their positive
+        counterparts.
+
+    Returns
+    -------
+    shape : tuple
+        The shape of the result as a tuple of integers.
+    axes : list
+        Axes along which the calculation is computed, as a list of integers.
+    """
+    noshape = shape is None
+    noaxes = axes is None
+
+    if not noaxes:
+        axes = _iterable_of_int(axes, 'axes')
+        axes = [a + x.ndim if a < 0 else a for a in axes]
+
+        if any(a >= x.ndim or a < 0 for a in axes):
+            raise ValueError("axes exceeds dimensionality of input")
+        if len(set(axes)) != len(axes):
+            raise ValueError("all axes must be unique")
+
+    if not noshape:
+        shape = _iterable_of_int(shape, 'shape')
+
+        if axes and len(axes) != len(shape):
+            raise ValueError("when given, axes and shape arguments"
+                             " have to be of the same length")
+        if noaxes:
+            if len(shape) > x.ndim:
+                raise ValueError("shape requires more axes than are present")
+            axes = range(x.ndim - len(shape), x.ndim)
+
+        shape = [x.shape[a] if s == -1 else s for s, a in zip(shape, axes)]
+    elif noaxes:
+        shape = list(x.shape)
+        axes = range(x.ndim)
+    else:
+        shape = [x.shape[a] for a in axes]
+
+    if any(s < 1 for s in shape):
+        raise ValueError(
+            f"invalid number of data points ({shape}) specified")
+
+    return tuple(shape), list(axes)
+
+
+def _asfarray(x):
+    """
+    Convert to array with floating or complex dtype.
+
+    float16 values are also promoted to float32.
+    """
+    if not hasattr(x, "dtype"):
+        x = np.asarray(x)
+
+    if x.dtype == np.float16:
+        return np.asarray(x, np.float32)
+    elif x.dtype.kind not in 'fc':
+        return np.asarray(x, np.float64)
+
+    # Require native byte order
+    dtype = x.dtype.newbyteorder('=')
+    # Always align input
+    copy = True if not x.flags['ALIGNED'] else copy_if_needed
+    return np.array(x, dtype=dtype, copy=copy)
+
+def _datacopied(arr, original):
+    """
+    Strict check for `arr` not sharing any data with `original`,
+    under the assumption that arr = asarray(original)
+    """
+    if arr is original:
+        return False
+    if not isinstance(original, np.ndarray) and hasattr(original, '__array__'):
+        return False
+    return arr.base is None
+
+
+def _fix_shape(x, shape, axes):
+    """Internal auxiliary function for _raw_fft, _raw_fftnd."""
+    must_copy = False
+
+    # Build an nd slice with the dimensions to be read from x
+    index = [slice(None)]*x.ndim
+    for n, ax in zip(shape, axes):
+        if x.shape[ax] >= n:
+            index[ax] = slice(0, n)
+        else:
+            index[ax] = slice(0, x.shape[ax])
+            must_copy = True
+
+    index = tuple(index)
+
+    if not must_copy:
+        return x[index], False
+
+    s = list(x.shape)
+    for n, axis in zip(shape, axes):
+        s[axis] = n
+
+    z = np.zeros(s, x.dtype)
+    z[index] = x[index]
+    return z, True
+
+
+def _fix_shape_1d(x, n, axis):
+    if n < 1:
+        raise ValueError(
+            f"invalid number of data points ({n}) specified")
+
+    return _fix_shape(x, (n,), (axis,))
+
+
+_NORM_MAP = {None: 0, 'backward': 0, 'ortho': 1, 'forward': 2}
+
+
+def _normalization(norm, forward):
+    """Returns the pypocketfft normalization mode from the norm argument"""
+    try:
+        inorm = _NORM_MAP[norm]
+        return inorm if forward else (2 - inorm)
+    except KeyError:
+        raise ValueError(
+            f'Invalid norm value {norm!r}, should '
+            'be "backward", "ortho" or "forward"') from None
+
+
+def _workers(workers):
+    if workers is None:
+        return getattr(_config, 'default_workers', 1)
+
+    if workers < 0:
+        if workers >= -_cpu_count:
+            workers += 1 + _cpu_count
+        else:
+            raise ValueError(f"workers value out of range; got {workers}, must not be"
+                             f" less than {-_cpu_count}")
+    elif workers == 0:
+        raise ValueError("workers must not be zero")
+
+    return workers
+
+
+@xp_capabilities(out_of_scope=True)
+@contextlib.contextmanager
+def set_workers(workers):
+    """Context manager for the default number of workers used in `scipy.fft`
+
+    Parameters
+    ----------
+    workers : int
+        The default number of workers to use
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import fft, signal
+    >>> rng = np.random.default_rng()
+    >>> x = rng.standard_normal((128, 64))
+    >>> with fft.set_workers(4):
+    ...     y = signal.fftconvolve(x, x)
+
+    """
+    old_workers = get_workers()
+    _config.default_workers = _workers(operator.index(workers))
+    try:
+        yield
+    finally:
+        _config.default_workers = old_workers
+
+
+@xp_capabilities(out_of_scope=True)
+def get_workers():
+    """Returns the default number of workers within the current context
+
+    Examples
+    --------
+    >>> from scipy import fft
+    >>> fft.get_workers()
+    1
+    >>> with fft.set_workers(4):
+    ...     fft.get_workers()
+    4
+    """
+    return getattr(_config, 'default_workers', 1)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/pypocketfft.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/pypocketfft.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..3f18e99f37cb0e429c09cf12f1410103fbd42e21
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/pypocketfft.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c8630667b867f525fee7ce272b25cf5930b17808d803d51cf7b6e9c537ba06e9
+size 946368
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/realtransforms.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/realtransforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..5a0c616742305444d51258e650344c060129dfab
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/realtransforms.py
@@ -0,0 +1,109 @@
+import numpy as np
+from . import pypocketfft as pfft
+from .helper import (_asfarray, _init_nd_shape_and_axes, _datacopied,
+                     _fix_shape, _fix_shape_1d, _normalization, _workers)
+import functools
+
+
+def _r2r(forward, transform, x, type=2, n=None, axis=-1, norm=None,
+         overwrite_x=False, workers=None, orthogonalize=None):
+    """Forward or backward 1-D DCT/DST
+
+    Parameters
+    ----------
+    forward : bool
+        Transform direction (determines type and normalisation)
+    transform : {pypocketfft.dct, pypocketfft.dst}
+        The transform to perform
+    """
+    tmp = _asfarray(x)
+    overwrite_x = overwrite_x or _datacopied(tmp, x)
+    norm = _normalization(norm, forward)
+    workers = _workers(workers)
+
+    if not forward:
+        if type == 2:
+            type = 3
+        elif type == 3:
+            type = 2
+
+    if n is not None:
+        tmp, copied = _fix_shape_1d(tmp, n, axis)
+        overwrite_x = overwrite_x or copied
+    elif tmp.shape[axis] < 1:
+        raise ValueError(f"invalid number of data points ({tmp.shape[axis]}) specified")
+
+    out = (tmp if overwrite_x else None)
+
+    # For complex input, transform real and imaginary components separably
+    if np.iscomplexobj(x):
+        out = np.empty_like(tmp) if out is None else out
+        transform(tmp.real, type, (axis,), norm, out.real, workers)
+        transform(tmp.imag, type, (axis,), norm, out.imag, workers)
+        return out
+
+    return transform(tmp, type, (axis,), norm, out, workers, orthogonalize)
+
+
+dct = functools.partial(_r2r, True, pfft.dct)
+dct.__name__ = 'dct'
+idct = functools.partial(_r2r, False, pfft.dct)
+idct.__name__ = 'idct'
+
+dst = functools.partial(_r2r, True, pfft.dst)
+dst.__name__ = 'dst'
+idst = functools.partial(_r2r, False, pfft.dst)
+idst.__name__ = 'idst'
+
+
+def _r2rn(forward, transform, x, type=2, s=None, axes=None, norm=None,
+          overwrite_x=False, workers=None, orthogonalize=None):
+    """Forward or backward nd DCT/DST
+
+    Parameters
+    ----------
+    forward : bool
+        Transform direction (determines type and normalisation)
+    transform : {pypocketfft.dct, pypocketfft.dst}
+        The transform to perform
+    """
+    tmp = _asfarray(x)
+
+    shape, axes = _init_nd_shape_and_axes(tmp, s, axes)
+    overwrite_x = overwrite_x or _datacopied(tmp, x)
+
+    if len(axes) == 0:
+        return x
+
+    tmp, copied = _fix_shape(tmp, shape, axes)
+    overwrite_x = overwrite_x or copied
+
+    if not forward:
+        if type == 2:
+            type = 3
+        elif type == 3:
+            type = 2
+
+    norm = _normalization(norm, forward)
+    workers = _workers(workers)
+    out = (tmp if overwrite_x else None)
+
+    # For complex input, transform real and imaginary components separably
+    if np.iscomplexobj(x):
+        out = np.empty_like(tmp) if out is None else out
+        transform(tmp.real, type, axes, norm, out.real, workers)
+        transform(tmp.imag, type, axes, norm, out.imag, workers)
+        return out
+
+    return transform(tmp, type, axes, norm, out, workers, orthogonalize)
+
+
+dctn = functools.partial(_r2rn, True, pfft.dct)
+dctn.__name__ = 'dctn'
+idctn = functools.partial(_r2rn, False, pfft.dct)
+idctn.__name__ = 'idctn'
+
+dstn = functools.partial(_r2rn, True, pfft.dst)
+dstn.__name__ = 'dstn'
+idstn = functools.partial(_r2rn, False, pfft.dst)
+idstn.__name__ = 'idstn'
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/.___init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/._test_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/._test_basic.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/._test_real_transforms.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/._test_real_transforms.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/__init__.py
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/test_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/test_basic.py
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index 0000000000000000000000000000000000000000..4ed1abe818ce1769f480dadebc80e588babaff87
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/test_basic.py
@@ -0,0 +1,1011 @@
+# Created by Pearu Peterson, September 2002
+
+from numpy.testing import (assert_, assert_equal, assert_array_almost_equal,
+                           assert_array_almost_equal_nulp, assert_array_less,
+                           assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+from scipy.fft._pocketfft import (ifft, fft, fftn, ifftn,
+                                  rfft, irfft, rfftn, irfftn,
+                                  hfft, ihfft, hfftn, ihfftn)
+
+from numpy import (arange, array, asarray, zeros, dot, exp, pi,
+                   swapaxes, cdouble)
+import numpy as np
+import numpy.fft
+from numpy.random import rand
+
+# "large" composite numbers supported by FFT._PYPOCKETFFT
+LARGE_COMPOSITE_SIZES = [
+    2**13,
+    2**5 * 3**5,
+    2**3 * 3**3 * 5**2,
+]
+SMALL_COMPOSITE_SIZES = [
+    2,
+    2*3*5,
+    2*2*3*3,
+]
+# prime
+LARGE_PRIME_SIZES = [
+    2011
+]
+SMALL_PRIME_SIZES = [
+    29
+]
+
+
+def _assert_close_in_norm(x, y, rtol, size, rdt):
+    # helper function for testing
+    err_msg = f"size: {size}  rdt: {rdt}"
+    assert_array_less(np.linalg.norm(x - y), rtol*np.linalg.norm(x), err_msg)
+
+
+def random(size):
+    return rand(*size)
+
+def swap_byteorder(arr):
+    """Returns the same array with swapped byteorder"""
+    dtype = arr.dtype.newbyteorder('S')
+    return arr.astype(dtype)
+
+def direct_dft(x):
+    x = asarray(x)
+    n = len(x)
+    y = zeros(n, dtype=cdouble)
+    w = -arange(n)*(2j*pi/n)
+    for i in range(n):
+        y[i] = dot(exp(i*w), x)
+    return y
+
+
+def direct_idft(x):
+    x = asarray(x)
+    n = len(x)
+    y = zeros(n, dtype=cdouble)
+    w = arange(n)*(2j*pi/n)
+    for i in range(n):
+        y[i] = dot(exp(i*w), x)/n
+    return y
+
+
+def direct_dftn(x):
+    x = asarray(x)
+    for axis in range(x.ndim):
+        x = fft(x, axis=axis)
+    return x
+
+
+def direct_idftn(x):
+    x = asarray(x)
+    for axis in range(x.ndim):
+        x = ifft(x, axis=axis)
+    return x
+
+
+def direct_rdft(x):
+    x = asarray(x)
+    n = len(x)
+    w = -arange(n)*(2j*pi/n)
+    y = zeros(n//2+1, dtype=cdouble)
+    for i in range(n//2+1):
+        y[i] = dot(exp(i*w), x)
+    return y
+
+
+def direct_irdft(x, n):
+    x = asarray(x)
+    x1 = zeros(n, dtype=cdouble)
+    for i in range(n//2+1):
+        x1[i] = x[i]
+        if i > 0 and 2*i < n:
+            x1[n-i] = np.conj(x[i])
+    return direct_idft(x1).real
+
+
+def direct_rdftn(x):
+    return fftn(rfft(x), axes=range(x.ndim - 1))
+
+
+class _TestFFTBase:
+    def setup_method(self):
+        self.cdt = None
+        self.rdt = None
+        np.random.seed(1234)
+
+    def test_definition(self):
+        x = np.array([1,2,3,4+1j,1,2,3,4+2j], dtype=self.cdt)
+        y = fft(x)
+        assert_equal(y.dtype, self.cdt)
+        y1 = direct_dft(x)
+        assert_array_almost_equal(y,y1)
+        x = np.array([1,2,3,4+0j,5], dtype=self.cdt)
+        assert_array_almost_equal(fft(x),direct_dft(x))
+
+    def test_n_argument_real(self):
+        x1 = np.array([1,2,3,4], dtype=self.rdt)
+        x2 = np.array([1,2,3,4], dtype=self.rdt)
+        y = fft([x1,x2],n=4)
+        assert_equal(y.dtype, self.cdt)
+        assert_equal(y.shape,(2,4))
+        assert_array_almost_equal(y[0],direct_dft(x1))
+        assert_array_almost_equal(y[1],direct_dft(x2))
+
+    def _test_n_argument_complex(self):
+        x1 = np.array([1,2,3,4+1j], dtype=self.cdt)
+        x2 = np.array([1,2,3,4+1j], dtype=self.cdt)
+        y = fft([x1,x2],n=4)
+        assert_equal(y.dtype, self.cdt)
+        assert_equal(y.shape,(2,4))
+        assert_array_almost_equal(y[0],direct_dft(x1))
+        assert_array_almost_equal(y[1],direct_dft(x2))
+
+    def test_djbfft(self):
+        for i in range(2,14):
+            n = 2**i
+            x = np.arange(n)
+            y = fft(x.astype(complex))
+            y2 = numpy.fft.fft(x)
+            assert_array_almost_equal(y,y2)
+            y = fft(x)
+            assert_array_almost_equal(y,y2)
+
+    def test_invalid_sizes(self):
+        assert_raises(ValueError, fft, [])
+        assert_raises(ValueError, fft, [[1,1],[2,2]], -5)
+
+
+class TestLongDoubleFFT(_TestFFTBase):
+    def setup_method(self):
+        self.cdt = np.clongdouble
+        self.rdt = np.longdouble
+
+
+class TestDoubleFFT(_TestFFTBase):
+    def setup_method(self):
+        self.cdt = np.cdouble
+        self.rdt = np.float64
+
+
+class TestSingleFFT(_TestFFTBase):
+    def setup_method(self):
+        self.cdt = np.complex64
+        self.rdt = np.float32
+
+
+class TestFloat16FFT:
+
+    def test_1_argument_real(self):
+        x1 = np.array([1, 2, 3, 4], dtype=np.float16)
+        y = fft(x1, n=4)
+        assert_equal(y.dtype, np.complex64)
+        assert_equal(y.shape, (4, ))
+        assert_array_almost_equal(y, direct_dft(x1.astype(np.float32)))
+
+    def test_n_argument_real(self):
+        x1 = np.array([1, 2, 3, 4], dtype=np.float16)
+        x2 = np.array([1, 2, 3, 4], dtype=np.float16)
+        y = fft([x1, x2], n=4)
+        assert_equal(y.dtype, np.complex64)
+        assert_equal(y.shape, (2, 4))
+        assert_array_almost_equal(y[0], direct_dft(x1.astype(np.float32)))
+        assert_array_almost_equal(y[1], direct_dft(x2.astype(np.float32)))
+
+
+class _TestIFFTBase:
+    def setup_method(self):
+        np.random.seed(1234)
+
+    def test_definition(self):
+        x = np.array([1,2,3,4+1j,1,2,3,4+2j], self.cdt)
+        y = ifft(x)
+        y1 = direct_idft(x)
+        assert_equal(y.dtype, self.cdt)
+        assert_array_almost_equal(y,y1)
+
+        x = np.array([1,2,3,4+0j,5], self.cdt)
+        assert_array_almost_equal(ifft(x),direct_idft(x))
+
+    def test_definition_real(self):
+        x = np.array([1,2,3,4,1,2,3,4], self.rdt)
+        y = ifft(x)
+        assert_equal(y.dtype, self.cdt)
+        y1 = direct_idft(x)
+        assert_array_almost_equal(y,y1)
+
+        x = np.array([1,2,3,4,5], dtype=self.rdt)
+        assert_equal(y.dtype, self.cdt)
+        assert_array_almost_equal(ifft(x),direct_idft(x))
+
+    def test_djbfft(self):
+        for i in range(2,14):
+            n = 2**i
+            x = np.arange(n)
+            y = ifft(x.astype(self.cdt))
+            y2 = numpy.fft.ifft(x.astype(self.cdt))
+            assert_allclose(y,y2, rtol=self.rtol, atol=self.atol)
+            y = ifft(x)
+            assert_allclose(y,y2, rtol=self.rtol, atol=self.atol)
+
+    def test_random_complex(self):
+        for size in [1,51,111,100,200,64,128,256,1024]:
+            x = random([size]).astype(self.cdt)
+            x = random([size]).astype(self.cdt) + 1j*x
+            y1 = ifft(fft(x))
+            y2 = fft(ifft(x))
+            assert_equal(y1.dtype, self.cdt)
+            assert_equal(y2.dtype, self.cdt)
+            assert_array_almost_equal(y1, x)
+            assert_array_almost_equal(y2, x)
+
+    def test_random_real(self):
+        for size in [1,51,111,100,200,64,128,256,1024]:
+            x = random([size]).astype(self.rdt)
+            y1 = ifft(fft(x))
+            y2 = fft(ifft(x))
+            assert_equal(y1.dtype, self.cdt)
+            assert_equal(y2.dtype, self.cdt)
+            assert_array_almost_equal(y1, x)
+            assert_array_almost_equal(y2, x)
+
+    def test_size_accuracy(self):
+        # Sanity check for the accuracy for prime and non-prime sized inputs
+        for size in LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES:
+            np.random.seed(1234)
+            x = np.random.rand(size).astype(self.rdt)
+            y = ifft(fft(x))
+            _assert_close_in_norm(x, y, self.rtol, size, self.rdt)
+            y = fft(ifft(x))
+            _assert_close_in_norm(x, y, self.rtol, size, self.rdt)
+
+            x = (x + 1j*np.random.rand(size)).astype(self.cdt)
+            y = ifft(fft(x))
+            _assert_close_in_norm(x, y, self.rtol, size, self.rdt)
+            y = fft(ifft(x))
+            _assert_close_in_norm(x, y, self.rtol, size, self.rdt)
+
+    def test_invalid_sizes(self):
+        assert_raises(ValueError, ifft, [])
+        assert_raises(ValueError, ifft, [[1,1],[2,2]], -5)
+
+
+@pytest.mark.skipif(np.longdouble is np.float64,
+                    reason="Long double is aliased to double")
+class TestLongDoubleIFFT(_TestIFFTBase):
+    def setup_method(self):
+        self.cdt = np.clongdouble
+        self.rdt = np.longdouble
+        self.rtol = 1e-10
+        self.atol = 1e-10
+
+
+class TestDoubleIFFT(_TestIFFTBase):
+    def setup_method(self):
+        self.cdt = np.complex128
+        self.rdt = np.float64
+        self.rtol = 1e-10
+        self.atol = 1e-10
+
+
+class TestSingleIFFT(_TestIFFTBase):
+    def setup_method(self):
+        self.cdt = np.complex64
+        self.rdt = np.float32
+        self.rtol = 1e-5
+        self.atol = 1e-4
+
+
+class _TestRFFTBase:
+    def setup_method(self):
+        np.random.seed(1234)
+
+    def test_definition(self):
+        for t in [[1, 2, 3, 4, 1, 2, 3, 4], [1, 2, 3, 4, 1, 2, 3, 4, 5]]:
+            x = np.array(t, dtype=self.rdt)
+            y = rfft(x)
+            y1 = direct_rdft(x)
+            assert_array_almost_equal(y,y1)
+            assert_equal(y.dtype, self.cdt)
+
+    def test_djbfft(self):
+        for i in range(2,14):
+            n = 2**i
+            x = np.arange(n)
+            y1 = np.fft.rfft(x)
+            y = rfft(x)
+            assert_array_almost_equal(y,y1)
+
+    def test_invalid_sizes(self):
+        assert_raises(ValueError, rfft, [])
+        assert_raises(ValueError, rfft, [[1,1],[2,2]], -5)
+
+    def test_complex_input(self):
+        x = np.zeros(10, dtype=self.cdt)
+        with assert_raises(TypeError, match="x must be a real sequence"):
+            rfft(x)
+
+    # See gh-5790
+    class MockSeries:
+        def __init__(self, data):
+            self.data = np.asarray(data)
+
+        def __getattr__(self, item):
+            try:
+                return getattr(self.data, item)
+            except AttributeError as e:
+                raise AttributeError("'MockSeries' object "
+                                      f"has no attribute '{item}'") from e
+
+    def test_non_ndarray_with_dtype(self):
+        x = np.array([1., 2., 3., 4., 5.])
+        xs = _TestRFFTBase.MockSeries(x)
+
+        expected = [1, 2, 3, 4, 5]
+        rfft(xs)
+
+        # Data should not have been overwritten
+        assert_equal(x, expected)
+        assert_equal(xs.data, expected)
+
+@pytest.mark.skipif(np.longdouble is np.float64,
+                    reason="Long double is aliased to double")
+class TestRFFTLongDouble(_TestRFFTBase):
+    def setup_method(self):
+        self.cdt = np.clongdouble
+        self.rdt = np.longdouble
+
+
+class TestRFFTDouble(_TestRFFTBase):
+    def setup_method(self):
+        self.cdt = np.complex128
+        self.rdt = np.float64
+
+
+class TestRFFTSingle(_TestRFFTBase):
+    def setup_method(self):
+        self.cdt = np.complex64
+        self.rdt = np.float32
+
+
+class _TestIRFFTBase:
+    def setup_method(self):
+        np.random.seed(1234)
+
+    def test_definition(self):
+        x1 = [1,2+3j,4+1j,1+2j,3+4j]
+        x1_1 = [1,2+3j,4+1j,2+3j,4,2-3j,4-1j,2-3j]
+        x1 = x1_1[:5]
+        x2_1 = [1,2+3j,4+1j,2+3j,4+5j,4-5j,2-3j,4-1j,2-3j]
+        x2 = x2_1[:5]
+
+        def _test(x, xr):
+            y = irfft(np.array(x, dtype=self.cdt), n=len(xr))
+            y1 = direct_irdft(x, len(xr))
+            assert_equal(y.dtype, self.rdt)
+            assert_array_almost_equal(y,y1, decimal=self.ndec)
+            assert_array_almost_equal(y,ifft(xr), decimal=self.ndec)
+
+        _test(x1, x1_1)
+        _test(x2, x2_1)
+
+    def test_djbfft(self):
+        for i in range(2,14):
+            n = 2**i
+            x = np.arange(-1, n, 2) + 1j * np.arange(0, n+1, 2)
+            x[0] = 0
+            if n % 2 == 0:
+                x[-1] = np.real(x[-1])
+            y1 = np.fft.irfft(x)
+            y = irfft(x)
+            assert_array_almost_equal(y,y1)
+
+    def test_random_real(self):
+        for size in [1,51,111,100,200,64,128,256,1024]:
+            x = random([size]).astype(self.rdt)
+            y1 = irfft(rfft(x), n=size)
+            y2 = rfft(irfft(x, n=(size*2-1)))
+            assert_equal(y1.dtype, self.rdt)
+            assert_equal(y2.dtype, self.cdt)
+            assert_array_almost_equal(y1, x, decimal=self.ndec, err_msg=f"size={size}")
+            assert_array_almost_equal(y2, x, decimal=self.ndec, err_msg=f"size={size}")
+
+    def test_size_accuracy(self):
+        # Sanity check for the accuracy for prime and non-prime sized inputs
+        if self.rdt == np.float32:
+            rtol = 1e-5
+        elif self.rdt == np.float64:
+            rtol = 1e-10
+
+        for size in LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES:
+            np.random.seed(1234)
+            x = np.random.rand(size).astype(self.rdt)
+            y = irfft(rfft(x), len(x))
+            _assert_close_in_norm(x, y, rtol, size, self.rdt)
+            y = rfft(irfft(x, 2 * len(x) - 1))
+            _assert_close_in_norm(x, y, rtol, size, self.rdt)
+
+    def test_invalid_sizes(self):
+        assert_raises(ValueError, irfft, [])
+        assert_raises(ValueError, irfft, [[1,1],[2,2]], -5)
+
+
+# self.ndec is bogus; we should have a assert_array_approx_equal for number of
+# significant digits
+
+@pytest.mark.skipif(np.longdouble is np.float64,
+                    reason="Long double is aliased to double")
+class TestIRFFTLongDouble(_TestIRFFTBase):
+    def setup_method(self):
+        self.cdt = np.complex128
+        self.rdt = np.float64
+        self.ndec = 14
+
+
+class TestIRFFTDouble(_TestIRFFTBase):
+    def setup_method(self):
+        self.cdt = np.complex128
+        self.rdt = np.float64
+        self.ndec = 14
+
+
+class TestIRFFTSingle(_TestIRFFTBase):
+    def setup_method(self):
+        self.cdt = np.complex64
+        self.rdt = np.float32
+        self.ndec = 5
+
+
+class TestFftnSingle:
+    def setup_method(self):
+        np.random.seed(1234)
+
+    def test_definition(self):
+        x = [[1, 2, 3],
+             [4, 5, 6],
+             [7, 8, 9]]
+        y = fftn(np.array(x, np.float32))
+        assert_(y.dtype == np.complex64,
+                msg="double precision output with single precision")
+
+        y_r = np.array(fftn(x), np.complex64)
+        assert_array_almost_equal_nulp(y, y_r)
+
+    @pytest.mark.parametrize('size', SMALL_COMPOSITE_SIZES + SMALL_PRIME_SIZES)
+    def test_size_accuracy_small(self, size):
+        rng = np.random.default_rng(1234)
+        x = rng.random((size, size)) + 1j * rng.random((size, size))
+        y1 = fftn(x.real.astype(np.float32))
+        y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)
+
+        assert_equal(y1.dtype, np.complex64)
+        assert_array_almost_equal_nulp(y1, y2, 2000)
+
+    @pytest.mark.parametrize('size', LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES)
+    def test_size_accuracy_large(self, size):
+        rng = np.random.default_rng(1234)
+        x = rng.random((size, 3)) + 1j * rng.random((size, 3))
+        y1 = fftn(x.real.astype(np.float32))
+        y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)
+
+        assert_equal(y1.dtype, np.complex64)
+        assert_array_almost_equal_nulp(y1, y2, 2000)
+
+    def test_definition_float16(self):
+        x = [[1, 2, 3],
+             [4, 5, 6],
+             [7, 8, 9]]
+        y = fftn(np.array(x, np.float16))
+        assert_equal(y.dtype, np.complex64)
+        y_r = np.array(fftn(x), np.complex64)
+        assert_array_almost_equal_nulp(y, y_r)
+
+    @pytest.mark.parametrize('size', SMALL_COMPOSITE_SIZES + SMALL_PRIME_SIZES)
+    def test_float16_input_small(self, size):
+        rng = np.random.default_rng(1234)
+        x = rng.random((size, size)) + 1j*rng.random((size, size))
+        y1 = fftn(x.real.astype(np.float16))
+        y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)
+
+        assert_equal(y1.dtype, np.complex64)
+        assert_array_almost_equal_nulp(y1, y2, 5e5)
+
+    @pytest.mark.parametrize('size', LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES)
+    def test_float16_input_large(self, size):
+        rng = np.random.default_rng(1234)
+        x = rng.random((size, 3)) + 1j*rng.random((size, 3))
+        y1 = fftn(x.real.astype(np.float16))
+        y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)
+
+        assert_equal(y1.dtype, np.complex64)
+        assert_array_almost_equal_nulp(y1, y2, 2e6)
+
+
+class TestFftn:
+    def setup_method(self):
+        np.random.seed(1234)
+
+    def test_definition(self):
+        x = [[1, 2, 3],
+             [4, 5, 6],
+             [7, 8, 9]]
+        y = fftn(x)
+        assert_array_almost_equal(y, direct_dftn(x))
+
+        x = random((20, 26))
+        assert_array_almost_equal(fftn(x), direct_dftn(x))
+
+        x = random((5, 4, 3, 20))
+        assert_array_almost_equal(fftn(x), direct_dftn(x))
+
+    def test_axes_argument(self):
+        # plane == ji_plane, x== kji_space
+        plane1 = [[1, 2, 3],
+                  [4, 5, 6],
+                  [7, 8, 9]]
+        plane2 = [[10, 11, 12],
+                  [13, 14, 15],
+                  [16, 17, 18]]
+        plane3 = [[19, 20, 21],
+                  [22, 23, 24],
+                  [25, 26, 27]]
+        ki_plane1 = [[1, 2, 3],
+                     [10, 11, 12],
+                     [19, 20, 21]]
+        ki_plane2 = [[4, 5, 6],
+                     [13, 14, 15],
+                     [22, 23, 24]]
+        ki_plane3 = [[7, 8, 9],
+                     [16, 17, 18],
+                     [25, 26, 27]]
+        jk_plane1 = [[1, 10, 19],
+                     [4, 13, 22],
+                     [7, 16, 25]]
+        jk_plane2 = [[2, 11, 20],
+                     [5, 14, 23],
+                     [8, 17, 26]]
+        jk_plane3 = [[3, 12, 21],
+                     [6, 15, 24],
+                     [9, 18, 27]]
+        kj_plane1 = [[1, 4, 7],
+                     [10, 13, 16], [19, 22, 25]]
+        kj_plane2 = [[2, 5, 8],
+                     [11, 14, 17], [20, 23, 26]]
+        kj_plane3 = [[3, 6, 9],
+                     [12, 15, 18], [21, 24, 27]]
+        ij_plane1 = [[1, 4, 7],
+                     [2, 5, 8],
+                     [3, 6, 9]]
+        ij_plane2 = [[10, 13, 16],
+                     [11, 14, 17],
+                     [12, 15, 18]]
+        ij_plane3 = [[19, 22, 25],
+                     [20, 23, 26],
+                     [21, 24, 27]]
+        ik_plane1 = [[1, 10, 19],
+                     [2, 11, 20],
+                     [3, 12, 21]]
+        ik_plane2 = [[4, 13, 22],
+                     [5, 14, 23],
+                     [6, 15, 24]]
+        ik_plane3 = [[7, 16, 25],
+                     [8, 17, 26],
+                     [9, 18, 27]]
+        ijk_space = [jk_plane1, jk_plane2, jk_plane3]
+        ikj_space = [kj_plane1, kj_plane2, kj_plane3]
+        jik_space = [ik_plane1, ik_plane2, ik_plane3]
+        jki_space = [ki_plane1, ki_plane2, ki_plane3]
+        kij_space = [ij_plane1, ij_plane2, ij_plane3]
+        x = array([plane1, plane2, plane3])
+
+        assert_array_almost_equal(fftn(x),
+                                  fftn(x, axes=(-3, -2, -1)))  # kji_space
+        assert_array_almost_equal(fftn(x), fftn(x, axes=(0, 1, 2)))
+        assert_array_almost_equal(fftn(x, axes=(0, 2)), fftn(x, axes=(0, -1)))
+        y = fftn(x, axes=(2, 1, 0))  # ijk_space
+        assert_array_almost_equal(swapaxes(y, -1, -3), fftn(ijk_space))
+        y = fftn(x, axes=(2, 0, 1))  # ikj_space
+        assert_array_almost_equal(swapaxes(swapaxes(y, -1, -3), -1, -2),
+                                  fftn(ikj_space))
+        y = fftn(x, axes=(1, 2, 0))  # jik_space
+        assert_array_almost_equal(swapaxes(swapaxes(y, -1, -3), -3, -2),
+                                  fftn(jik_space))
+        y = fftn(x, axes=(1, 0, 2))  # jki_space
+        assert_array_almost_equal(swapaxes(y, -2, -3), fftn(jki_space))
+        y = fftn(x, axes=(0, 2, 1))  # kij_space
+        assert_array_almost_equal(swapaxes(y, -2, -1), fftn(kij_space))
+
+        y = fftn(x, axes=(-2, -1))  # ji_plane
+        assert_array_almost_equal(fftn(plane1), y[0])
+        assert_array_almost_equal(fftn(plane2), y[1])
+        assert_array_almost_equal(fftn(plane3), y[2])
+
+        y = fftn(x, axes=(1, 2))  # ji_plane
+        assert_array_almost_equal(fftn(plane1), y[0])
+        assert_array_almost_equal(fftn(plane2), y[1])
+        assert_array_almost_equal(fftn(plane3), y[2])
+
+        y = fftn(x, axes=(-3, -2))  # kj_plane
+        assert_array_almost_equal(fftn(x[:, :, 0]), y[:, :, 0])
+        assert_array_almost_equal(fftn(x[:, :, 1]), y[:, :, 1])
+        assert_array_almost_equal(fftn(x[:, :, 2]), y[:, :, 2])
+
+        y = fftn(x, axes=(-3, -1))  # ki_plane
+        assert_array_almost_equal(fftn(x[:, 0, :]), y[:, 0, :])
+        assert_array_almost_equal(fftn(x[:, 1, :]), y[:, 1, :])
+        assert_array_almost_equal(fftn(x[:, 2, :]), y[:, 2, :])
+
+        y = fftn(x, axes=(-1, -2))  # ij_plane
+        assert_array_almost_equal(fftn(ij_plane1), swapaxes(y[0], -2, -1))
+        assert_array_almost_equal(fftn(ij_plane2), swapaxes(y[1], -2, -1))
+        assert_array_almost_equal(fftn(ij_plane3), swapaxes(y[2], -2, -1))
+
+        y = fftn(x, axes=(-1, -3))  # ik_plane
+        assert_array_almost_equal(fftn(ik_plane1),
+                                  swapaxes(y[:, 0, :], -1, -2))
+        assert_array_almost_equal(fftn(ik_plane2),
+                                  swapaxes(y[:, 1, :], -1, -2))
+        assert_array_almost_equal(fftn(ik_plane3),
+                                  swapaxes(y[:, 2, :], -1, -2))
+
+        y = fftn(x, axes=(-2, -3))  # jk_plane
+        assert_array_almost_equal(fftn(jk_plane1),
+                                  swapaxes(y[:, :, 0], -1, -2))
+        assert_array_almost_equal(fftn(jk_plane2),
+                                  swapaxes(y[:, :, 1], -1, -2))
+        assert_array_almost_equal(fftn(jk_plane3),
+                                  swapaxes(y[:, :, 2], -1, -2))
+
+        y = fftn(x, axes=(-1,))  # i_line
+        for i in range(3):
+            for j in range(3):
+                assert_array_almost_equal(fft(x[i, j, :]), y[i, j, :])
+        y = fftn(x, axes=(-2,))  # j_line
+        for i in range(3):
+            for j in range(3):
+                assert_array_almost_equal(fft(x[i, :, j]), y[i, :, j])
+        y = fftn(x, axes=(0,))  # k_line
+        for i in range(3):
+            for j in range(3):
+                assert_array_almost_equal(fft(x[:, i, j]), y[:, i, j])
+
+        y = fftn(x, axes=())  # point
+        assert_array_almost_equal(y, x)
+
+    def test_shape_argument(self):
+        small_x = [[1, 2, 3],
+                   [4, 5, 6]]
+        large_x1 = [[1, 2, 3, 0],
+                    [4, 5, 6, 0],
+                    [0, 0, 0, 0],
+                    [0, 0, 0, 0]]
+
+        y = fftn(small_x, s=(4, 4))
+        assert_array_almost_equal(y, fftn(large_x1))
+
+        y = fftn(small_x, s=(3, 4))
+        assert_array_almost_equal(y, fftn(large_x1[:-1]))
+
+    def test_shape_axes_argument(self):
+        small_x = [[1, 2, 3],
+                   [4, 5, 6],
+                   [7, 8, 9]]
+        large_x1 = array([[1, 2, 3, 0],
+                          [4, 5, 6, 0],
+                          [7, 8, 9, 0],
+                          [0, 0, 0, 0]])
+        y = fftn(small_x, s=(4, 4), axes=(-2, -1))
+        assert_array_almost_equal(y, fftn(large_x1))
+        y = fftn(small_x, s=(4, 4), axes=(-1, -2))
+
+        assert_array_almost_equal(y, swapaxes(
+            fftn(swapaxes(large_x1, -1, -2)), -1, -2))
+
+    def test_shape_axes_argument2(self):
+        # Change shape of the last axis
+        x = numpy.random.random((10, 5, 3, 7))
+        y = fftn(x, axes=(-1,), s=(8,))
+        assert_array_almost_equal(y, fft(x, axis=-1, n=8))
+
+        # Change shape of an arbitrary axis which is not the last one
+        x = numpy.random.random((10, 5, 3, 7))
+        y = fftn(x, axes=(-2,), s=(8,))
+        assert_array_almost_equal(y, fft(x, axis=-2, n=8))
+
+        # Change shape of axes: cf #244, where shape and axes were mixed up
+        x = numpy.random.random((4, 4, 2))
+        y = fftn(x, axes=(-3, -2), s=(8, 8))
+        assert_array_almost_equal(y,
+                                  numpy.fft.fftn(x, axes=(-3, -2), s=(8, 8)))
+
+    def test_shape_argument_more(self):
+        x = zeros((4, 4, 2))
+        with assert_raises(ValueError,
+                           match="shape requires more axes than are present"):
+            fftn(x, s=(8, 8, 2, 1))
+
+    def test_invalid_sizes(self):
+        with assert_raises(ValueError,
+                           match="invalid number of data points"
+                           r" \(\[1, 0\]\) specified"):
+            fftn([[]])
+
+        with assert_raises(ValueError,
+                           match="invalid number of data points"
+                           r" \(\[4, -3\]\) specified"):
+            fftn([[1, 1], [2, 2]], (4, -3))
+
+    def test_no_axes(self):
+        x = numpy.random.random((2,2,2))
+        assert_allclose(fftn(x, axes=[]), x, atol=1e-7)
+
+    def test_regression_244(self):
+        """FFT returns wrong result with axes parameter."""
+        # fftn (and hence fft2) used to break when both axes and shape were used
+        x = numpy.ones((4, 4, 2))
+        y = fftn(x, s=(8, 8), axes=(-3, -2))
+        y_r = numpy.fft.fftn(x, s=(8, 8), axes=(-3, -2))
+        assert_allclose(y, y_r)
+
+
+class TestIfftn:
+    dtype = None
+    cdtype = None
+
+    def setup_method(self):
+        np.random.seed(1234)
+
+    @pytest.mark.parametrize('dtype,cdtype,maxnlp',
+                             [(np.float64, np.complex128, 2000),
+                              (np.float32, np.complex64, 3500)])
+    def test_definition(self, dtype, cdtype, maxnlp):
+        rng = np.random.default_rng(1234)
+        x = np.array([[1, 2, 3],
+                      [4, 5, 6],
+                      [7, 8, 9]], dtype=dtype)
+        y = ifftn(x)
+        assert_equal(y.dtype, cdtype)
+        assert_array_almost_equal_nulp(y, direct_idftn(x), maxnlp)
+
+        x = rng.random((20, 26))
+        assert_array_almost_equal_nulp(ifftn(x), direct_idftn(x), maxnlp)
+
+        x = rng.random((5, 4, 3, 20))
+        assert_array_almost_equal_nulp(ifftn(x), direct_idftn(x), maxnlp)
+
+    @pytest.mark.parametrize('maxnlp', [2000, 3500])
+    @pytest.mark.parametrize('size', [1, 2, 51, 32, 64, 92])
+    def test_random_complex(self, maxnlp, size):
+        rng = np.random.default_rng(1234)
+        x = rng.random([size, size]) + 1j * rng.random([size, size])
+        assert_array_almost_equal_nulp(ifftn(fftn(x)), x, maxnlp)
+        assert_array_almost_equal_nulp(fftn(ifftn(x)), x, maxnlp)
+
+    def test_invalid_sizes(self):
+        with assert_raises(ValueError,
+                           match="invalid number of data points"
+                           r" \(\[1, 0\]\) specified"):
+            ifftn([[]])
+
+        with assert_raises(ValueError,
+                           match="invalid number of data points"
+                           r" \(\[4, -3\]\) specified"):
+            ifftn([[1, 1], [2, 2]], (4, -3))
+
+    def test_no_axes(self):
+        x = numpy.random.random((2,2,2))
+        assert_allclose(ifftn(x, axes=[]), x, atol=1e-7)
+
+class TestRfftn:
+    dtype = None
+    cdtype = None
+
+    def setup_method(self):
+        np.random.seed(1234)
+
+    @pytest.mark.parametrize('dtype,cdtype,maxnlp',
+                             [(np.float64, np.complex128, 2000),
+                              (np.float32, np.complex64, 3500)])
+    def test_definition(self, dtype, cdtype, maxnlp):
+        rng = np.random.default_rng(1234)
+        x = np.array([[1, 2, 3],
+                      [4, 5, 6],
+                      [7, 8, 9]], dtype=dtype)
+        y = rfftn(x)
+        assert_equal(y.dtype, cdtype)
+        assert_array_almost_equal_nulp(y, direct_rdftn(x), maxnlp)
+
+        x = rng.random((20, 26))
+        assert_array_almost_equal_nulp(rfftn(x), direct_rdftn(x), maxnlp)
+
+        x = rng.random((5, 4, 3, 20))
+        assert_array_almost_equal_nulp(rfftn(x), direct_rdftn(x), maxnlp)
+
+    @pytest.mark.parametrize('size', [1, 2, 51, 32, 64, 92])
+    def test_random(self, size):
+        rng = np.random.default_rng(1234)
+        x = rng.random([size, size])
+        assert_allclose(irfftn(rfftn(x), x.shape), x, atol=1e-10)
+
+    @pytest.mark.parametrize('func', [rfftn, irfftn])
+    def test_invalid_sizes(self, func):
+        with assert_raises(ValueError,
+                           match="invalid number of data points"
+                           r" \(\[1, 0\]\) specified"):
+            func([[]])
+
+        with assert_raises(ValueError,
+                           match="invalid number of data points"
+                           r" \(\[4, -3\]\) specified"):
+            func([[1, 1], [2, 2]], (4, -3))
+
+    @pytest.mark.parametrize('func', [rfftn, irfftn])
+    def test_no_axes(self, func):
+        with assert_raises(ValueError,
+                           match="at least 1 axis must be transformed"):
+            func([], axes=[])
+
+    def test_complex_input(self):
+        with assert_raises(TypeError, match="x must be a real sequence"):
+            rfftn(np.zeros(10, dtype=np.complex64))
+
+
+class FakeArray:
+    def __init__(self, data):
+        self._data = data
+        self.__array_interface__ = data.__array_interface__
+
+
+class FakeArray2:
+    def __init__(self, data):
+        self._data = data
+
+    def __array__(self, dtype=None, copy=None):
+        return self._data
+
+# TODO: Is this test actually valuable? The behavior it's testing shouldn't be
+# relied upon by users except for overwrite_x = False
+class TestOverwrite:
+    """Check input overwrite behavior of the FFT functions."""
+
+    real_dtypes = [np.float32, np.float64, np.longdouble]
+    dtypes = real_dtypes + [np.complex64, np.complex128, np.clongdouble]
+    fftsizes = [8, 16, 32]
+
+    def _check(self, x, routine, fftsize, axis, overwrite_x, should_overwrite):
+        x2 = x.copy()
+        for fake in [lambda x: x, FakeArray, FakeArray2]:
+            routine(fake(x2), fftsize, axis, overwrite_x=overwrite_x)
+
+            sig = (f"{routine.__name__}({x.dtype}{x.shape!r}, {fftsize!r}, "
+                   f"axis={axis!r}, overwrite_x={overwrite_x!r})")
+            if not should_overwrite:
+                assert_equal(x2, x, err_msg=f"spurious overwrite in {sig}")
+
+    def _check_1d(self, routine, dtype, shape, axis, overwritable_dtypes,
+                  fftsize, overwrite_x):
+        np.random.seed(1234)
+        if np.issubdtype(dtype, np.complexfloating):
+            data = np.random.randn(*shape) + 1j*np.random.randn(*shape)
+        else:
+            data = np.random.randn(*shape)
+        data = data.astype(dtype)
+
+        should_overwrite = (overwrite_x
+                            and dtype in overwritable_dtypes
+                            and fftsize <= shape[axis])
+        self._check(data, routine, fftsize, axis,
+                    overwrite_x=overwrite_x,
+                    should_overwrite=should_overwrite)
+
+    @pytest.mark.parametrize('dtype', dtypes)
+    @pytest.mark.parametrize('fftsize', fftsizes)
+    @pytest.mark.parametrize('overwrite_x', [True, False])
+    @pytest.mark.parametrize('shape,axes', [((16,), -1),
+                                            ((16, 2), 0),
+                                            ((2, 16), 1)])
+    def test_fft_ifft(self, dtype, fftsize, overwrite_x, shape, axes):
+        overwritable = (np.clongdouble, np.complex128, np.complex64)
+        self._check_1d(fft, dtype, shape, axes, overwritable,
+                       fftsize, overwrite_x)
+        self._check_1d(ifft, dtype, shape, axes, overwritable,
+                       fftsize, overwrite_x)
+
+    @pytest.mark.parametrize('dtype', real_dtypes)
+    @pytest.mark.parametrize('fftsize', fftsizes)
+    @pytest.mark.parametrize('overwrite_x', [True, False])
+    @pytest.mark.parametrize('shape,axes', [((16,), -1),
+                                            ((16, 2), 0),
+                                            ((2, 16), 1)])
+    def test_rfft_irfft(self, dtype, fftsize, overwrite_x, shape, axes):
+        overwritable = self.real_dtypes
+        self._check_1d(irfft, dtype, shape, axes, overwritable,
+                       fftsize, overwrite_x)
+        self._check_1d(rfft, dtype, shape, axes, overwritable,
+                       fftsize, overwrite_x)
+
+    def _check_nd_one(self, routine, dtype, shape, axes, overwritable_dtypes,
+                      overwrite_x):
+        np.random.seed(1234)
+        if np.issubdtype(dtype, np.complexfloating):
+            data = np.random.randn(*shape) + 1j*np.random.randn(*shape)
+        else:
+            data = np.random.randn(*shape)
+        data = data.astype(dtype)
+
+        def fftshape_iter(shp):
+            if len(shp) <= 0:
+                yield ()
+            else:
+                for j in (shp[0]//2, shp[0], shp[0]*2):
+                    for rest in fftshape_iter(shp[1:]):
+                        yield (j,) + rest
+
+        def part_shape(shape, axes):
+            if axes is None:
+                return shape
+            else:
+                return tuple(np.take(shape, axes))
+
+        def should_overwrite(data, shape, axes):
+            s = part_shape(data.shape, axes)
+            return (overwrite_x and
+                    np.prod(shape) <= np.prod(s)
+                    and dtype in overwritable_dtypes)
+
+        for fftshape in fftshape_iter(part_shape(shape, axes)):
+            self._check(data, routine, fftshape, axes,
+                        overwrite_x=overwrite_x,
+                        should_overwrite=should_overwrite(data, fftshape, axes))
+            if data.ndim > 1:
+                # check fortran order
+                self._check(data.T, routine, fftshape, axes,
+                            overwrite_x=overwrite_x,
+                            should_overwrite=should_overwrite(
+                                data.T, fftshape, axes))
+
+    @pytest.mark.parametrize('dtype', dtypes)
+    @pytest.mark.parametrize('overwrite_x', [True, False])
+    @pytest.mark.parametrize('shape,axes', [((16,), None),
+                                            ((16,), (0,)),
+                                            ((16, 2), (0,)),
+                                            ((2, 16), (1,)),
+                                            ((8, 16), None),
+                                            ((8, 16), (0, 1)),
+                                            ((8, 16, 2), (0, 1)),
+                                            ((8, 16, 2), (1, 2)),
+                                            ((8, 16, 2), (0,)),
+                                            ((8, 16, 2), (1,)),
+                                            ((8, 16, 2), (2,)),
+                                            ((8, 16, 2), None),
+                                            ((8, 16, 2), (0, 1, 2))])
+    def test_fftn_ifftn(self, dtype, overwrite_x, shape, axes):
+        overwritable = (np.clongdouble, np.complex128, np.complex64)
+        self._check_nd_one(fftn, dtype, shape, axes, overwritable,
+                           overwrite_x)
+        self._check_nd_one(ifftn, dtype, shape, axes, overwritable,
+                           overwrite_x)
+
+
+@pytest.mark.parametrize('func', [fft, ifft, fftn, ifftn,
+                                 rfft, irfft, rfftn, irfftn])
+def test_invalid_norm(func):
+    x = np.arange(10, dtype=float)
+    with assert_raises(ValueError,
+                       match='Invalid norm value \'o\', should be'
+                             ' "backward", "ortho" or "forward"'):
+        func(x, norm='o')
+
+
+@pytest.mark.parametrize('func', [fft, ifft, fftn, ifftn,
+                                   irfft, irfftn, hfft, hfftn])
+def test_swapped_byte_order_complex(func):
+    rng = np.random.RandomState(1234)
+    x = rng.rand(10) + 1j * rng.rand(10)
+    assert_allclose(func(swap_byteorder(x)), func(x))
+
+
+@pytest.mark.parametrize('func', [ihfft, ihfftn, rfft, rfftn])
+def test_swapped_byte_order_real(func):
+    rng = np.random.RandomState(1234)
+    x = rng.rand(10)
+    assert_allclose(func(swap_byteorder(x)), func(x))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/test_real_transforms.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/test_real_transforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..16477375397e05ccbf7b87f84d66b1d450dcb3bd
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_pocketfft/tests/test_real_transforms.py
@@ -0,0 +1,506 @@
+from os.path import join, dirname
+from collections.abc import Callable
+from threading import Lock
+
+import numpy as np
+from numpy.testing import (
+    assert_array_almost_equal, assert_equal, assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+
+from scipy.fft._pocketfft.realtransforms import (
+    dct, idct, dst, idst, dctn, idctn, dstn, idstn)
+
+fftpack_test_dir = join(dirname(__file__), '..', '..', '..', 'fftpack', 'tests')
+
+MDATA_COUNT = 8
+FFTWDATA_COUNT = 14
+
+
+def is_longdouble_binary_compatible():
+    try:
+        one = np.frombuffer(
+            b'\x00\x00\x00\x00\x00\x00\x00\x80\xff\x3f\x00\x00\x00\x00\x00\x00',
+            dtype=' decimal
+dec_map: DecMapType = {
+    # DCT
+    (dct, np.float64, 1): 13,
+    (dct, np.float32, 1): 6,
+
+    (dct, np.float64, 2): 14,
+    (dct, np.float32, 2): 5,
+
+    (dct, np.float64, 3): 14,
+    (dct, np.float32, 3): 5,
+
+    (dct, np.float64, 4): 13,
+    (dct, np.float32, 4): 6,
+
+    # IDCT
+    (idct, np.float64, 1): 14,
+    (idct, np.float32, 1): 6,
+
+    (idct, np.float64, 2): 14,
+    (idct, np.float32, 2): 5,
+
+    (idct, np.float64, 3): 14,
+    (idct, np.float32, 3): 5,
+
+    (idct, np.float64, 4): 14,
+    (idct, np.float32, 4): 6,
+
+    # DST
+    (dst, np.float64, 1): 13,
+    (dst, np.float32, 1): 6,
+
+    (dst, np.float64, 2): 14,
+    (dst, np.float32, 2): 6,
+
+    (dst, np.float64, 3): 14,
+    (dst, np.float32, 3): 7,
+
+    (dst, np.float64, 4): 13,
+    (dst, np.float32, 4): 5,
+
+    # IDST
+    (idst, np.float64, 1): 14,
+    (idst, np.float32, 1): 6,
+
+    (idst, np.float64, 2): 14,
+    (idst, np.float32, 2): 6,
+
+    (idst, np.float64, 3): 14,
+    (idst, np.float32, 3): 6,
+
+    (idst, np.float64, 4): 14,
+    (idst, np.float32, 4): 6,
+}
+
+for k,v in dec_map.copy().items():
+    if k[1] == np.float64:
+        dec_map[(k[0], np.longdouble, k[2])] = v
+    elif k[1] == np.float32:
+        dec_map[(k[0], int, k[2])] = v
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+@pytest.mark.parametrize('type', [1, 2, 3, 4])
+class TestDCT:
+    def test_definition(self, rdt, type, fftwdata_size,
+                        reference_data, ref_lock):
+        with ref_lock:
+            x, yr, dt = fftw_dct_ref(type, fftwdata_size, rdt, reference_data)
+        y = dct(x, type=type)
+        assert_equal(y.dtype, dt)
+        dec = dec_map[(dct, rdt, type)]
+        assert_allclose(y, yr, rtol=0., atol=np.max(yr)*10**(-dec))
+
+    @pytest.mark.parametrize('size', [7, 8, 9, 16, 32, 64])
+    def test_axis(self, rdt, type, size):
+        nt = 2
+        dec = dec_map[(dct, rdt, type)]
+        x = np.random.randn(nt, size)
+        y = dct(x, type=type)
+        for j in range(nt):
+            assert_array_almost_equal(y[j], dct(x[j], type=type),
+                                      decimal=dec)
+
+        x = x.T
+        y = dct(x, axis=0, type=type)
+        for j in range(nt):
+            assert_array_almost_equal(y[:,j], dct(x[:,j], type=type),
+                                      decimal=dec)
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+def test_dct1_definition_ortho(rdt, mdata_x):
+    # Test orthornomal mode.
+    dec = dec_map[(dct, rdt, 1)]
+    x = np.array(mdata_x, dtype=rdt)
+    dt = np.result_type(np.float32, rdt)
+    y = dct(x, norm='ortho', type=1)
+    y2 = naive_dct1(x, norm='ortho')
+    assert_equal(y.dtype, dt)
+    assert_allclose(y, y2, rtol=0., atol=np.max(y2)*10**(-dec))
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+def test_dct2_definition_matlab(mdata_xy, rdt):
+    # Test correspondence with matlab (orthornomal mode).
+    dt = np.result_type(np.float32, rdt)
+    x = np.array(mdata_xy[0], dtype=dt)
+
+    yr = mdata_xy[1]
+    y = dct(x, norm="ortho", type=2)
+    dec = dec_map[(dct, rdt, 2)]
+    assert_equal(y.dtype, dt)
+    assert_array_almost_equal(y, yr, decimal=dec)
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+def test_dct3_definition_ortho(mdata_x, rdt):
+    # Test orthornomal mode.
+    x = np.array(mdata_x, dtype=rdt)
+    dt = np.result_type(np.float32, rdt)
+    y = dct(x, norm='ortho', type=2)
+    xi = dct(y, norm="ortho", type=3)
+    dec = dec_map[(dct, rdt, 3)]
+    assert_equal(xi.dtype, dt)
+    assert_array_almost_equal(xi, x, decimal=dec)
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+def test_dct4_definition_ortho(mdata_x, rdt):
+    # Test orthornomal mode.
+    x = np.array(mdata_x, dtype=rdt)
+    dt = np.result_type(np.float32, rdt)
+    y = dct(x, norm='ortho', type=4)
+    y2 = naive_dct4(x, norm='ortho')
+    dec = dec_map[(dct, rdt, 4)]
+    assert_equal(y.dtype, dt)
+    assert_allclose(y, y2, rtol=0., atol=np.max(y2)*10**(-dec))
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+@pytest.mark.parametrize('type', [1, 2, 3, 4])
+def test_idct_definition(fftwdata_size, rdt, type, reference_data, ref_lock):
+    with ref_lock:
+        xr, yr, dt = fftw_dct_ref(type, fftwdata_size, rdt, reference_data)
+    x = idct(yr, type=type)
+    dec = dec_map[(idct, rdt, type)]
+    assert_equal(x.dtype, dt)
+    assert_allclose(x, xr, rtol=0., atol=np.max(xr)*10**(-dec))
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+@pytest.mark.parametrize('type', [1, 2, 3, 4])
+def test_definition(fftwdata_size, rdt, type, reference_data, ref_lock):
+    with ref_lock:
+        xr, yr, dt = fftw_dst_ref(type, fftwdata_size, rdt, reference_data)
+    y = dst(xr, type=type)
+    dec = dec_map[(dst, rdt, type)]
+    assert_equal(y.dtype, dt)
+    assert_allclose(y, yr, rtol=0., atol=np.max(yr)*10**(-dec))
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+def test_dst1_definition_ortho(rdt, mdata_x):
+    # Test orthornomal mode.
+    dec = dec_map[(dst, rdt, 1)]
+    x = np.array(mdata_x, dtype=rdt)
+    dt = np.result_type(np.float32, rdt)
+    y = dst(x, norm='ortho', type=1)
+    y2 = naive_dst1(x, norm='ortho')
+    assert_equal(y.dtype, dt)
+    assert_allclose(y, y2, rtol=0., atol=np.max(y2)*10**(-dec))
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+def test_dst4_definition_ortho(rdt, mdata_x):
+    # Test orthornomal mode.
+    dec = dec_map[(dst, rdt, 4)]
+    x = np.array(mdata_x, dtype=rdt)
+    dt = np.result_type(np.float32, rdt)
+    y = dst(x, norm='ortho', type=4)
+    y2 = naive_dst4(x, norm='ortho')
+    assert_equal(y.dtype, dt)
+    assert_array_almost_equal(y, y2, decimal=dec)
+
+
+@pytest.mark.parametrize('rdt', [np.longdouble, np.float64, np.float32, int])
+@pytest.mark.parametrize('type', [1, 2, 3, 4])
+def test_idst_definition(fftwdata_size, rdt, type, reference_data, ref_lock):
+    with ref_lock:
+        xr, yr, dt = fftw_dst_ref(type, fftwdata_size, rdt, reference_data)
+    x = idst(yr, type=type)
+    dec = dec_map[(idst, rdt, type)]
+    assert_equal(x.dtype, dt)
+    assert_allclose(x, xr, rtol=0., atol=np.max(xr)*10**(-dec))
+
+
+@pytest.mark.parametrize('routine', [dct, dst, idct, idst])
+@pytest.mark.parametrize('dtype', [np.float32, np.float64, np.longdouble])
+@pytest.mark.parametrize('shape, axis', [
+    ((16,), -1), ((16, 2), 0), ((2, 16), 1)
+])
+@pytest.mark.parametrize('type', [1, 2, 3, 4])
+@pytest.mark.parametrize('overwrite_x', [True, False])
+@pytest.mark.parametrize('norm', [None, 'ortho'])
+def test_overwrite(routine, dtype, shape, axis, type, norm, overwrite_x):
+    # Check input overwrite behavior
+    np.random.seed(1234)
+    if np.issubdtype(dtype, np.complexfloating):
+        x = np.random.randn(*shape) + 1j*np.random.randn(*shape)
+    else:
+        x = np.random.randn(*shape)
+    x = x.astype(dtype)
+    x2 = x.copy()
+    routine(x2, type, None, axis, norm, overwrite_x=overwrite_x)
+
+    sig = (f"{routine.__name__}({x.dtype}{x.shape!r}, {None!r}, axis={axis!r}, "
+           f"overwrite_x={overwrite_x!r})")
+    if not overwrite_x:
+        assert_equal(x2, x, err_msg=f"spurious overwrite in {sig}")
+
+
+class Test_DCTN_IDCTN:
+    dec = 14
+    dct_type = [1, 2, 3, 4]
+    norms = [None, 'backward', 'ortho', 'forward']
+    rstate = np.random.RandomState(1234)
+    shape = (32, 16)
+    data = rstate.randn(*shape)
+
+    @pytest.mark.parametrize('fforward,finverse', [(dctn, idctn),
+                                                   (dstn, idstn)])
+    @pytest.mark.parametrize('axes', [None,
+                                      1, (1,), [1],
+                                      0, (0,), [0],
+                                      (0, 1), [0, 1],
+                                      (-2, -1), [-2, -1]])
+    @pytest.mark.parametrize('dct_type', dct_type)
+    @pytest.mark.parametrize('norm', ['ortho'])
+    def test_axes_round_trip(self, fforward, finverse, axes, dct_type, norm):
+        tmp = fforward(self.data, type=dct_type, axes=axes, norm=norm)
+        tmp = finverse(tmp, type=dct_type, axes=axes, norm=norm)
+        assert_array_almost_equal(self.data, tmp, decimal=12)
+
+    @pytest.mark.parametrize('funcn,func', [(dctn, dct), (dstn, dst)])
+    @pytest.mark.parametrize('dct_type', dct_type)
+    @pytest.mark.parametrize('norm', norms)
+    def test_dctn_vs_2d_reference(self, funcn, func, dct_type, norm):
+        y1 = funcn(self.data, type=dct_type, axes=None, norm=norm)
+        y2 = ref_2d(func, self.data, type=dct_type, norm=norm)
+        assert_array_almost_equal(y1, y2, decimal=11)
+
+    @pytest.mark.parametrize('funcn,func', [(idctn, idct), (idstn, idst)])
+    @pytest.mark.parametrize('dct_type', dct_type)
+    @pytest.mark.parametrize('norm', norms)
+    def test_idctn_vs_2d_reference(self, funcn, func, dct_type, norm):
+        fdata = dctn(self.data, type=dct_type, norm=norm)
+        y1 = funcn(fdata, type=dct_type, norm=norm)
+        y2 = ref_2d(func, fdata, type=dct_type, norm=norm)
+        assert_array_almost_equal(y1, y2, decimal=11)
+
+    @pytest.mark.parametrize('fforward,finverse', [(dctn, idctn),
+                                                   (dstn, idstn)])
+    def test_axes_and_shape(self, fforward, finverse):
+        with assert_raises(ValueError,
+                           match="when given, axes and shape arguments"
+                           " have to be of the same length"):
+            fforward(self.data, s=self.data.shape[0], axes=(0, 1))
+
+        with assert_raises(ValueError,
+                           match="when given, axes and shape arguments"
+                           " have to be of the same length"):
+            fforward(self.data, s=self.data.shape, axes=0)
+
+    @pytest.mark.parametrize('fforward', [dctn, dstn])
+    def test_shape(self, fforward):
+        tmp = fforward(self.data, s=(128, 128), axes=None)
+        assert_equal(tmp.shape, (128, 128))
+
+    @pytest.mark.parametrize('fforward,finverse', [(dctn, idctn),
+                                                   (dstn, idstn)])
+    @pytest.mark.parametrize('axes', [1, (1,), [1],
+                                      0, (0,), [0]])
+    def test_shape_is_none_with_axes(self, fforward, finverse, axes):
+        tmp = fforward(self.data, s=None, axes=axes, norm='ortho')
+        tmp = finverse(tmp, s=None, axes=axes, norm='ortho')
+        assert_array_almost_equal(self.data, tmp, decimal=self.dec)
+
+
+@pytest.mark.parametrize('func', [dct, dctn, idct, idctn,
+                                  dst, dstn, idst, idstn])
+def test_swapped_byte_order(func):
+    rng = np.random.RandomState(1234)
+    x = rng.rand(10)
+    swapped_dt = x.dtype.newbyteorder('S')
+    assert_allclose(func(x.astype(swapped_dt)), func(x))
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_realtransforms.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_realtransforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..c18da398fa2b7f7449022c4874e0694d9a34e984
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_realtransforms.py
@@ -0,0 +1,717 @@
+from ._basic import _dispatch
+from scipy._lib.uarray import Dispatchable
+from scipy._lib._array_api import xp_capabilities
+import numpy as np
+
+__all__ = ['dct', 'idct', 'dst', 'idst', 'dctn', 'idctn', 'dstn', 'idstn']
+
+
+@xp_capabilities(cpu_only=True, allow_dask_compute=True)
+@_dispatch
+def dctn(x, type=2, s=None, axes=None, norm=None, overwrite_x=False,
+         workers=None, *, orthogonalize=None):
+    """
+    Return multidimensional Discrete Cosine Transform along the specified axes.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DCT (see Notes). Default type is 2.
+    s : int or array_like of ints or None, optional
+        The shape of the result. If both `s` and `axes` (see below) are None,
+        `s` is ``x.shape``; if `s` is None but `axes` is not None, then `s` is
+        ``numpy.take(x.shape, axes, axis=0)``.
+        If ``s[i] > x.shape[i]``, the ith dimension of the input is padded with zeros.
+        If ``s[i] < x.shape[i]``, the ith dimension of the input is truncated to length
+        ``s[i]``.
+        If any element of `s` is -1, the size of the corresponding dimension of
+        `x` is used.
+    axes : int or array_like of ints or None, optional
+        Axes over which the DCT is computed. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see Notes). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    orthogonalize : bool, optional
+        Whether to use the orthogonalized DCT variant (see Notes).
+        Defaults to ``True`` when ``norm="ortho"`` and ``False`` otherwise.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    idctn : Inverse multidimensional DCT
+
+    Notes
+    -----
+    For full details of the DCT types and normalization modes, as well as
+    references, see `dct`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fft import dctn, idctn
+    >>> rng = np.random.default_rng()
+    >>> y = rng.standard_normal((16, 16))
+    >>> np.allclose(y, idctn(dctn(y)))
+    True
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(cpu_only=True, allow_dask_compute=True)
+@_dispatch
+def idctn(x, type=2, s=None, axes=None, norm=None, overwrite_x=False,
+          workers=None, orthogonalize=None):
+    """
+    Return multidimensional Inverse Discrete Cosine Transform along the specified axes.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DCT (see Notes). Default type is 2.
+    s : int or array_like of ints or None, optional
+        The shape of the result.  If both `s` and `axes` (see below) are
+        None, `s` is ``x.shape``; if `s` is None but `axes` is
+        not None, then `s` is ``numpy.take(x.shape, axes, axis=0)``.
+        If ``s[i] > x.shape[i]``, the ith dimension of the input is padded with zeros.
+        If ``s[i] < x.shape[i]``, the ith dimension of the input is truncated to length
+        ``s[i]``.
+        If any element of `s` is -1, the size of the corresponding dimension of
+        `x` is used.
+    axes : int or array_like of ints or None, optional
+        Axes over which the IDCT is computed. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see Notes). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    orthogonalize : bool, optional
+        Whether to use the orthogonalized IDCT variant (see Notes).
+        Defaults to ``True`` when ``norm="ortho"`` and ``False`` otherwise.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    dctn : multidimensional DCT
+
+    Notes
+    -----
+    For full details of the IDCT types and normalization modes, as well as
+    references, see `idct`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fft import dctn, idctn
+    >>> rng = np.random.default_rng()
+    >>> y = rng.standard_normal((16, 16))
+    >>> np.allclose(y, idctn(dctn(y)))
+    True
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(cpu_only=True, allow_dask_compute=True)
+@_dispatch
+def dstn(x, type=2, s=None, axes=None, norm=None, overwrite_x=False,
+         workers=None, orthogonalize=None):
+    """
+    Return multidimensional Discrete Sine Transform along the specified axes.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DST (see Notes). Default type is 2.
+    s : int or array_like of ints or None, optional
+        The shape of the result.  If both `s` and `axes` (see below) are None,
+        `s` is ``x.shape``; if `s` is None but `axes` is not None, then `s` is
+        ``numpy.take(x.shape, axes, axis=0)``.
+        If ``s[i] > x.shape[i]``, the ith dimension of the input is padded with zeros.
+        If ``s[i] < x.shape[i]``, the ith dimension of the input is truncated to length
+        ``s[i]``.
+        If any element of `shape` is -1, the size of the corresponding dimension
+        of `x` is used.
+    axes : int or array_like of ints or None, optional
+        Axes over which the DST is computed. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see Notes). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    orthogonalize : bool, optional
+        Whether to use the orthogonalized DST variant (see Notes).
+        Defaults to ``True`` when ``norm="ortho"`` and ``False`` otherwise.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    idstn : Inverse multidimensional DST
+
+    Notes
+    -----
+    For full details of the DST types and normalization modes, as well as
+    references, see `dst`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fft import dstn, idstn
+    >>> rng = np.random.default_rng()
+    >>> y = rng.standard_normal((16, 16))
+    >>> np.allclose(y, idstn(dstn(y)))
+    True
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(cpu_only=True, allow_dask_compute=True)
+@_dispatch
+def idstn(x, type=2, s=None, axes=None, norm=None, overwrite_x=False,
+          workers=None, orthogonalize=None):
+    """
+    Return multidimensional Inverse Discrete Sine Transform along the specified axes.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DST (see Notes). Default type is 2.
+    s : int or array_like of ints or None, optional
+        The shape of the result.  If both `s` and `axes` (see below) are None,
+        `s` is ``x.shape``; if `s` is None but `axes` is not None, then `s` is
+        ``numpy.take(x.shape, axes, axis=0)``.
+        If ``s[i] > x.shape[i]``, the ith dimension of the input is padded with zeros.
+        If ``s[i] < x.shape[i]``, the ith dimension of the input is truncated to length
+        ``s[i]``.
+        If any element of `s` is -1, the size of the corresponding dimension of
+        `x` is used.
+    axes : int or array_like of ints or None, optional
+        Axes over which the IDST is computed. If not given, the last ``len(s)``
+        axes are used, or all axes if `s` is also not specified.
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see Notes). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    orthogonalize : bool, optional
+        Whether to use the orthogonalized IDST variant (see Notes).
+        Defaults to ``True`` when ``norm="ortho"`` and ``False`` otherwise.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    dstn : multidimensional DST
+
+    Notes
+    -----
+    For full details of the IDST types and normalization modes, as well as
+    references, see `idst`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fft import dstn, idstn
+    >>> rng = np.random.default_rng()
+    >>> y = rng.standard_normal((16, 16))
+    >>> np.allclose(y, idstn(dstn(y)))
+    True
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(cpu_only=True, allow_dask_compute=True,
+                 skip_backends=[('jax.numpy', 'XXX large tolerance violations')])
+@_dispatch
+def dct(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False, workers=None,
+        orthogonalize=None):
+    r"""Return the Discrete Cosine Transform of arbitrary type sequence x.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DCT (see Notes). Default type is 2.
+    n : int, optional
+        Length of the transform.  If ``n < x.shape[axis]``, `x` is
+        truncated.  If ``n > x.shape[axis]``, `x` is zero-padded. The
+        default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the dct is computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see Notes). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    orthogonalize : bool, optional
+        Whether to use the orthogonalized DCT variant (see Notes).
+        Defaults to ``True`` when ``norm="ortho"`` and ``False`` otherwise.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    idct : Inverse DCT
+
+    Notes
+    -----
+    For a single dimension array ``x``, ``dct(x, norm='ortho')`` is equal to
+    MATLAB ``dct(x)``.
+
+    .. warning:: For ``type in {1, 2, 3}``, ``norm="ortho"`` breaks the direct
+                 correspondence with the direct Fourier transform. To recover
+                 it you must specify ``orthogonalize=False``.
+
+    For ``norm="ortho"`` both the `dct` and `idct` are scaled by the same
+    overall factor in both directions. By default, the transform is also
+    orthogonalized which for types 1, 2 and 3 means the transform definition is
+    modified to give orthogonality of the DCT matrix (see below).
+
+    For ``norm="backward"``, there is no scaling on `dct` and the `idct` is
+    scaled by ``1/N`` where ``N`` is the "logical" size of the DCT. For
+    ``norm="forward"`` the ``1/N`` normalization is applied to the forward
+    `dct` instead and the `idct` is unnormalized.
+
+    There are, theoretically, 8 types of the DCT, only the first 4 types are
+    implemented in SciPy.'The' DCT generally refers to DCT type 2, and 'the'
+    Inverse DCT generally refers to DCT type 3.
+
+    **Type I**
+
+    There are several definitions of the DCT-I; we use the following
+    (for ``norm="backward"``)
+
+    .. math::
+
+       y_k = x_0 + (-1)^k x_{N-1} + 2 \sum_{n=1}^{N-2} x_n \cos\left(
+       \frac{\pi k n}{N-1} \right)
+
+    If ``orthogonalize=True``, ``x[0]`` and ``x[N-1]`` are multiplied by a
+    scaling factor of :math:`\sqrt{2}`, and ``y[0]`` and ``y[N-1]`` are divided
+    by :math:`\sqrt{2}`. When combined with ``norm="ortho"``, this makes the
+    corresponding matrix of coefficients orthonormal (``O @ O.T = np.eye(N)``).
+
+    .. note::
+       The DCT-I is only supported for input size > 1.
+
+    **Type II**
+
+    There are several definitions of the DCT-II; we use the following
+    (for ``norm="backward"``)
+
+    .. math::
+
+       y_k = 2 \sum_{n=0}^{N-1} x_n \cos\left(\frac{\pi k(2n+1)}{2N} \right)
+
+    If ``orthogonalize=True``, ``y[0]`` is divided by :math:`\sqrt{2}` which,
+    when combined with ``norm="ortho"``, makes the corresponding matrix of
+    coefficients orthonormal (``O @ O.T = np.eye(N)``).
+
+    **Type III**
+
+    There are several definitions, we use the following (for
+    ``norm="backward"``)
+
+    .. math::
+
+       y_k = x_0 + 2 \sum_{n=1}^{N-1} x_n \cos\left(\frac{\pi(2k+1)n}{2N}\right)
+
+    If ``orthogonalize=True``, ``x[0]`` terms are multiplied by
+    :math:`\sqrt{2}` which, when combined with ``norm="ortho"``, makes the
+    corresponding matrix of coefficients orthonormal (``O @ O.T = np.eye(N)``).
+
+    The (unnormalized) DCT-III is the inverse of the (unnormalized) DCT-II, up
+    to a factor `2N`. The orthonormalized DCT-III is exactly the inverse of
+    the orthonormalized DCT-II.
+
+    **Type IV**
+
+    There are several definitions of the DCT-IV; we use the following
+    (for ``norm="backward"``)
+
+    .. math::
+
+       y_k = 2 \sum_{n=0}^{N-1} x_n \cos\left(\frac{\pi(2k+1)(2n+1)}{4N} \right)
+
+    ``orthogonalize`` has no effect here, as the DCT-IV matrix is already
+    orthogonal up to a scale factor of ``2N``.
+
+    References
+    ----------
+    .. [1] 'A Fast Cosine Transform in One and Two Dimensions', by J.
+           Makhoul, `IEEE Transactions on acoustics, speech and signal
+           processing` vol. 28(1), pp. 27-34,
+           :doi:`10.1109/TASSP.1980.1163351` (1980).
+    .. [2] Wikipedia, "Discrete cosine transform",
+           https://en.wikipedia.org/wiki/Discrete_cosine_transform
+
+    Examples
+    --------
+    The Type 1 DCT is equivalent to the FFT (though faster) for real,
+    even-symmetrical inputs. The output is also real and even-symmetrical.
+    Half of the FFT input is used to generate half of the FFT output:
+
+    >>> from scipy.fft import fft, dct
+    >>> import numpy as np
+    >>> fft(np.array([4., 3., 5., 10., 5., 3.])).real
+    array([ 30.,  -8.,   6.,  -2.,   6.,  -8.])
+    >>> dct(np.array([4., 3., 5., 10.]), 1)
+    array([ 30.,  -8.,   6.,  -2.])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(cpu_only=True, allow_dask_compute=True)
+@_dispatch
+def idct(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False,
+         workers=None, orthogonalize=None):
+    """
+    Return the Inverse Discrete Cosine Transform of an arbitrary type sequence.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DCT (see Notes). Default type is 2.
+    n : int, optional
+        Length of the transform.  If ``n < x.shape[axis]``, `x` is
+        truncated.  If ``n > x.shape[axis]``, `x` is zero-padded. The
+        default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the idct is computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see Notes). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    orthogonalize : bool, optional
+        Whether to use the orthogonalized IDCT variant (see Notes).
+        Defaults to ``True`` when ``norm="ortho"`` and ``False`` otherwise.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    idct : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    dct : Forward DCT
+
+    Notes
+    -----
+    For a single dimension array `x`, ``idct(x, norm='ortho')`` is equal to
+    MATLAB ``idct(x)``.
+
+    .. warning:: For ``type in {1, 2, 3}``, ``norm="ortho"`` breaks the direct
+                 correspondence with the inverse direct Fourier transform. To
+                 recover it you must specify ``orthogonalize=False``.
+
+    For ``norm="ortho"`` both the `dct` and `idct` are scaled by the same
+    overall factor in both directions. By default, the transform is also
+    orthogonalized which for types 1, 2 and 3 means the transform definition is
+    modified to give orthogonality of the IDCT matrix (see `dct` for the full
+    definitions).
+
+    'The' IDCT is the IDCT-II, which is the same as the normalized DCT-III.
+
+    The IDCT is equivalent to a normal DCT except for the normalization and
+    type. DCT type 1 and 4 are their own inverse and DCTs 2 and 3 are each
+    other's inverses.
+
+    Examples
+    --------
+    The Type 1 DCT is equivalent to the DFT for real, even-symmetrical
+    inputs. The output is also real and even-symmetrical. Half of the IFFT
+    input is used to generate half of the IFFT output:
+
+    >>> from scipy.fft import ifft, idct
+    >>> import numpy as np
+    >>> ifft(np.array([ 30.,  -8.,   6.,  -2.,   6.,  -8.])).real
+    array([  4.,   3.,   5.,  10.,   5.,   3.])
+    >>> idct(np.array([ 30.,  -8.,   6.,  -2.]), 1)
+    array([  4.,   3.,   5.,  10.])
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(cpu_only=True, allow_dask_compute=True,
+                 skip_backends=[('jax.numpy', 'XXX large tolerance violations')])
+@_dispatch
+def dst(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False, workers=None,
+        orthogonalize=None):
+    r"""
+    Return the Discrete Sine Transform of arbitrary type sequence x.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DST (see Notes). Default type is 2.
+    n : int, optional
+        Length of the transform. If ``n < x.shape[axis]``, `x` is
+        truncated.  If ``n > x.shape[axis]``, `x` is zero-padded. The
+        default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the dst is computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see Notes). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    orthogonalize : bool, optional
+        Whether to use the orthogonalized DST variant (see Notes).
+        Defaults to ``True`` when ``norm="ortho"`` and ``False`` otherwise.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    dst : ndarray of reals
+        The transformed input array.
+
+    See Also
+    --------
+    idst : Inverse DST
+
+    Notes
+    -----
+    .. warning:: For ``type in {2, 3}``, ``norm="ortho"`` breaks the direct
+                 correspondence with the direct Fourier transform. To recover
+                 it you must specify ``orthogonalize=False``.
+
+    For ``norm="ortho"`` both the `dst` and `idst` are scaled by the same
+    overall factor in both directions. By default, the transform is also
+    orthogonalized which for types 2 and 3 means the transform definition is
+    modified to give orthogonality of the DST matrix (see below).
+
+    For ``norm="backward"``, there is no scaling on the `dst` and the `idst` is
+    scaled by ``1/N`` where ``N`` is the "logical" size of the DST.
+
+    There are, theoretically, 8 types of the DST for different combinations of
+    even/odd boundary conditions and boundary off sets [1]_, only the first
+    4 types are implemented in SciPy.
+
+    **Type I**
+
+    There are several definitions of the DST-I; we use the following for
+    ``norm="backward"``. DST-I assumes the input is odd around :math:`n=-1` and
+    :math:`n=N`.
+
+    .. math::
+
+        y_k = 2 \sum_{n=0}^{N-1} x_n \sin\left(\frac{\pi(k+1)(n+1)}{N+1}\right)
+
+    Note that the DST-I is only supported for input size > 1.
+    The (unnormalized) DST-I is its own inverse, up to a factor :math:`2(N+1)`.
+    The orthonormalized DST-I is exactly its own inverse.
+
+    ``orthogonalize`` has no effect here, as the DST-I matrix is already
+    orthogonal up to a scale factor of ``2N``.
+
+    **Type II**
+
+    There are several definitions of the DST-II; we use the following for
+    ``norm="backward"``. DST-II assumes the input is odd around :math:`n=-1/2` and
+    :math:`n=N-1/2`; the output is odd around :math:`k=-1` and even around :math:`k=N-1`
+
+    .. math::
+
+        y_k = 2 \sum_{n=0}^{N-1} x_n \sin\left(\frac{\pi(k+1)(2n+1)}{2N}\right)
+
+    If ``orthogonalize=True``, ``y[-1]`` is divided :math:`\sqrt{2}` which, when
+    combined with ``norm="ortho"``, makes the corresponding matrix of
+    coefficients orthonormal (``O @ O.T = np.eye(N)``).
+
+    **Type III**
+
+    There are several definitions of the DST-III, we use the following (for
+    ``norm="backward"``). DST-III assumes the input is odd around :math:`n=-1` and
+    even around :math:`n=N-1`
+
+    .. math::
+
+        y_k = (-1)^k x_{N-1} + 2 \sum_{n=0}^{N-2} x_n \sin\left(
+        \frac{\pi(2k+1)(n+1)}{2N}\right)
+
+    If ``orthogonalize=True``, ``x[-1]`` is multiplied by :math:`\sqrt{2}`
+    which, when combined with ``norm="ortho"``, makes the corresponding matrix
+    of coefficients orthonormal (``O @ O.T = np.eye(N)``).
+
+    The (unnormalized) DST-III is the inverse of the (unnormalized) DST-II, up
+    to a factor :math:`2N`. The orthonormalized DST-III is exactly the inverse of the
+    orthonormalized DST-II.
+
+    **Type IV**
+
+    There are several definitions of the DST-IV, we use the following (for
+    ``norm="backward"``). DST-IV assumes the input is odd around :math:`n=-0.5` and
+    even around :math:`n=N-0.5`
+
+    .. math::
+
+        y_k = 2 \sum_{n=0}^{N-1} x_n \sin\left(\frac{\pi(2k+1)(2n+1)}{4N}\right)
+
+    ``orthogonalize`` has no effect here, as the DST-IV matrix is already
+    orthogonal up to a scale factor of ``2N``.
+
+    The (unnormalized) DST-IV is its own inverse, up to a factor :math:`2N`. The
+    orthonormalized DST-IV is exactly its own inverse.
+
+    Examples
+    --------
+    Compute the DST of a simple 1D array:
+
+    >>> import numpy as np
+    >>> from scipy.fft import dst
+    >>> x = np.array([1, -1, 1, -1])
+    >>> dst(x, type=2)
+    array([0., 0., 0., 8.])
+
+    This computes the Discrete Sine Transform (DST) of type-II for the input array. 
+    The output contains the transformed values corresponding to the given input sequence
+
+    References
+    ----------
+    .. [1] Wikipedia, "Discrete sine transform",
+           https://en.wikipedia.org/wiki/Discrete_sine_transform
+
+    """
+    return (Dispatchable(x, np.ndarray),)
+
+
+@xp_capabilities(cpu_only=True, allow_dask_compute=True)
+@_dispatch
+def idst(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False,
+         workers=None, orthogonalize=None):
+    """
+    Return the Inverse Discrete Sine Transform of an arbitrary type sequence.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DST (see Notes). Default type is 2.
+    n : int, optional
+        Length of the transform. If ``n < x.shape[axis]``, `x` is
+        truncated.  If ``n > x.shape[axis]``, `x` is zero-padded. The
+        default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the idst is computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    norm : {"backward", "ortho", "forward"}, optional
+        Normalization mode (see Notes). Default is "backward".
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+    workers : int, optional
+        Maximum number of workers to use for parallel computation. If negative,
+        the value wraps around from ``os.cpu_count()``.
+        See :func:`~scipy.fft.fft` for more details.
+    orthogonalize : bool, optional
+        Whether to use the orthogonalized IDST variant (see Notes).
+        Defaults to ``True`` when ``norm="ortho"`` and ``False`` otherwise.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    idst : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    dst : Forward DST
+
+    Notes
+    -----
+    .. warning:: For ``type in {2, 3}``, ``norm="ortho"`` breaks the direct
+                 correspondence with the inverse direct Fourier transform.
+
+    For ``norm="ortho"`` both the `dst` and `idst` are scaled by the same
+    overall factor in both directions. By default, the transform is also
+    orthogonalized which for types 2 and 3 means the transform definition is
+    modified to give orthogonality of the DST matrix (see `dst` for the full
+    definitions).
+
+    'The' IDST is the IDST-II, which is the same as the normalized DST-III.
+
+    The IDST is equivalent to a normal DST except for the normalization and
+    type. DST type 1 and 4 are their own inverse and DSTs 2 and 3 are each
+    other's inverses.
+
+    """
+    return (Dispatchable(x, np.ndarray),)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_realtransforms_backend.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_realtransforms_backend.py
new file mode 100644
index 0000000000000000000000000000000000000000..2042453733bec54860974cc1e20ba908e8c9b94d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/_realtransforms_backend.py
@@ -0,0 +1,63 @@
+from scipy._lib._array_api import array_namespace
+import numpy as np
+from . import _pocketfft
+
+__all__ = ['dct', 'idct', 'dst', 'idst', 'dctn', 'idctn', 'dstn', 'idstn']
+
+
+def _execute(pocketfft_func, x, type, s, axes, norm, 
+             overwrite_x, workers, orthogonalize):
+    xp = array_namespace(x)
+    x = np.asarray(x)
+    y = pocketfft_func(x, type, s, axes, norm,
+                       overwrite_x=overwrite_x, workers=workers,
+                       orthogonalize=orthogonalize)
+    return xp.asarray(y)
+
+
+def dctn(x, type=2, s=None, axes=None, norm=None,
+         overwrite_x=False, workers=None, *, orthogonalize=None):
+    return _execute(_pocketfft.dctn, x, type, s, axes, norm, 
+                    overwrite_x, workers, orthogonalize)
+
+
+def idctn(x, type=2, s=None, axes=None, norm=None,
+          overwrite_x=False, workers=None, *, orthogonalize=None):
+    return _execute(_pocketfft.idctn, x, type, s, axes, norm, 
+                    overwrite_x, workers, orthogonalize)
+
+
+def dstn(x, type=2, s=None, axes=None, norm=None,
+         overwrite_x=False, workers=None, orthogonalize=None):
+    return _execute(_pocketfft.dstn, x, type, s, axes, norm, 
+                    overwrite_x, workers, orthogonalize)
+
+
+def idstn(x, type=2, s=None, axes=None, norm=None,
+          overwrite_x=False, workers=None, *, orthogonalize=None):
+    return _execute(_pocketfft.idstn, x, type, s, axes, norm, 
+                    overwrite_x, workers, orthogonalize)
+
+
+def dct(x, type=2, n=None, axis=-1, norm=None,
+        overwrite_x=False, workers=None, orthogonalize=None):
+    return _execute(_pocketfft.dct, x, type, n, axis, norm, 
+                    overwrite_x, workers, orthogonalize)
+
+
+def idct(x, type=2, n=None, axis=-1, norm=None,
+         overwrite_x=False, workers=None, orthogonalize=None):
+    return _execute(_pocketfft.idct, x, type, n, axis, norm, 
+                    overwrite_x, workers, orthogonalize)
+
+
+def dst(x, type=2, n=None, axis=-1, norm=None,
+        overwrite_x=False, workers=None, orthogonalize=None):
+    return _execute(_pocketfft.dst, x, type, n, axis, norm, 
+                    overwrite_x, workers, orthogonalize)
+
+
+def idst(x, type=2, n=None, axis=-1, norm=None,
+         overwrite_x=False, workers=None, orthogonalize=None):
+    return _execute(_pocketfft.idst, x, type, n, axis, norm, 
+                    overwrite_x, workers, orthogonalize)
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/mock_backend.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/mock_backend.py
new file mode 100644
index 0000000000000000000000000000000000000000..48a7d2b3b50501b84f7c18e366ad2e66782b4ab6
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/mock_backend.py
@@ -0,0 +1,96 @@
+import numpy as np
+import scipy.fft
+import threading
+
+class _MockFunction:
+    def __init__(self, return_value = None):
+        self.number_calls = threading.local()
+        self.return_value = return_value
+        self.last_args = threading.local()
+
+    def __call__(self, *args, **kwargs):
+        if not hasattr(self.number_calls, 'c'):
+            self.number_calls.c = 0
+
+        self.number_calls.c += 1
+        self.last_args.l = (args, kwargs)
+        return self.return_value
+
+
+fft = _MockFunction(np.random.random(10))
+fft2 = _MockFunction(np.random.random(10))
+fftn = _MockFunction(np.random.random(10))
+
+ifft = _MockFunction(np.random.random(10))
+ifft2 = _MockFunction(np.random.random(10))
+ifftn = _MockFunction(np.random.random(10))
+
+rfft = _MockFunction(np.random.random(10))
+rfft2 = _MockFunction(np.random.random(10))
+rfftn = _MockFunction(np.random.random(10))
+
+irfft = _MockFunction(np.random.random(10))
+irfft2 = _MockFunction(np.random.random(10))
+irfftn = _MockFunction(np.random.random(10))
+
+hfft = _MockFunction(np.random.random(10))
+hfft2 = _MockFunction(np.random.random(10))
+hfftn = _MockFunction(np.random.random(10))
+
+ihfft = _MockFunction(np.random.random(10))
+ihfft2 = _MockFunction(np.random.random(10))
+ihfftn = _MockFunction(np.random.random(10))
+
+dct = _MockFunction(np.random.random(10))
+idct = _MockFunction(np.random.random(10))
+dctn = _MockFunction(np.random.random(10))
+idctn = _MockFunction(np.random.random(10))
+
+dst = _MockFunction(np.random.random(10))
+idst = _MockFunction(np.random.random(10))
+dstn = _MockFunction(np.random.random(10))
+idstn = _MockFunction(np.random.random(10))
+
+fht = _MockFunction(np.random.random(10))
+ifht = _MockFunction(np.random.random(10))
+
+
+__ua_domain__ = "numpy.scipy.fft"
+
+
+_implements = {
+    scipy.fft.fft: fft,
+    scipy.fft.fft2: fft2,
+    scipy.fft.fftn: fftn,
+    scipy.fft.ifft: ifft,
+    scipy.fft.ifft2: ifft2,
+    scipy.fft.ifftn: ifftn,
+    scipy.fft.rfft: rfft,
+    scipy.fft.rfft2: rfft2,
+    scipy.fft.rfftn: rfftn,
+    scipy.fft.irfft: irfft,
+    scipy.fft.irfft2: irfft2,
+    scipy.fft.irfftn: irfftn,
+    scipy.fft.hfft: hfft,
+    scipy.fft.hfft2: hfft2,
+    scipy.fft.hfftn: hfftn,
+    scipy.fft.ihfft: ihfft,
+    scipy.fft.ihfft2: ihfft2,
+    scipy.fft.ihfftn: ihfftn,
+    scipy.fft.dct: dct,
+    scipy.fft.idct: idct,
+    scipy.fft.dctn: dctn,
+    scipy.fft.idctn: idctn,
+    scipy.fft.dst: dst,
+    scipy.fft.idst: idst,
+    scipy.fft.dstn: dstn,
+    scipy.fft.idstn: idstn,
+    scipy.fft.fht: fht,
+    scipy.fft.ifht: ifht
+}
+
+
+def __ua_function__(method, args, kwargs):
+    fn = _implements.get(method)
+    return (fn(*args, **kwargs) if fn is not None
+            else NotImplemented)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_backend.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_backend.py
new file mode 100644
index 0000000000000000000000000000000000000000..933e9c0302d46faf33b3dc015d58996e3e46c058
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_backend.py
@@ -0,0 +1,98 @@
+from functools import partial
+
+import numpy as np
+import scipy.fft
+from scipy.fft import _fftlog, _pocketfft, set_backend
+from scipy.fft.tests import mock_backend
+
+from numpy.testing import assert_allclose, assert_equal
+import pytest
+
+fnames = ('fft', 'fft2', 'fftn',
+          'ifft', 'ifft2', 'ifftn',
+          'rfft', 'rfft2', 'rfftn',
+          'irfft', 'irfft2', 'irfftn',
+          'dct', 'idct', 'dctn', 'idctn',
+          'dst', 'idst', 'dstn', 'idstn',
+          'fht', 'ifht')
+
+np_funcs = (np.fft.fft, np.fft.fft2, np.fft.fftn,
+            np.fft.ifft, np.fft.ifft2, np.fft.ifftn,
+            np.fft.rfft, np.fft.rfft2, np.fft.rfftn,
+            np.fft.irfft, np.fft.irfft2, np.fft.irfftn,
+            np.fft.hfft, _pocketfft.hfft2, _pocketfft.hfftn,  # np has no hfftn
+            np.fft.ihfft, _pocketfft.ihfft2, _pocketfft.ihfftn,
+            _pocketfft.dct, _pocketfft.idct, _pocketfft.dctn, _pocketfft.idctn,
+            _pocketfft.dst, _pocketfft.idst, _pocketfft.dstn, _pocketfft.idstn,
+            # must provide required kwargs for fht, ifht
+            partial(_fftlog.fht, dln=2, mu=0.5),
+            partial(_fftlog.ifht, dln=2, mu=0.5))
+
+funcs = (scipy.fft.fft, scipy.fft.fft2, scipy.fft.fftn,
+         scipy.fft.ifft, scipy.fft.ifft2, scipy.fft.ifftn,
+         scipy.fft.rfft, scipy.fft.rfft2, scipy.fft.rfftn,
+         scipy.fft.irfft, scipy.fft.irfft2, scipy.fft.irfftn,
+         scipy.fft.hfft, scipy.fft.hfft2, scipy.fft.hfftn,
+         scipy.fft.ihfft, scipy.fft.ihfft2, scipy.fft.ihfftn,
+         scipy.fft.dct, scipy.fft.idct, scipy.fft.dctn, scipy.fft.idctn,
+         scipy.fft.dst, scipy.fft.idst, scipy.fft.dstn, scipy.fft.idstn,
+         # must provide required kwargs for fht, ifht
+         partial(scipy.fft.fht, dln=2, mu=0.5),
+         partial(scipy.fft.ifht, dln=2, mu=0.5))
+
+mocks = (mock_backend.fft, mock_backend.fft2, mock_backend.fftn,
+         mock_backend.ifft, mock_backend.ifft2, mock_backend.ifftn,
+         mock_backend.rfft, mock_backend.rfft2, mock_backend.rfftn,
+         mock_backend.irfft, mock_backend.irfft2, mock_backend.irfftn,
+         mock_backend.hfft, mock_backend.hfft2, mock_backend.hfftn,
+         mock_backend.ihfft, mock_backend.ihfft2, mock_backend.ihfftn,
+         mock_backend.dct, mock_backend.idct,
+         mock_backend.dctn, mock_backend.idctn,
+         mock_backend.dst, mock_backend.idst,
+         mock_backend.dstn, mock_backend.idstn,
+         mock_backend.fht, mock_backend.ifht)
+
+
+@pytest.mark.parametrize("func, np_func, mock", zip(funcs, np_funcs, mocks))
+def test_backend_call(func, np_func, mock):
+    x = np.arange(20).reshape((10,2))
+    answer = np_func(x.astype(np.float64))
+    assert_allclose(func(x), answer, atol=1e-10)
+
+    with set_backend(mock_backend, only=True):
+        mock.number_calls.c = 0
+        y = func(x)
+        assert_equal(y, mock.return_value)
+        assert_equal(mock.number_calls.c, 1)
+
+    assert_allclose(func(x), answer, atol=1e-10)
+
+
+plan_funcs = (scipy.fft.fft, scipy.fft.fft2, scipy.fft.fftn,
+              scipy.fft.ifft, scipy.fft.ifft2, scipy.fft.ifftn,
+              scipy.fft.rfft, scipy.fft.rfft2, scipy.fft.rfftn,
+              scipy.fft.irfft, scipy.fft.irfft2, scipy.fft.irfftn,
+              scipy.fft.hfft, scipy.fft.hfft2, scipy.fft.hfftn,
+              scipy.fft.ihfft, scipy.fft.ihfft2, scipy.fft.ihfftn)
+
+plan_mocks = (mock_backend.fft, mock_backend.fft2, mock_backend.fftn,
+              mock_backend.ifft, mock_backend.ifft2, mock_backend.ifftn,
+              mock_backend.rfft, mock_backend.rfft2, mock_backend.rfftn,
+              mock_backend.irfft, mock_backend.irfft2, mock_backend.irfftn,
+              mock_backend.hfft, mock_backend.hfft2, mock_backend.hfftn,
+              mock_backend.ihfft, mock_backend.ihfft2, mock_backend.ihfftn)
+
+
+@pytest.mark.parametrize("func, mock", zip(plan_funcs, plan_mocks))
+def test_backend_plan(func, mock):
+    x = np.arange(20).reshape((10, 2))
+
+    with pytest.raises(NotImplementedError, match='precomputed plan'):
+        func(x, plan='foo')
+
+    with set_backend(mock_backend, only=True):
+        mock.number_calls.c = 0
+        y = func(x, plan='foo')
+        assert_equal(y, mock.return_value)
+        assert_equal(mock.number_calls.c, 1)
+        assert_equal(mock.last_args.l[1]['plan'], 'foo')
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..8d25baba624de6a639b815cc6bf15cddf5cdac69
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_basic.py
@@ -0,0 +1,549 @@
+import queue
+import threading
+import multiprocessing
+import numpy as np
+import pytest
+from numpy.random import random
+from numpy.testing import assert_array_almost_equal, assert_allclose
+from pytest import raises as assert_raises
+import scipy.fft as fft
+from scipy._lib._array_api import (
+    is_numpy, xp_size, xp_assert_close, xp_assert_equal, make_xp_test_case,
+    make_xp_pytest_param
+)
+
+lazy_xp_modules = [fft]
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+
+# Expected input dtypes. Note that `scipy.fft` is more flexible for numpy,
+# but for C2C transforms like `fft.fft`, the array API standard only mandates
+# that complex dtypes should work, float32/float64 aren't guaranteed to.
+def get_expected_input_dtype(func, xp):
+    # use __name__ so that `lazy_xp_function` doesn't break things
+    if func.__name__ in ["fft", "fftn", "fft2", "ifft", "ifftn", "ifft2", "hfft",
+                         "hfftn", "hfft2", "irfft", "irfftn", "irfft2"]:
+        dtype = xp.complex128
+    elif func.__name__ in ["rfft", "rfftn", "rfft2", "ihfft", "ihfftn", "ihfft2"]:
+        dtype = xp.float64
+    else:
+        raise ValueError(f'Unknown FFT function: {func}')
+
+    return dtype
+
+
+def fft1(x):
+    L = len(x)
+    phase = -2j*np.pi*(np.arange(L)/float(L))
+    phase = np.arange(L).reshape(-1, 1) * phase
+    return np.sum(x*np.exp(phase), axis=1)
+
+
+class TestFFT:
+    @make_xp_test_case(fft.ifft, fft.fft, fft.rfft, fft.irfft)
+    def test_identity(self, xp):
+        maxlen = 512
+        x = xp.asarray(random(maxlen) + 1j*random(maxlen))
+        xr = xp.asarray(random(maxlen))
+        # Check some powers of 2 and some primes
+        for i in [1, 2, 16, 128, 512, 53, 149, 281, 397]:
+            xp_assert_close(fft.ifft(fft.fft(x[0:i])), x[0:i])
+            xp_assert_close(fft.irfft(fft.rfft(xr[0:i]), i), xr[0:i])
+
+    @skip_xp_backends(np_only=True, reason='significant overhead for some backends')
+    def test_identity_extensive(self, xp):
+        maxlen = 512
+        x = xp.asarray(random(maxlen) + 1j*random(maxlen))
+        xr = xp.asarray(random(maxlen))
+        for i in range(1, maxlen):
+            xp_assert_close(fft.ifft(fft.fft(x[0:i])), x[0:i])
+            xp_assert_close(fft.irfft(fft.rfft(xr[0:i]), i), xr[0:i])
+
+    @make_xp_test_case(fft.fft)
+    def test_fft(self, xp):
+        x = random(30) + 1j*random(30)
+        expect = xp.asarray(fft1(x))
+        x = xp.asarray(x)
+        xp_assert_close(fft.fft(x), expect)
+        xp_assert_close(fft.fft(x, norm="backward"), expect)
+        xp_assert_close(fft.fft(x, norm="ortho"),
+                        expect / xp.sqrt(xp.asarray(30, dtype=xp.float64)),)
+        xp_assert_close(fft.fft(x, norm="forward"), expect / 30)
+
+    @skip_xp_backends(np_only=True, reason='some backends allow `n=0`')
+    def test_fft_n(self, xp):
+        x = xp.asarray([1, 2, 3], dtype=xp.complex128)
+        assert_raises(ValueError, fft.fft, x, 0)
+
+    @make_xp_test_case(fft.fft, fft.ifft)
+    def test_ifft(self, xp):
+        x = xp.asarray(random(30) + 1j*random(30))
+        xp_assert_close(fft.ifft(fft.fft(x)), x)
+        for norm in ["backward", "ortho", "forward"]:
+            xp_assert_close(fft.ifft(fft.fft(x, norm=norm), norm=norm), x)
+
+    @make_xp_test_case(fft.fft, fft.fft2)
+    def test_fft2(self, xp):
+        x = xp.asarray(random((30, 20)) + 1j*random((30, 20)))
+        expect = fft.fft(fft.fft(x, axis=1), axis=0)
+        xp_assert_close(fft.fft2(x), expect)
+        xp_assert_close(fft.fft2(x, norm="backward"), expect)
+        xp_assert_close(fft.fft2(x, norm="ortho"),
+                        expect / xp.sqrt(xp.asarray(30 * 20, dtype=xp.float64)))
+        xp_assert_close(fft.fft2(x, norm="forward"), expect / (30 * 20))
+
+    @make_xp_test_case(fft.ifft, fft.ifft2)
+    def test_ifft2(self, xp):
+        x = xp.asarray(random((30, 20)) + 1j*random((30, 20)))
+        expect = fft.ifft(fft.ifft(x, axis=1), axis=0)
+        xp_assert_close(fft.ifft2(x), expect)
+        xp_assert_close(fft.ifft2(x, norm="backward"), expect)
+        xp_assert_close(fft.ifft2(x, norm="ortho"),
+                        expect * xp.sqrt(xp.asarray(30 * 20, dtype=xp.float64)))
+        xp_assert_close(fft.ifft2(x, norm="forward"), expect * (30 * 20))
+
+    @make_xp_test_case(fft.fft, fft.fftn)
+    def test_fftn(self, xp):
+        x = xp.asarray(random((30, 20, 10)) + 1j*random((30, 20, 10)))
+        expect = fft.fft(fft.fft(fft.fft(x, axis=2), axis=1), axis=0)
+        xp_assert_close(fft.fftn(x), expect)
+        xp_assert_close(fft.fftn(x, norm="backward"), expect)
+        xp_assert_close(fft.fftn(x, norm="ortho"),
+                        expect / xp.sqrt(xp.asarray(30 * 20 * 10, dtype=xp.float64)))
+        xp_assert_close(fft.fftn(x, norm="forward"), expect / (30 * 20 * 10))
+
+    @make_xp_test_case(fft.ifft, fft.ifftn)
+    def test_ifftn(self, xp):
+        x = xp.asarray(random((30, 20, 10)) + 1j*random((30, 20, 10)))
+        expect = fft.ifft(fft.ifft(fft.ifft(x, axis=2), axis=1), axis=0)
+        xp_assert_close(fft.ifftn(x), expect, rtol=1e-7)
+        xp_assert_close(fft.ifftn(x, norm="backward"), expect, rtol=1e-7)
+        xp_assert_close(
+            fft.ifftn(x, norm="ortho"),
+            fft.ifftn(x) * xp.sqrt(xp.asarray(30 * 20 * 10, dtype=xp.float64))
+        )
+        xp_assert_close(fft.ifftn(x, norm="forward"),
+                        expect * (30 * 20 * 10),
+                        rtol=1e-7)
+
+    @make_xp_test_case(fft.fft, fft.rfft)
+    def test_rfft(self, xp):
+        x = xp.asarray(random(29), dtype=xp.float64)
+        for n in [xp_size(x), 2*xp_size(x)]:
+            for norm in [None, "backward", "ortho", "forward"]:
+                xp_assert_close(fft.rfft(x, n=n, norm=norm),
+                                fft.fft(xp.asarray(x, dtype=xp.complex128),
+                                        n=n, norm=norm)[:(n//2 + 1)])
+            xp_assert_close(
+                fft.rfft(x, n=n, norm="ortho"),
+                fft.rfft(x, n=n) / xp.sqrt(xp.asarray(n, dtype=xp.float64))
+            )
+
+    @make_xp_test_case(fft.irfft, fft.rfft)
+    def test_irfft(self, xp):
+        x = xp.asarray(random(30))
+        xp_assert_close(fft.irfft(fft.rfft(x)), x)
+        for norm in ["backward", "ortho", "forward"]:
+            xp_assert_close(fft.irfft(fft.rfft(x, norm=norm), norm=norm), x)
+
+    @make_xp_test_case(fft.rfft2)
+    def test_rfft2(self, xp):
+        x = xp.asarray(random((30, 20)), dtype=xp.float64)
+        expect = fft.fft2(xp.asarray(x, dtype=xp.complex128))[:, :11]
+        xp_assert_close(fft.rfft2(x), expect)
+        xp_assert_close(fft.rfft2(x, norm="backward"), expect)
+        xp_assert_close(fft.rfft2(x, norm="ortho"),
+                        expect / xp.sqrt(xp.asarray(30 * 20, dtype=xp.float64)))
+        xp_assert_close(fft.rfft2(x, norm="forward"), expect / (30 * 20))
+
+    @make_xp_test_case(fft.rfft2, fft.irfft2)
+    def test_irfft2(self, xp):
+        x = xp.asarray(random((30, 20)))
+        xp_assert_close(fft.irfft2(fft.rfft2(x)), x)
+        for norm in ["backward", "ortho", "forward"]:
+            xp_assert_close(fft.irfft2(fft.rfft2(x, norm=norm), norm=norm), x)
+
+    @make_xp_test_case(fft.fftn, fft.rfftn)
+    def test_rfftn(self, xp):
+        x = xp.asarray(random((30, 20, 10)), dtype=xp.float64)
+        expect = fft.fftn(xp.asarray(x, dtype=xp.complex128))[:, :, :6]
+        xp_assert_close(fft.rfftn(x), expect)
+        xp_assert_close(fft.rfftn(x, norm="backward"), expect)
+        xp_assert_close(fft.rfftn(x, norm="ortho"),
+                        expect / xp.sqrt(xp.asarray(30 * 20 * 10, dtype=xp.float64)))
+        xp_assert_close(fft.rfftn(x, norm="forward"), expect / (30 * 20 * 10))
+
+    @make_xp_test_case(fft.irfftn, fft.rfftn)
+    def test_irfftn(self, xp):
+        x = xp.asarray(random((30, 20, 10)))
+        xp_assert_close(fft.irfftn(fft.rfftn(x)), x)
+        for norm in ["backward", "ortho", "forward"]:
+            xp_assert_close(fft.irfftn(fft.rfftn(x, norm=norm), norm=norm), x)
+
+    @make_xp_test_case(fft.hfft, fft.fft)
+    def test_hfft(self, xp):
+        x = random(14) + 1j*random(14)
+        x_herm = np.concatenate((random(1), x, random(1)))
+        x = np.concatenate((x_herm, x[::-1].conj()))
+        x = xp.asarray(x)
+        x_herm = xp.asarray(x_herm)
+        expect = xp.real(fft.fft(x))
+        xp_assert_close(fft.hfft(x_herm), expect)
+        xp_assert_close(fft.hfft(x_herm, norm="backward"), expect)
+        xp_assert_close(fft.hfft(x_herm, norm="ortho"),
+                        expect / xp.sqrt(xp.asarray(30, dtype=xp.float64)))
+        xp_assert_close(fft.hfft(x_herm, norm="forward"), expect / 30)
+
+    @make_xp_test_case(fft.hfft, fft.ihfft)
+    def test_ihfft(self, xp):
+        x = random(14) + 1j*random(14)
+        x_herm = np.concatenate((random(1), x, random(1)))
+        x = np.concatenate((x_herm, x[::-1].conj()))
+        x = xp.asarray(x)
+        x_herm = xp.asarray(x_herm)
+        xp_assert_close(fft.ihfft(fft.hfft(x_herm)), x_herm)
+        for norm in ["backward", "ortho", "forward"]:
+            xp_assert_close(fft.ihfft(fft.hfft(x_herm, norm=norm), norm=norm), x_herm)
+
+    @make_xp_test_case(fft.hfft2, fft.ihfft2)
+    def test_hfft2(self, xp):
+        x = xp.asarray(random((30, 20)))
+        xp_assert_close(fft.hfft2(fft.ihfft2(x)), x)
+        for norm in ["backward", "ortho", "forward"]:
+            xp_assert_close(fft.hfft2(fft.ihfft2(x, norm=norm), norm=norm), x)
+
+    @make_xp_test_case(fft.ifft2)
+    def test_ihfft2(self, xp):
+        x = xp.asarray(random((30, 20)), dtype=xp.float64)
+        expect = fft.ifft2(xp.asarray(x, dtype=xp.complex128))[:, :11]
+        xp_assert_close(fft.ihfft2(x), expect)
+        xp_assert_close(fft.ihfft2(x, norm="backward"), expect)
+        xp_assert_close(
+            fft.ihfft2(x, norm="ortho"),
+            expect * xp.sqrt(xp.asarray(30 * 20, dtype=xp.float64))
+        )
+        xp_assert_close(fft.ihfft2(x, norm="forward"), expect * (30 * 20))
+
+    @make_xp_test_case(fft.hfftn, fft.ihfftn)
+    def test_hfftn(self, xp):
+        x = xp.asarray(random((30, 20, 10)))
+        xp_assert_close(fft.hfftn(fft.ihfftn(x)), x)
+        for norm in ["backward", "ortho", "forward"]:
+            xp_assert_close(fft.hfftn(fft.ihfftn(x, norm=norm), norm=norm), x)
+
+    @make_xp_test_case(fft.ifftn, fft.ihfftn)
+    def test_ihfftn(self, xp):
+        x = xp.asarray(random((30, 20, 10)), dtype=xp.float64)
+        expect = fft.ifftn(xp.asarray(x, dtype=xp.complex128))[:, :, :6]
+        xp_assert_close(expect, fft.ihfftn(x))
+        xp_assert_close(expect, fft.ihfftn(x, norm="backward"))
+        xp_assert_close(
+            fft.ihfftn(x, norm="ortho"),
+            expect * xp.sqrt(xp.asarray(30 * 20 * 10, dtype=xp.float64))
+        )
+        xp_assert_close(fft.ihfftn(x, norm="forward"), expect * (30 * 20 * 10))
+
+    def _check_axes(self, op, xp):
+        dtype = get_expected_input_dtype(op, xp)
+        x = xp.asarray(random((30, 20, 10)), dtype=dtype)
+        axes = [(0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0)]
+
+        for a in axes:
+            op_tr = op(xp.permute_dims(x, axes=a))
+            tr_op = xp.permute_dims(op(x, axes=a), axes=a)
+            xp_assert_close(op_tr, tr_op)
+
+    @pytest.mark.parametrize("op", [make_xp_pytest_param(fft.fftn),
+                                    make_xp_pytest_param(fft.ifftn),
+                                    make_xp_pytest_param(fft.rfftn),
+                                    make_xp_pytest_param(fft.irfftn)])
+    def test_axes_standard(self, op, xp):
+        self._check_axes(op, xp)
+
+    @pytest.mark.parametrize("op", [make_xp_pytest_param(fft.hfftn),
+                                    make_xp_pytest_param(fft.ihfftn)])
+    def test_axes_non_standard(self, op, xp):
+        self._check_axes(op, xp)
+
+    @pytest.mark.parametrize("op", [make_xp_pytest_param(fft.fftn),
+                                    make_xp_pytest_param(fft.ifftn),
+                                    make_xp_pytest_param(fft.rfftn),
+                                    make_xp_pytest_param(fft.irfftn)])
+    def test_axes_subset_with_shape_standard(self, op, xp):
+        dtype = get_expected_input_dtype(op, xp)
+        x = xp.asarray(random((16, 8, 4)), dtype=dtype)
+        axes = [(0, 1, 2), (0, 2, 1), (1, 2, 0)]
+
+        for a in axes:
+            # different shape on the first two axes
+            shape = tuple([2*x.shape[ax] if ax in a[:2] else x.shape[ax]
+                           for ax in range(x.ndim)])
+            # transform only the first two axes
+            op_tr = op(xp.permute_dims(x, axes=a),
+                       s=shape[:2], axes=(0, 1))
+            tr_op = xp.permute_dims(op(x, s=shape[:2], axes=a[:2]),
+                                         axes=a)
+            xp_assert_close(op_tr, tr_op)
+
+    @pytest.mark.parametrize("op", [make_xp_pytest_param(fft.fft2),
+                                    make_xp_pytest_param(fft.ifft2),
+                                    make_xp_pytest_param(fft.rfft2),
+                                    make_xp_pytest_param(fft.irfft2),
+                                    make_xp_pytest_param(fft.hfft2),
+                                    make_xp_pytest_param(fft.ihfft2),
+                                    make_xp_pytest_param(fft.hfftn),
+                                    make_xp_pytest_param(fft.ihfftn)])
+    def test_axes_subset_with_shape_non_standard(self, op, xp):
+        dtype = get_expected_input_dtype(op, xp)
+        x = xp.asarray(random((16, 8, 4)), dtype=dtype)
+        axes = [(0, 1, 2), (0, 2, 1), (1, 2, 0)]
+
+        for a in axes:
+            # different shape on the first two axes
+            shape = tuple([2*x.shape[ax] if ax in a[:2] else x.shape[ax]
+                           for ax in range(x.ndim)])
+            # transform only the first two axes
+            op_tr = op(xp.permute_dims(x, axes=a), s=shape[:2], axes=(0, 1))
+            tr_op = xp.permute_dims(op(x, s=shape[:2], axes=a[:2]), axes=a)
+            xp_assert_close(op_tr, tr_op)
+
+    @make_xp_test_case(fft.rfft, fft.irfft, fft.ihfft, fft.hfft, fft.fft, fft.ifft)
+    def test_all_1d_norm_preserving(self, xp):
+        # verify that round-trip transforms are norm-preserving
+        x = xp.asarray(random(30), dtype=xp.float64)
+
+        x_norm = xp.linalg.vector_norm(x)
+        n = xp_size(x) * 2
+        func_pairs = [(fft.rfft, fft.irfft),
+                      # hfft: order so the first function takes x.size samples
+                      #       (necessary for comparison to x_norm above)
+                      (fft.ihfft, fft.hfft),
+                      # functions that expect complex dtypes at the end
+                      (fft.fft, fft.ifft),
+                      ]
+        for forw, back in func_pairs:
+            if forw == fft.fft:
+                x = xp.asarray(x, dtype=xp.complex128)
+                x_norm = xp.linalg.vector_norm(x)
+            for n in [xp_size(x), 2*xp_size(x)]:
+                for norm in ['backward', 'ortho', 'forward']:
+                    tmp = forw(x, n=n, norm=norm)
+                    tmp = back(tmp, n=n, norm=norm)
+                    xp_assert_close(xp.linalg.vector_norm(tmp), x_norm)
+
+    @pytest.mark.parametrize("dtype", [np.float16, np.longdouble])
+    def test_dtypes_nonstandard(self, dtype):
+        x = random(30).astype(dtype)
+        out_dtypes = {np.float16: np.complex64, np.longdouble: np.clongdouble}
+        x_complex = x.astype(out_dtypes[dtype])
+
+        res_fft = fft.ifft(fft.fft(x))
+        res_rfft = fft.irfft(fft.rfft(x))
+        res_hfft = fft.hfft(fft.ihfft(x), x.shape[0])
+        # Check both numerical results and exact dtype matches
+        assert_array_almost_equal(res_fft, x_complex)
+        assert_array_almost_equal(res_rfft, x)
+        assert_array_almost_equal(res_hfft, x)
+        assert res_fft.dtype == x_complex.dtype
+        assert res_rfft.dtype == np.result_type(np.float32, x.dtype)
+        assert res_hfft.dtype == np.result_type(np.float32, x.dtype)
+
+    @make_xp_test_case(fft.irfft, fft.rfft)
+    @pytest.mark.parametrize("dtype", ["float32", "float64"])
+    def test_dtypes_real(self, dtype, xp):
+        x = xp.asarray(random(30), dtype=getattr(xp, dtype))
+
+        res_rfft = fft.irfft(fft.rfft(x))
+        res_hfft = fft.hfft(fft.ihfft(x), x.shape[0])
+        # Check both numerical results and exact dtype matches
+        xp_assert_close(res_rfft, x)
+        xp_assert_close(res_hfft, x)
+
+    @make_xp_test_case(fft.fft, fft.ifft)
+    @pytest.mark.parametrize("dtype", ["complex64", "complex128"])
+    def test_dtypes_complex(self, dtype, xp):
+        rng = np.random.default_rng(1234)
+        x = xp.asarray(rng.random(30), dtype=getattr(xp, dtype))
+
+        res_fft = fft.ifft(fft.fft(x))
+        # Check both numerical results and exact dtype matches
+        xp_assert_close(res_fft, x)
+
+    @pytest.mark.parametrize("op", [fft.fft, fft.ifft,
+                                    fft.fft2, fft.ifft2,
+                                    fft.fftn, fft.ifftn,
+                                    fft.rfft, fft.irfft,
+                                    fft.rfft2, fft.irfft2,
+                                    fft.rfftn, fft.irfftn,
+                                    fft.hfft, fft.ihfft,
+                                    fft.hfft2, fft.ihfft2,
+                                    fft.hfftn, fft.ihfftn,])
+    def test_array_like(self, op):
+        x = [[[1.0, 1.0], [1.0, 1.0]],
+             [[1.0, 1.0], [1.0, 1.0]],
+             [[1.0, 1.0], [1.0, 1.0]]]
+        xp_assert_close(op(x), op(np.asarray(x)))
+
+
+@pytest.mark.parametrize(
+        "dtype",
+        [np.float32, np.float64, np.longdouble,
+         np.complex64, np.complex128, np.clongdouble])
+@pytest.mark.parametrize("order", ["F", 'non-contiguous'])
+@pytest.mark.parametrize(
+        "fft",
+        [fft.fft, fft.fft2, fft.fftn, fft.ifft, fft.ifft2, fft.ifftn])
+def test_fft_with_order(dtype, order, fft):
+    # Check that FFT/IFFT produces identical results for C, Fortran and
+    # non contiguous arrays
+    rng = np.random.RandomState(42)
+    X = rng.rand(8, 7, 13).astype(dtype, copy=False)
+    if order == 'F':
+        Y = np.asfortranarray(X)
+    else:
+        # Make a non contiguous array
+        Y = X[::-1]
+        X = np.ascontiguousarray(X[::-1])
+
+    if fft.__name__.endswith('fft'):
+        for axis in range(3):
+            X_res = fft(X, axis=axis)
+            Y_res = fft(Y, axis=axis)
+            assert_array_almost_equal(X_res, Y_res)
+    elif fft.__name__.endswith(('fft2', 'fftn')):
+        axes = [(0, 1), (1, 2), (0, 2)]
+        if fft.__name__.endswith('fftn'):
+            axes.extend([(0,), (1,), (2,), None])
+        for ax in axes:
+            X_res = fft(X, axes=ax)
+            Y_res = fft(Y, axes=ax)
+            assert_array_almost_equal(X_res, Y_res)
+    else:
+        raise ValueError
+
+
+@skip_xp_backends(cpu_only=True)
+class TestFFTThreadSafe:
+    threads = 16
+    input_shape = (800, 200)
+
+    def _test_mtsame(self, func, *args, xp=None):
+        def worker(args, q):
+            q.put(func(*args))
+
+        q = queue.Queue()
+        expected = func(*args)
+
+        # Spin off a bunch of threads to call the same function simultaneously
+        t = [threading.Thread(target=worker, args=(args, q))
+             for i in range(self.threads)]
+        [x.start() for x in t]
+
+        [x.join() for x in t]
+
+        # Make sure all threads returned the correct value
+        for i in range(self.threads):
+            xp_assert_equal(
+                q.get(timeout=5), expected,
+                err_msg='Function returned wrong value in multithreaded context'
+            )
+
+    @make_xp_test_case(fft.fft)
+    def test_fft(self, xp):
+        a = xp.ones(self.input_shape, dtype=xp.complex128)
+        self._test_mtsame(fft.fft, a, xp=xp)
+
+    @make_xp_test_case(fft.ifft)
+    def test_ifft(self, xp):
+        a = xp.full(self.input_shape, 1+0j)
+        self._test_mtsame(fft.ifft, a, xp=xp)
+
+    @make_xp_test_case(fft.rfft)
+    def test_rfft(self, xp):
+        a = xp.ones(self.input_shape)
+        self._test_mtsame(fft.rfft, a, xp=xp)
+
+    @make_xp_test_case(fft.irfft)
+    def test_irfft(self, xp):
+        a = xp.full(self.input_shape, 1+0j)
+        self._test_mtsame(fft.irfft, a, xp=xp)
+
+    @make_xp_test_case(fft.hfft)
+    def test_hfft(self, xp):
+        a = xp.ones(self.input_shape, dtype=xp.complex64)
+        self._test_mtsame(fft.hfft, a, xp=xp)
+
+    @make_xp_test_case(fft.ihfft)
+    def test_ihfft(self, xp):
+        a = xp.ones(self.input_shape)
+        self._test_mtsame(fft.ihfft, a, xp=xp)
+
+
+@pytest.mark.parametrize("func", [fft.fft, fft.ifft, fft.rfft, fft.irfft])
+def test_multiprocess(func):
+    # Test that fft still works after fork (gh-10422)
+
+    with multiprocessing.Pool(2) as p:
+        res = p.map(func, [np.ones(100) for _ in range(4)])
+
+    expect = func(np.ones(100))
+    for x in res:
+        assert_allclose(x, expect)
+
+
+@make_xp_test_case(fft.irfftn)
+class TestIRFFTN:
+
+    def test_not_last_axis_success(self, xp):
+        ar, ai = np.random.random((2, 16, 8, 32))
+        a = ar + 1j*ai
+        a = xp.asarray(a)
+
+        axes = (-2,)
+
+        # Should not raise error
+        fft.irfftn(a, axes=axes)
+
+
+@pytest.mark.parametrize("func", [make_xp_pytest_param(fft.fft),
+                                  make_xp_pytest_param(fft.ifft),
+                                  make_xp_pytest_param(fft.rfft),
+                                  make_xp_pytest_param(fft.irfft),
+                                  make_xp_pytest_param(fft.fftn),
+                                  make_xp_pytest_param(fft.ifftn),
+                                  make_xp_pytest_param(fft.rfftn),
+                                  make_xp_pytest_param(fft.irfftn),
+                                  make_xp_pytest_param(fft.hfft),
+                                  make_xp_pytest_param(fft.ihfft)])
+def test_non_standard_params(func, xp):
+    # use __name__ so that `lazy_xp_function` doesn't break things
+    if func.__name__ in ["rfft", "rfftn", "ihfft"]:
+        dtype = xp.float64
+    else:
+        dtype = xp.complex128
+
+    x = xp.asarray([1, 2, 3], dtype=dtype)
+    # func(x) should not raise an exception
+    func(x)
+
+    if is_numpy(xp):
+        func(x, workers=2)
+    else:
+        assert_raises(ValueError, func, x, workers=2)
+
+    # `plan` param is not tested since SciPy does not use it currently
+    # but should be tested if it comes into use
+
+
+@pytest.mark.parametrize("dtype", ['float32', 'float64'])
+@pytest.mark.parametrize("func", [make_xp_pytest_param(fft.fft),
+                                  make_xp_pytest_param(fft.ifft),
+                                  make_xp_pytest_param(fft.irfft),
+                                  make_xp_pytest_param(fft.fftn),
+                                  make_xp_pytest_param(fft.ifftn),
+                                  make_xp_pytest_param(fft.irfftn),
+                                  make_xp_pytest_param(fft.hfft)])
+def test_real_input(func, dtype, xp):
+    x = xp.asarray([1, 2, 3], dtype=getattr(xp, dtype))
+    # func(x) should not raise an exception
+    func(x)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_fftlog.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_fftlog.py
new file mode 100644
index 0000000000000000000000000000000000000000..636d3fa8ffec108971385371213c4680b6a74035
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_fftlog.py
@@ -0,0 +1,214 @@
+import warnings
+import math
+
+import numpy as np
+import pytest
+
+from scipy.fft._fftlog import fht, ifht, fhtoffset
+from scipy.special import poch
+
+from scipy._lib._array_api import xp_assert_close, xp_assert_less
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+
+def test_fht_agrees_with_fftlog(xp):
+    # check that fht numerically agrees with the output from Fortran FFTLog,
+    # the results were generated with the provided `fftlogtest` program,
+    # after fixing how the k array is generated (divide range by n-1, not n)
+
+    # test function, analytical Hankel transform is of the same form
+    def f(r, mu):
+        return r**(mu+1)*np.exp(-r**2/2)
+
+    r = np.logspace(-4, 4, 16)
+
+    dln = math.log(r[1]/r[0])
+    mu = 0.3
+    offset = 0.0
+    bias = 0.0
+
+    a = xp.asarray(f(r, mu))
+
+    # test 1: compute as given
+    ours = fht(a, dln, mu, offset=offset, bias=bias)
+    theirs = [-0.1159922613593045E-02, +0.1625822618458832E-02,
+              -0.1949518286432330E-02, +0.3789220182554077E-02,
+              +0.5093959119952945E-03, +0.2785387803618774E-01,
+              +0.9944952700848897E-01, +0.4599202164586588E+00,
+              +0.3157462160881342E+00, -0.8201236844404755E-03,
+              -0.7834031308271878E-03, +0.3931444945110708E-03,
+              -0.2697710625194777E-03, +0.3568398050238820E-03,
+              -0.5554454827797206E-03, +0.8286331026468585E-03]
+    theirs = xp.asarray(theirs, dtype=xp.float64)
+    xp_assert_close(ours, theirs)
+
+    # test 2: change to optimal offset
+    offset = fhtoffset(dln, mu, bias=bias)
+    ours = fht(a, dln, mu, offset=offset, bias=bias)
+    theirs = [+0.4353768523152057E-04, -0.9197045663594285E-05,
+              +0.3150140927838524E-03, +0.9149121960963704E-03,
+              +0.5808089753959363E-02, +0.2548065256377240E-01,
+              +0.1339477692089897E+00, +0.4821530509479356E+00,
+              +0.2659899781579785E+00, -0.1116475278448113E-01,
+              +0.1791441617592385E-02, -0.4181810476548056E-03,
+              +0.1314963536765343E-03, -0.5422057743066297E-04,
+              +0.3208681804170443E-04, -0.2696849476008234E-04]
+    theirs = xp.asarray(theirs, dtype=xp.float64)
+    xp_assert_close(ours, theirs)
+
+    # test 3: positive bias
+    bias = 0.8
+    offset = fhtoffset(dln, mu, bias=bias)
+    # offset is a np.float64, which array-api-strict disallows
+    # even if it's technically a subclass of float
+    offset = float(offset)
+
+    ours = fht(a, dln, mu, offset=offset, bias=bias)
+    theirs = [-7.3436673558316850E+00, +0.1710271207817100E+00,
+              +0.1065374386206564E+00, -0.5121739602708132E-01,
+              +0.2636649319269470E-01, +0.1697209218849693E-01,
+              +0.1250215614723183E+00, +0.4739583261486729E+00,
+              +0.2841149874912028E+00, -0.8312764741645729E-02,
+              +0.1024233505508988E-02, -0.1644902767389120E-03,
+              +0.3305775476926270E-04, -0.7786993194882709E-05,
+              +0.1962258449520547E-05, -0.8977895734909250E-06]
+    theirs = xp.asarray(theirs, dtype=xp.float64)
+    xp_assert_close(ours, theirs)
+
+    # test 4: negative bias
+    bias = -0.8
+    offset = fhtoffset(dln, mu, bias=bias)
+    offset = float(offset)
+
+    ours = fht(a, dln, mu, offset=offset, bias=bias)
+    theirs = [+0.8985777068568745E-05, +0.4074898209936099E-04,
+              +0.2123969254700955E-03, +0.1009558244834628E-02,
+              +0.5131386375222176E-02, +0.2461678673516286E-01,
+              +0.1235812845384476E+00, +0.4719570096404403E+00,
+              +0.2893487490631317E+00, -0.1686570611318716E-01,
+              +0.2231398155172505E-01, -0.1480742256379873E-01,
+              +0.1692387813500801E+00, +0.3097490354365797E+00,
+              +2.7593607182401860E+00, 10.5251075070045800E+00]
+    theirs = xp.asarray(theirs, dtype=xp.float64)
+    xp_assert_close(ours, theirs)
+
+
+@pytest.mark.parametrize('optimal', [True, False])
+@pytest.mark.parametrize('offset', [0.0, 1.0, -1.0])
+@pytest.mark.parametrize('bias', [0, 0.1, -0.1])
+@pytest.mark.parametrize('n', [64, 63])
+def test_fht_identity(n, bias, offset, optimal, xp):
+    rng = np.random.RandomState(3491349965)
+
+    a = xp.asarray(rng.standard_normal(n))
+    dln = rng.uniform(-1, 1)
+    mu = rng.uniform(-2, 2)
+
+    if optimal:
+        offset = fhtoffset(dln, mu, initial=offset, bias=bias)
+        # offset is a np.float64, which array-api-strict disallows
+        # even if it's technically a subclass of float
+        offset = float(offset)
+
+    A = fht(a, dln, mu, offset=offset, bias=bias)
+    a_ = ifht(A, dln, mu, offset=offset, bias=bias)
+
+    xp_assert_close(a_, a, rtol=1.5e-7)
+
+
+
+
+def test_fht_special_cases(xp):
+    rng = np.random.RandomState(3491349965)
+
+    a = xp.asarray(rng.standard_normal(64))
+    dln = rng.uniform(-1, 1)
+
+    # let x = (mu+1+q)/2, y = (mu+1-q)/2, M = {0, -1, -2, ...}
+
+    # case 1: x in M, y in M => well-defined transform
+    mu, bias = -4.0, 1.0
+    with warnings.catch_warnings(record=True) as record:
+        fht(a, dln, mu, bias=bias)
+        assert not record, 'fht warned about a well-defined transform'
+
+    # case 2: x not in M, y in M => well-defined transform
+    mu, bias = -2.5, 0.5
+    with warnings.catch_warnings(record=True) as record:
+        fht(a, dln, mu, bias=bias)
+        assert not record, 'fht warned about a well-defined transform'
+
+    # with fht_lock:
+    # case 3: x in M, y not in M => singular transform
+    mu, bias = -3.5, 0.5
+    with pytest.warns(Warning) as record:
+        fht(a, dln, mu, bias=bias)
+        assert record, 'fht did not warn about a singular transform'
+
+    # with fht_lock:
+    # case 4: x not in M, y in M => singular inverse transform
+    mu, bias = -2.5, 0.5
+    with pytest.warns(Warning) as record:
+        ifht(a, dln, mu, bias=bias)
+        assert record, 'ifht did not warn about a singular transform'
+
+
+@pytest.mark.parametrize('n', [64, 63])
+def test_fht_exact(n, xp):
+    rng = np.random.RandomState(3491349965)
+
+    # for a(r) a power law r^\gamma, the fast Hankel transform produces the
+    # exact continuous Hankel transform if biased with q = \gamma
+
+    mu = rng.uniform(0, 3)
+
+    # convergence of HT: -1-mu < gamma < 1/2
+    gamma = rng.uniform(-1-mu, 1/2)
+
+    r = np.logspace(-2, 2, n)
+    a = xp.asarray(r**gamma)
+
+    dln = math.log(r[1]/r[0])
+
+    offset = fhtoffset(dln, mu, initial=0.0, bias=gamma)
+    # offset is a np.float64, which array-api-strict disallows
+    # even if it's technically a subclass of float
+    offset = float(offset)
+
+    A = fht(a, dln, mu, offset=offset, bias=gamma)
+
+    k = np.exp(offset)/r[::-1]
+
+    # analytical result
+    At = xp.asarray((2/k)**gamma * poch((mu+1-gamma)/2, gamma))
+
+    xp_assert_close(A, At)
+
+@skip_xp_backends(np_only=True,
+                  reason='array-likes only supported for NumPy backend')
+@pytest.mark.parametrize("op", [fht, ifht])
+def test_array_like(xp, op):
+    x = [[[1.0, 1.0], [1.0, 1.0]],
+         [[1.0, 1.0], [1.0, 1.0]],
+         [[1.0, 1.0], [1.0, 1.0]]]
+    xp_assert_close(op(x, 1.0, 2.0), op(xp.asarray(x), 1.0, 2.0))
+
+@pytest.mark.parametrize('n', [128, 129])
+def test_gh_21661(xp, n):
+    one = xp.asarray(1.0)
+    mu = 0.0
+    r = np.logspace(-7, 1, n)
+    dln = math.log(r[1] / r[0])
+    offset = fhtoffset(dln, initial=-6 * np.log(10), mu=mu)
+    r = xp.asarray(r, dtype=one.dtype)
+    k = math.exp(offset) / xp.flip(r, axis=-1)
+
+    def f(x, mu):
+        return x**(mu + 1)*xp.exp(-x**2/2)
+
+    a_r = f(r, mu)
+    fht_val = fht(a_r, dln, mu=mu, offset=offset)
+    a_k = f(k, mu)
+    rel_err = xp.max(xp.abs((fht_val - a_k) / a_k))
+    xp_assert_less(rel_err, xp.asarray(7.28e+16)[()])
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_helper.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_helper.py
new file mode 100644
index 0000000000000000000000000000000000000000..b0427966c256ab7b919f75f4ae773a4b18be818a
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_helper.py
@@ -0,0 +1,555 @@
+"""Includes test functions for fftpack.helper module
+
+Copied from fftpack.helper by Pearu Peterson, October 2005
+Modified for Array API, 2023
+
+"""
+from scipy.fft._helper import next_fast_len, prev_fast_len, _init_nd_shape_and_axes
+from numpy.testing import assert_equal
+from pytest import raises as assert_raises
+import pytest
+import numpy as np
+import sys
+from scipy._lib._array_api import xp_assert_close, xp_device
+from scipy import fft
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+_5_smooth_numbers = [
+    2, 3, 4, 5, 6, 8, 9, 10,
+    2 * 3 * 5,
+    2**3 * 3**5,
+    2**3 * 3**3 * 5**2,
+]
+
+
+def test_next_fast_len():
+    for n in _5_smooth_numbers:
+        assert_equal(next_fast_len(n), n)
+
+
+def _assert_n_smooth(x, n):
+    x_orig = x
+    if n < 2:
+        assert False
+
+    while True:
+        q, r = divmod(x, 2)
+        if r != 0:
+            break
+        x = q
+
+    for d in range(3, n+1, 2):
+        while True:
+            q, r = divmod(x, d)
+            if r != 0:
+                break
+            x = q
+
+    assert x == 1, \
+           f'x={x_orig} is not {n}-smooth, remainder={x}'
+
+
+class TestNextFastLen:
+
+    def test_next_fast_len(self):
+        np.random.seed(1234)
+
+        def nums():
+            yield from range(1, 1000)
+            yield 2**5 * 3**5 * 4**5 + 1
+
+        for n in nums():
+            m = next_fast_len(n)
+            _assert_n_smooth(m, 11)
+            assert m == next_fast_len(n, False)
+
+            m = next_fast_len(n, True)
+            _assert_n_smooth(m, 5)
+
+    def test_np_integers(self):
+        ITYPES = [np.int16, np.int32, np.int64, np.uint16, np.uint32, np.uint64]
+        for ityp in ITYPES:
+            x = ityp(12345)
+            testN = next_fast_len(x)
+            assert_equal(testN, next_fast_len(int(x)))
+
+    def testnext_fast_len_small(self):
+        hams = {
+            1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 8, 8: 8, 14: 15, 15: 15,
+            16: 16, 17: 18, 1021: 1024, 1536: 1536, 51200000: 51200000
+        }
+        for x, y in hams.items():
+            assert_equal(next_fast_len(x, True), y)
+
+    @pytest.mark.xfail(sys.maxsize < 2**32,
+                       reason="Hamming Numbers too large for 32-bit",
+                       raises=ValueError, strict=True)
+    def testnext_fast_len_big(self):
+        hams = {
+            510183360: 510183360, 510183360 + 1: 512000000,
+            511000000: 512000000,
+            854296875: 854296875, 854296875 + 1: 859963392,
+            196608000000: 196608000000, 196608000000 + 1: 196830000000,
+            8789062500000: 8789062500000, 8789062500000 + 1: 8796093022208,
+            206391214080000: 206391214080000,
+            206391214080000 + 1: 206624260800000,
+            470184984576000: 470184984576000,
+            470184984576000 + 1: 470715894135000,
+            7222041363087360: 7222041363087360,
+            7222041363087360 + 1: 7230196133913600,
+            # power of 5    5**23
+            11920928955078125: 11920928955078125,
+            11920928955078125 - 1: 11920928955078125,
+            # power of 3    3**34
+            16677181699666569: 16677181699666569,
+            16677181699666569 - 1: 16677181699666569,
+            # power of 2   2**54
+            18014398509481984: 18014398509481984,
+            18014398509481984 - 1: 18014398509481984,
+            # above this, int(ceil(n)) == int(ceil(n+1))
+            19200000000000000: 19200000000000000,
+            19200000000000000 + 1: 19221679687500000,
+            288230376151711744: 288230376151711744,
+            288230376151711744 + 1: 288325195312500000,
+            288325195312500000 - 1: 288325195312500000,
+            288325195312500000: 288325195312500000,
+            288325195312500000 + 1: 288555831593533440,
+        }
+        for x, y in hams.items():
+            assert_equal(next_fast_len(x, True), y)
+
+    def test_keyword_args(self, xp):
+        assert next_fast_len(11, real=True) == 12
+        assert next_fast_len(target=7, real=False) == 7
+
+
+class TestPrevFastLen:
+
+    def test_prev_fast_len(self):
+        np.random.seed(1234)
+
+        def nums():
+            yield from range(1, 1000)
+            yield 2**5 * 3**5 * 4**5 + 1
+
+        for n in nums():
+            m = prev_fast_len(n)
+            _assert_n_smooth(m, 11)
+            assert m == prev_fast_len(n, False)
+
+            m = prev_fast_len(n, True)
+            _assert_n_smooth(m, 5)
+
+    def test_np_integers(self):
+        ITYPES = [np.int16, np.int32, np.int64, np.uint16, np.uint32,
+                    np.uint64]
+        for ityp in ITYPES:
+            x = ityp(12345)
+            testN = prev_fast_len(x)
+            assert_equal(testN, prev_fast_len(int(x)))
+
+            testN = prev_fast_len(x, real=True)
+            assert_equal(testN, prev_fast_len(int(x), real=True))
+
+    def testprev_fast_len_small(self):
+        hams = {
+            1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 6, 8: 8, 14: 12, 15: 15,
+            16: 16, 17: 16, 1021: 1000, 1536: 1536, 51200000: 51200000
+        }
+        for x, y in hams.items():
+            assert_equal(prev_fast_len(x, True), y)
+
+        hams = {
+            1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10,
+            11: 11, 12: 12, 13: 12, 14: 14, 15: 15, 16: 16, 17: 16, 18: 18,
+            19: 18, 20: 20, 21: 21, 22: 22, 120: 120, 121: 121, 122: 121,
+            1021: 1008, 1536: 1536, 51200000: 51200000
+        }
+        for x, y in hams.items():
+            assert_equal(prev_fast_len(x, False), y)
+
+    @pytest.mark.xfail(sys.maxsize < 2**32,
+                       reason="Hamming Numbers too large for 32-bit",
+                       raises=ValueError, strict=True)
+    def testprev_fast_len_big(self):
+        hams = {
+            # 2**6 * 3**13 * 5**1
+            510183360: 510183360,
+            510183360 + 1: 510183360,
+            510183360 - 1: 509607936,  # 2**21 * 3**5
+            # 2**6 * 5**6 * 7**1 * 73**1
+            511000000: 510183360,
+            511000000 + 1: 510183360,
+            511000000 - 1: 510183360,  # 2**6 * 3**13 * 5**1
+            # 3**7 * 5**8
+            854296875: 854296875,
+            854296875 + 1: 854296875,
+            854296875 - 1: 850305600,  # 2**6 * 3**12 * 5**2
+            # 2**22 * 3**1 * 5**6
+            196608000000: 196608000000,
+            196608000000 + 1: 196608000000,
+            196608000000 - 1: 195910410240,  # 2**13 * 3**14 * 5**1
+            # 2**5 * 3**2 * 5**15
+            8789062500000: 8789062500000,
+            8789062500000 + 1: 8789062500000,
+            8789062500000 - 1: 8748000000000,  # 2**11 * 3**7 * 5**9
+            # 2**24 * 3**9 * 5**4
+            206391214080000: 206391214080000,
+            206391214080000 + 1: 206391214080000,
+            206391214080000 - 1: 206158430208000,  # 2**39 * 3**1 * 5**3
+            # 2**18 * 3**15 * 5**3
+            470184984576000: 470184984576000,
+            470184984576000 + 1: 470184984576000,
+            470184984576000 - 1: 469654673817600,  # 2**33 * 3**7 **5**2
+            # 2**25 * 3**16 * 5**1
+            7222041363087360: 7222041363087360,
+            7222041363087360 + 1: 7222041363087360,
+            7222041363087360 - 1: 7213895789838336,  # 2**40 * 3**8
+            # power of 5    5**23
+            11920928955078125: 11920928955078125,
+            11920928955078125 + 1: 11920928955078125,
+            11920928955078125 - 1: 11901557422080000,  # 2**14 * 3**19 * 5**4
+            # power of 3    3**34
+            16677181699666569: 16677181699666569,
+            16677181699666569 + 1: 16677181699666569,
+            16677181699666569 - 1: 16607531250000000,  # 2**7 * 3**12 * 5**12
+            # power of 2   2**54
+            18014398509481984: 18014398509481984,
+            18014398509481984 + 1: 18014398509481984,
+            18014398509481984 - 1: 18000000000000000,  # 2**16 * 3**2 * 5**15
+            # 2**20 * 3**1 * 5**14
+            19200000000000000: 19200000000000000,
+            19200000000000000 + 1: 19200000000000000,
+            19200000000000000 - 1: 19131876000000000,  # 2**11 * 3**14 * 5**9
+            # 2**58
+            288230376151711744: 288230376151711744,
+            288230376151711744 + 1: 288230376151711744,
+            288230376151711744 - 1: 288000000000000000,  # 2**20 * 3**2 * 5**15
+            # 2**5 * 3**10 * 5**16
+            288325195312500000: 288325195312500000,
+            288325195312500000 + 1: 288325195312500000,
+            288325195312500000 - 1: 288230376151711744,  # 2**58
+        }
+        for x, y in hams.items():
+            assert_equal(prev_fast_len(x, True), y)
+
+    def test_keyword_args(self):
+        assert prev_fast_len(11, real=True) == 10
+        assert prev_fast_len(target=7, real=False) == 7
+
+
+@skip_xp_backends(cpu_only=True)
+class Test_init_nd_shape_and_axes:
+
+    def test_py_0d_defaults(self, xp):
+        x = xp.asarray(4)
+        shape = None
+        axes = None
+
+        shape_expected = ()
+        axes_expected = []
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_xp_0d_defaults(self, xp):
+        x = xp.asarray(7.)
+        shape = None
+        axes = None
+
+        shape_expected = ()
+        axes_expected = []
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_py_1d_defaults(self, xp):
+        x = xp.asarray([1, 2, 3])
+        shape = None
+        axes = None
+
+        shape_expected = (3,)
+        axes_expected = [0]
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_xp_1d_defaults(self, xp):
+        x = xp.arange(0, 1, .1)
+        shape = None
+        axes = None
+
+        shape_expected = (10,)
+        axes_expected = [0]
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_py_2d_defaults(self, xp):
+        x = xp.asarray([[1, 2, 3, 4],
+                        [5, 6, 7, 8]])
+        shape = None
+        axes = None
+
+        shape_expected = (2, 4)
+        axes_expected = [0, 1]
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_xp_2d_defaults(self, xp):
+        x = xp.arange(0, 1, .1)
+        x = xp.reshape(x, (5, 2))
+        shape = None
+        axes = None
+
+        shape_expected = (5, 2)
+        axes_expected = [0, 1]
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_xp_5d_defaults(self, xp):
+        x = xp.zeros([6, 2, 5, 3, 4])
+        shape = None
+        axes = None
+
+        shape_expected = (6, 2, 5, 3, 4)
+        axes_expected = [0, 1, 2, 3, 4]
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_xp_5d_set_shape(self, xp):
+        x = xp.zeros([6, 2, 5, 3, 4])
+        shape = [10, -1, -1, 1, 4]
+        axes = None
+
+        shape_expected = (10, 2, 5, 1, 4)
+        axes_expected = [0, 1, 2, 3, 4]
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_xp_5d_set_axes(self, xp):
+        x = xp.zeros([6, 2, 5, 3, 4])
+        shape = None
+        axes = [4, 1, 2]
+
+        shape_expected = (4, 2, 5)
+        axes_expected = [4, 1, 2]
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_xp_5d_set_shape_axes(self, xp):
+        x = xp.zeros([6, 2, 5, 3, 4])
+        shape = [10, -1, 2]
+        axes = [1, 0, 3]
+
+        shape_expected = (10, 6, 2)
+        axes_expected = [1, 0, 3]
+
+        shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
+
+        assert shape_res == shape_expected
+        assert axes_res == axes_expected
+
+    def test_shape_axes_subset(self, xp):
+        x = xp.zeros((2, 3, 4, 5))
+        shape, axes = _init_nd_shape_and_axes(x, shape=(5, 5, 5), axes=None)
+
+        assert shape == (5, 5, 5)
+        assert axes == [1, 2, 3]
+
+    def test_errors(self, xp):
+        x = xp.zeros(1)
+        with assert_raises(ValueError, match="axes must be a scalar or "
+                           "iterable of integers"):
+            _init_nd_shape_and_axes(x, shape=None, axes=[[1, 2], [3, 4]])
+
+        with assert_raises(ValueError, match="axes must be a scalar or "
+                           "iterable of integers"):
+            _init_nd_shape_and_axes(x, shape=None, axes=[1., 2., 3., 4.])
+
+        with assert_raises(ValueError,
+                           match="axes exceeds dimensionality of input"):
+            _init_nd_shape_and_axes(x, shape=None, axes=[1])
+
+        with assert_raises(ValueError,
+                           match="axes exceeds dimensionality of input"):
+            _init_nd_shape_and_axes(x, shape=None, axes=[-2])
+
+        with assert_raises(ValueError,
+                           match="all axes must be unique"):
+            _init_nd_shape_and_axes(x, shape=None, axes=[0, 0])
+
+        with assert_raises(ValueError, match="shape must be a scalar or "
+                           "iterable of integers"):
+            _init_nd_shape_and_axes(x, shape=[[1, 2], [3, 4]], axes=None)
+
+        with assert_raises(ValueError, match="shape must be a scalar or "
+                           "iterable of integers"):
+            _init_nd_shape_and_axes(x, shape=[1., 2., 3., 4.], axes=None)
+
+        with assert_raises(ValueError,
+                           match="when given, axes and shape arguments"
+                           " have to be of the same length"):
+            _init_nd_shape_and_axes(xp.zeros([1, 1, 1, 1]),
+                                    shape=[1, 2, 3], axes=[1])
+
+        with assert_raises(ValueError,
+                           match="invalid number of data points"
+                           r" \(\[0\]\) specified"):
+            _init_nd_shape_and_axes(x, shape=[0], axes=None)
+
+        with assert_raises(ValueError,
+                           match="invalid number of data points"
+                           r" \(\[-2\]\) specified"):
+            _init_nd_shape_and_axes(x, shape=-2, axes=None)
+
+
+class TestFFTShift:
+
+    def test_definition(self, xp):
+        x = xp.asarray([0., 1, 2, 3, 4, -4, -3, -2, -1])
+        y = xp.asarray([-4., -3, -2, -1, 0, 1, 2, 3, 4])
+        xp_assert_close(fft.fftshift(x), y)
+        xp_assert_close(fft.ifftshift(y), x)
+        x = xp.asarray([0., 1, 2, 3, 4, -5, -4, -3, -2, -1])
+        y = xp.asarray([-5., -4, -3, -2, -1, 0, 1, 2, 3, 4])
+        xp_assert_close(fft.fftshift(x), y)
+        xp_assert_close(fft.ifftshift(y), x)
+
+    def test_inverse(self, xp):
+        for n in [1, 4, 9, 100, 211]:
+            x = xp.asarray(np.random.random((n,)))
+            xp_assert_close(fft.ifftshift(fft.fftshift(x)), x)
+
+    def test_axes_keyword(self, xp):
+        freqs = xp.asarray([[0., 1, 2], [3, 4, -4], [-3, -2, -1]])
+        shifted = xp.asarray([[-1., -3, -2], [2, 0, 1], [-4, 3, 4]])
+        xp_assert_close(fft.fftshift(freqs, axes=(0, 1)), shifted)
+        xp_assert_close(fft.fftshift(freqs, axes=0), fft.fftshift(freqs, axes=(0,)))
+        xp_assert_close(fft.ifftshift(shifted, axes=(0, 1)), freqs)
+        xp_assert_close(fft.ifftshift(shifted, axes=0),
+                        fft.ifftshift(shifted, axes=(0,)))
+        xp_assert_close(fft.fftshift(freqs), shifted)
+        xp_assert_close(fft.ifftshift(shifted), freqs)
+
+    def test_uneven_dims(self, xp):
+        """ Test 2D input, which has uneven dimension sizes """
+        freqs = xp.asarray([
+            [0, 1],
+            [2, 3],
+            [4, 5]
+        ], dtype=xp.float64)
+
+        # shift in dimension 0
+        shift_dim0 = xp.asarray([
+            [4, 5],
+            [0, 1],
+            [2, 3]
+        ], dtype=xp.float64)
+        xp_assert_close(fft.fftshift(freqs, axes=0), shift_dim0)
+        xp_assert_close(fft.ifftshift(shift_dim0, axes=0), freqs)
+        xp_assert_close(fft.fftshift(freqs, axes=(0,)), shift_dim0)
+        xp_assert_close(fft.ifftshift(shift_dim0, axes=[0]), freqs)
+
+        # shift in dimension 1
+        shift_dim1 = xp.asarray([
+            [1, 0],
+            [3, 2],
+            [5, 4]
+        ], dtype=xp.float64)
+        xp_assert_close(fft.fftshift(freqs, axes=1), shift_dim1)
+        xp_assert_close(fft.ifftshift(shift_dim1, axes=1), freqs)
+
+        # shift in both dimensions
+        shift_dim_both = xp.asarray([
+            [5, 4],
+            [1, 0],
+            [3, 2]
+        ], dtype=xp.float64)
+        xp_assert_close(fft.fftshift(freqs, axes=(0, 1)), shift_dim_both)
+        xp_assert_close(fft.ifftshift(shift_dim_both, axes=(0, 1)), freqs)
+        xp_assert_close(fft.fftshift(freqs, axes=[0, 1]), shift_dim_both)
+        xp_assert_close(fft.ifftshift(shift_dim_both, axes=[0, 1]), freqs)
+
+        # axes=None (default) shift in all dimensions
+        xp_assert_close(fft.fftshift(freqs, axes=None), shift_dim_both)
+        xp_assert_close(fft.ifftshift(shift_dim_both, axes=None), freqs)
+        xp_assert_close(fft.fftshift(freqs), shift_dim_both)
+        xp_assert_close(fft.ifftshift(shift_dim_both), freqs)
+
+
+class TestFFTFreq:
+    def test_definition(self, xp):
+        x = xp.asarray([0, 1, 2, 3, 4, -4, -3, -2, -1], dtype=xp.float64)
+        x2 = xp.asarray([0, 1, 2, 3, 4, -5, -4, -3, -2, -1], dtype=xp.float64)
+
+        # default dtype varies across backends
+
+        y = 9 * fft.fftfreq(9, xp=xp)
+        xp_assert_close(y, x, check_dtype=False, check_namespace=True)
+
+        y = 9 * xp.pi * fft.fftfreq(9, xp.pi, xp=xp)
+        xp_assert_close(y, x, check_dtype=False)
+
+        y = 10 * fft.fftfreq(10, xp=xp)
+        xp_assert_close(y, x2, check_dtype=False)
+
+        y = 10 * xp.pi * fft.fftfreq(10, xp.pi, xp=xp)
+        xp_assert_close(y, x2, check_dtype=False)
+
+    def test_device(self, xp, devices):
+        for d in devices:
+            y = fft.fftfreq(9, xp=xp, device=d)
+            x = xp.empty(0, device=d)
+            assert xp_device(y) == xp_device(x)
+
+
+class TestRFFTFreq:
+
+    def test_definition(self, xp):
+        x = xp.asarray([0, 1, 2, 3, 4], dtype=xp.float64)
+        x2 = xp.asarray([0, 1, 2, 3, 4, 5], dtype=xp.float64)
+
+        # default dtype varies across backends
+
+        y = 9 * fft.rfftfreq(9, xp=xp)
+        xp_assert_close(y, x, check_dtype=False, check_namespace=True)
+
+        y = 9 * xp.pi * fft.rfftfreq(9, xp.pi, xp=xp)
+        xp_assert_close(y, x, check_dtype=False)
+
+        y = 10 * fft.rfftfreq(10, xp=xp)
+        xp_assert_close(y, x2, check_dtype=False)
+
+        y = 10 * xp.pi * fft.rfftfreq(10, xp.pi, xp=xp)
+        xp_assert_close(y, x2, check_dtype=False)
+
+    def test_device(self, xp, devices):
+        for d in devices:
+            y = fft.rfftfreq(9, xp=xp, device=d)
+            x = xp.empty(0, device=d)
+            assert xp_device(y) == xp_device(x)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_multithreading.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_multithreading.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a6b71b830211f8bcbe56e97ff71098be75021c8
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_multithreading.py
@@ -0,0 +1,84 @@
+from scipy import fft
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+import multiprocessing
+import os
+
+
+@pytest.fixture(scope='module')
+def x():
+    return np.random.randn(512, 128)  # Must be large enough to qualify for mt
+
+
+@pytest.mark.parametrize("func", [
+    fft.fft, fft.ifft, fft.fft2, fft.ifft2, fft.fftn, fft.ifftn,
+    fft.rfft, fft.irfft, fft.rfft2, fft.irfft2, fft.rfftn, fft.irfftn,
+    fft.hfft, fft.ihfft, fft.hfft2, fft.ihfft2, fft.hfftn, fft.ihfftn,
+    fft.dct, fft.idct, fft.dctn, fft.idctn,
+    fft.dst, fft.idst, fft.dstn, fft.idstn,
+])
+@pytest.mark.parametrize("workers", [2, -1])
+def test_threaded_same(x, func, workers):
+    expected = func(x, workers=1)
+    actual = func(x, workers=workers)
+    assert_allclose(actual, expected)
+
+
+def _mt_fft(x):
+    return fft.fft(x, workers=2)
+
+
+@pytest.mark.slow
+def test_mixed_threads_processes(x):
+    # Test that the fft threadpool is safe to use before & after fork
+
+    expect = fft.fft(x, workers=2)
+
+    with multiprocessing.Pool(2) as p:
+        res = p.map(_mt_fft, [x for _ in range(4)])
+
+    for r in res:
+        assert_allclose(r, expect)
+
+    fft.fft(x, workers=2)
+
+
+def test_invalid_workers(x):
+    cpus = os.cpu_count()
+
+    fft.ifft([1], workers=-cpus)
+
+    with pytest.raises(ValueError, match='workers must not be zero'):
+        fft.fft(x, workers=0)
+
+    with pytest.raises(ValueError, match='workers value out of range'):
+        fft.ifft(x, workers=-cpus-1)
+
+
+def test_set_get_workers():
+    cpus = os.cpu_count()
+    assert fft.get_workers() == 1
+    with fft.set_workers(4):
+        assert fft.get_workers() == 4
+
+        with fft.set_workers(-1):
+            assert fft.get_workers() == cpus
+
+        assert fft.get_workers() == 4
+
+    assert fft.get_workers() == 1
+
+    with fft.set_workers(-cpus):
+        assert fft.get_workers() == 1
+
+
+def test_set_workers_invalid():
+
+    with pytest.raises(ValueError, match='workers must not be zero'):
+        with fft.set_workers(0):
+            pass
+
+    with pytest.raises(ValueError, match='workers value out of range'):
+        with fft.set_workers(-os.cpu_count()-1):
+            pass
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_real_transforms.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_real_transforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..3add13d58ae70a567f3f4bf7b73dda72a15a47ae
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fft/tests/test_real_transforms.py
@@ -0,0 +1,249 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_equal
+import pytest
+import math
+
+from scipy.fft import dct, idct, dctn, idctn, dst, idst, dstn, idstn
+import scipy.fft as fft
+from scipy import fftpack
+from scipy._lib._array_api import (xp_copy, xp_assert_close, make_xp_test_case,
+                                   make_xp_pytest_param)
+import scipy._lib.array_api_extra as xpx
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+
+SQRT_2 = math.sqrt(2)
+
+# scipy.fft wraps the fftpack versions but with normalized inverse transforms.
+# So, the forward transforms and definitions are already thoroughly tested in
+# fftpack/test_real_transforms.py
+
+
+@pytest.mark.parametrize("forward, backward", [make_xp_pytest_param(dct, idct),
+                                               make_xp_pytest_param(dst, idst)])
+@pytest.mark.parametrize("type", [1, 2, 3, 4])
+@pytest.mark.parametrize("n", [2, 3, 4, 5, 10, 16])
+@pytest.mark.parametrize("axis", [0, 1])
+@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
+@pytest.mark.parametrize("orthogonalize", [False, True])
+def test_identity_1d(forward, backward, type, n, axis, norm, orthogonalize, xp):
+    # Test the identity f^-1(f(x)) == x
+    x = xp.asarray(np.random.rand(n, n))
+
+    y = forward(x, type, axis=axis, norm=norm, orthogonalize=orthogonalize)
+    z = backward(y, type, axis=axis, norm=norm, orthogonalize=orthogonalize)
+    xp_assert_close(z, x)
+
+    pad = [(0, 0)] * 2
+    pad[axis] = (0, 4)
+
+    y2 = xp.asarray(np.pad(np.asarray(y), pad, mode='edge'))
+    z2 = backward(y2, type, n, axis, norm, orthogonalize=orthogonalize)
+    xp_assert_close(z2, x)
+
+
+@skip_xp_backends(np_only=True,
+                  reason='`overwrite_x` only supported for NumPy backend.')
+@pytest.mark.parametrize("forward, backward", [(dct, idct), (dst, idst)])
+@pytest.mark.parametrize("type", [1, 2, 3, 4])
+@pytest.mark.parametrize("dtype", [np.float16, np.float32, np.float64,
+                                   np.complex64, np.complex128])
+@pytest.mark.parametrize("axis", [0, 1])
+@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
+@pytest.mark.parametrize("overwrite_x", [True, False])
+def test_identity_1d_overwrite(forward, backward, type, dtype, axis, norm,
+                               overwrite_x, xp):
+    # Test the identity f^-1(f(x)) == x
+    x = np.random.rand(7, 8).astype(dtype)
+    x_orig = x.copy()
+
+    y = forward(x, type, axis=axis, norm=norm, overwrite_x=overwrite_x)
+    y_orig = y.copy()
+    z = backward(y, type, axis=axis, norm=norm, overwrite_x=overwrite_x)
+    if not overwrite_x:
+        assert_allclose(z, x, rtol=1e-6, atol=1e-6)
+        assert_array_equal(x, x_orig)
+        assert_array_equal(y, y_orig)
+    else:
+        assert_allclose(z, x_orig, rtol=1e-6, atol=1e-6)
+
+
+@pytest.mark.parametrize("forward, backward", [make_xp_pytest_param(dctn, idctn),
+                                               make_xp_pytest_param(dstn, idstn)])
+@pytest.mark.parametrize("type", [1, 2, 3, 4])
+@pytest.mark.parametrize("shape, axes",
+                         [
+                             ((4, 4), 0),
+                             ((4, 4), 1),
+                             ((4, 4), None),
+                             ((4, 4), (0, 1)),
+                             ((10, 12), None),
+                             ((10, 12), (0, 1)),
+                             ((4, 5, 6), None),
+                             ((4, 5, 6), 1),
+                             ((4, 5, 6), (0, 2)),
+                         ])
+@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
+@pytest.mark.parametrize("orthogonalize", [False, True])
+def test_identity_nd(forward, backward, type, shape, axes, norm,
+                     orthogonalize, xp):
+    # Test the identity f^-1(f(x)) == x
+
+    x = xp.asarray(np.random.random(shape))
+
+    if axes is not None:
+        shape = np.take(shape, axes)
+
+    y = forward(x, type, axes=axes, norm=norm, orthogonalize=orthogonalize)
+    z = backward(y, type, axes=axes, norm=norm, orthogonalize=orthogonalize)
+    xp_assert_close(z, x)
+
+    if axes is None:
+        pad = [(0, 4)] * x.ndim
+    elif isinstance(axes, int):
+        pad = [(0, 0)] * x.ndim
+        pad[axes] = (0, 4)
+    else:
+        pad = [(0, 0)] * x.ndim
+
+        for a in axes:
+            pad[a] = (0, 4)
+
+    # TODO write an array-agnostic pad
+    y2 = xp.asarray(np.pad(np.asarray(y), pad, mode='edge'))
+    z2 = backward(y2, type, shape, axes, norm, orthogonalize=orthogonalize)
+    xp_assert_close(z2, x)
+
+
+@skip_xp_backends(np_only=True,
+                  reason='`overwrite_x` only supported for NumPy backend.')
+@pytest.mark.parametrize("forward, backward", [(dctn, idctn), (dstn, idstn)])
+@pytest.mark.parametrize("type", [1, 2, 3, 4])
+@pytest.mark.parametrize("shape, axes",
+                         [
+                             ((4, 5), 0),
+                             ((4, 5), 1),
+                             ((4, 5), None),
+                         ])
+@pytest.mark.parametrize("dtype", [np.float16, np.float32, np.float64,
+                                   np.complex64, np.complex128])
+@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
+@pytest.mark.parametrize("overwrite_x", [False, True])
+def test_identity_nd_overwrite(forward, backward, type, shape, axes, dtype,
+                               norm, overwrite_x, xp):
+    # Test the identity f^-1(f(x)) == x
+
+    x = np.random.random(shape).astype(dtype)
+    x_orig = x.copy()
+
+    if axes is not None:
+        shape = np.take(shape, axes)
+
+    y = forward(x, type, axes=axes, norm=norm)
+    y_orig = y.copy()
+    z = backward(y, type, axes=axes, norm=norm)
+    if overwrite_x:
+        assert_allclose(z, x_orig, rtol=1e-6, atol=1e-6)
+    else:
+        assert_allclose(z, x, rtol=1e-6, atol=1e-6)
+        assert_array_equal(x, x_orig)
+        assert_array_equal(y, y_orig)
+
+
+@pytest.mark.parametrize("func", [make_xp_pytest_param(dct),
+                                  make_xp_pytest_param(dst),
+                                  make_xp_pytest_param(dctn),
+                                  make_xp_pytest_param(dstn)])
+@pytest.mark.parametrize("type", [1, 2, 3, 4])
+@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
+def test_fftpack_equivalience(func, type, norm, xp):
+    x = np.random.rand(8, 16)
+    fftpack_res = xp.asarray(getattr(fftpack, func.__name__)(x, type, norm=norm))
+    x = xp.asarray(x)
+    fft_res = getattr(fft, func.__name__)(x, type, norm=norm)
+
+    xp_assert_close(fft_res, fftpack_res)
+
+
+@pytest.mark.parametrize("func", [make_xp_pytest_param(dct),
+                                  make_xp_pytest_param(dst),
+                                  make_xp_pytest_param(dctn),
+                                  make_xp_pytest_param(dstn)])
+@pytest.mark.parametrize("type", [1, 2, 3, 4])
+def test_orthogonalize_default(func, type, xp):
+    # Test orthogonalize is the default when norm="ortho", but not otherwise
+    x = xp.asarray(np.random.rand(100))
+
+    for norm, ortho in [
+            ("forward", False),
+            ("backward", False),
+            ("ortho", True),
+    ]:
+        a = func(x, type=type, norm=norm, orthogonalize=ortho)
+        b = func(x, type=type, norm=norm)
+        xp_assert_close(a, b)
+
+
+@pytest.mark.parametrize("norm", ["backward", "ortho", "forward"])
+@pytest.mark.parametrize("func, type", [make_xp_pytest_param(dct, 4),
+                                        make_xp_pytest_param(dst, 1),
+                                        make_xp_pytest_param(dst, 4)])
+def test_orthogonalize_noop(func, type, norm, xp):
+    # Transforms where orthogonalize is a no-op
+    x = xp.asarray(np.random.rand(100))
+    y1 = func(x, type=type, norm=norm, orthogonalize=True)
+    y2 = func(x, type=type, norm=norm, orthogonalize=False)
+    xp_assert_close(y1, y2)
+
+
+@make_xp_test_case(dct)
+@pytest.mark.parametrize("norm", ["backward", "ortho", "forward"])
+def test_orthogonalize_dct1(norm, xp):
+    x = xp.asarray(np.random.rand(100))
+
+    x2 = xp_copy(x, xp=xp)
+    xpx.at(x2, 0).multiply(SQRT_2)
+    xpx.at(x2, -1).multiply(SQRT_2)
+
+    y1 = dct(x, type=1, norm=norm, orthogonalize=True)
+    y2 = dct(x2, type=1, norm=norm, orthogonalize=False)
+
+    xpx.at(y2, 0).divide(SQRT_2)
+    xpx.at(y2, -1).divide(SQRT_2)
+    xp_assert_close(y1, y2)
+
+
+
+@pytest.mark.parametrize("norm", ["backward", "ortho", "forward"])
+@pytest.mark.parametrize("func", [make_xp_pytest_param(dct),
+                                  make_xp_pytest_param(dst)])
+def test_orthogonalize_dcst2(func, norm, xp):
+    x = xp.asarray(np.random.rand(100))
+    y1 = func(x, type=2, norm=norm, orthogonalize=True)
+    y2 = func(x, type=2, norm=norm, orthogonalize=False)
+
+    xpx.at(y2, 0 if func.__name__ == "dct" else -1).divide(SQRT_2)
+    xp_assert_close(y1, y2)
+
+
+@pytest.mark.parametrize("norm", ["backward", "ortho", "forward"])
+@pytest.mark.parametrize("func", [make_xp_pytest_param(dct),
+                                  make_xp_pytest_param(dst)])
+def test_orthogonalize_dcst3(func, norm, xp):
+    x = xp.asarray(np.random.rand(100))
+    x2 = xp_copy(x, xp=xp)
+    xpx.at(x2, 0 if func.__name__ == "dct" else -1).multiply(SQRT_2)
+
+    y1 = func(x, type=3, norm=norm, orthogonalize=True)
+    y2 = func(x2, type=3, norm=norm, orthogonalize=False)
+    xp_assert_close(y1, y2)
+
+
+@skip_xp_backends(np_only=True,
+                  reason='array-likes only supported for NumPy backend')
+@pytest.mark.parametrize("func", [dct, idct, dctn, idctn, dst, idst, dstn, idstn])
+def test_array_like(xp, func):
+    x = [[[1.0, 1.0], [1.0, 1.0]],
+         [[1.0, 1.0], [1.0, 1.0]],
+         [[1.0, 1.0], [1.0, 1.0]]]
+    xp_assert_close(func(x), func(xp.asarray(x)))
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diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/__init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..10f4b39e48e2d6c0b042582ca65f572bde6ba575
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/__init__.py
@@ -0,0 +1,103 @@
+"""
+=========================================================
+Legacy discrete Fourier transforms (:mod:`scipy.fftpack`)
+=========================================================
+
+.. legacy::
+
+   New code should use :mod:`scipy.fft`.
+
+Fast Fourier Transforms (FFTs)
+==============================
+
+.. autosummary::
+   :toctree: generated/
+
+   fft - Fast (discrete) Fourier Transform (FFT)
+   ifft - Inverse FFT
+   fft2 - 2-D FFT
+   ifft2 - 2-D inverse FFT
+   fftn - N-D FFT
+   ifftn - N-D inverse FFT
+   rfft - FFT of strictly real-valued sequence
+   irfft - Inverse of rfft
+   dct - Discrete cosine transform
+   idct - Inverse discrete cosine transform
+   dctn - N-D Discrete cosine transform
+   idctn - N-D Inverse discrete cosine transform
+   dst - Discrete sine transform
+   idst - Inverse discrete sine transform
+   dstn - N-D Discrete sine transform
+   idstn - N-D Inverse discrete sine transform
+
+Differential and pseudo-differential operators
+==============================================
+
+.. autosummary::
+   :toctree: generated/
+
+   diff - Differentiation and integration of periodic sequences
+   tilbert - Tilbert transform:         cs_diff(x,h,h)
+   itilbert - Inverse Tilbert transform: sc_diff(x,h,h)
+   hilbert - Hilbert transform:         cs_diff(x,inf,inf)
+   ihilbert - Inverse Hilbert transform: sc_diff(x,inf,inf)
+   cs_diff - cosh/sinh pseudo-derivative of periodic sequences
+   sc_diff - sinh/cosh pseudo-derivative of periodic sequences
+   ss_diff - sinh/sinh pseudo-derivative of periodic sequences
+   cc_diff - cosh/cosh pseudo-derivative of periodic sequences
+   shift - Shift periodic sequences
+
+Helper functions
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   fftshift - Shift the zero-frequency component to the center of the spectrum
+   ifftshift - The inverse of `fftshift`
+   fftfreq - Return the Discrete Fourier Transform sample frequencies
+   rfftfreq - DFT sample frequencies (for usage with rfft, irfft)
+   next_fast_len - Find the optimal length to zero-pad an FFT for speed
+
+Note that ``fftshift``, ``ifftshift`` and ``fftfreq`` are numpy functions
+exposed by ``fftpack``; importing them from ``numpy`` should be preferred.
+
+Convolutions (:mod:`scipy.fftpack.convolve`)
+============================================
+
+.. module:: scipy.fftpack.convolve
+
+.. autosummary::
+   :toctree: generated/
+
+   convolve
+   convolve_z
+   init_convolution_kernel
+   destroy_convolve_cache
+
+"""
+
+
+__all__ = ['fft','ifft','fftn','ifftn','rfft','irfft',
+           'fft2','ifft2',
+           'diff',
+           'tilbert','itilbert','hilbert','ihilbert',
+           'sc_diff','cs_diff','cc_diff','ss_diff',
+           'shift',
+           'fftfreq', 'rfftfreq',
+           'fftshift', 'ifftshift',
+           'next_fast_len',
+           'dct', 'idct', 'dst', 'idst', 'dctn', 'idctn', 'dstn', 'idstn'
+           ]
+
+from ._basic import *
+from ._pseudo_diffs import *
+from ._helper import *
+from ._realtransforms import *
+
+# Deprecated namespaces, to be removed in v2.0.0
+from . import basic, helper, pseudo_diffs, realtransforms
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..59c85ae4b364464a66489ef221f7f7ac45624694
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_basic.py
@@ -0,0 +1,428 @@
+"""
+Discrete Fourier Transforms - _basic.py
+"""
+# Created by Pearu Peterson, August,September 2002
+__all__ = ['fft','ifft','fftn','ifftn','rfft','irfft',
+           'fft2','ifft2']
+
+from scipy.fft import _pocketfft
+from ._helper import _good_shape
+
+
+def fft(x, n=None, axis=-1, overwrite_x=False):
+    """
+    Return discrete Fourier transform of real or complex sequence.
+
+    The returned complex array contains ``y(0), y(1),..., y(n-1)``, where
+
+    ``y(j) = (x * exp(-2*pi*sqrt(-1)*j*np.arange(n)/n)).sum()``.
+
+    Parameters
+    ----------
+    x : array_like
+        Array to Fourier transform.
+    n : int, optional
+        Length of the Fourier transform. If ``n < x.shape[axis]``, `x` is
+        truncated. If ``n > x.shape[axis]``, `x` is zero-padded. The
+        default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the fft's are computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    z : complex ndarray
+        with the elements::
+
+            [y(0),y(1),..,y(n/2),y(1-n/2),...,y(-1)]        if n is even
+            [y(0),y(1),..,y((n-1)/2),y(-(n-1)/2),...,y(-1)]  if n is odd
+
+        where::
+
+            y(j) = sum[k=0..n-1] x[k] * exp(-sqrt(-1)*j*k* 2*pi/n), j = 0..n-1
+
+    See Also
+    --------
+    ifft : Inverse FFT
+    rfft : FFT of a real sequence
+
+    Notes
+    -----
+    The packing of the result is "standard": If ``A = fft(a, n)``, then
+    ``A[0]`` contains the zero-frequency term, ``A[1:n/2]`` contains the
+    positive-frequency terms, and ``A[n/2:]`` contains the negative-frequency
+    terms, in order of decreasingly negative frequency. So ,for an 8-point
+    transform, the frequencies of the result are [0, 1, 2, 3, -4, -3, -2, -1].
+    To rearrange the fft output so that the zero-frequency component is
+    centered, like [-4, -3, -2, -1,  0,  1,  2,  3], use `fftshift`.
+
+    Both single and double precision routines are implemented. Half precision
+    inputs will be converted to single precision. Non-floating-point inputs
+    will be converted to double precision. Long-double precision inputs are
+    not supported.
+
+    This function is most efficient when `n` is a power of two, and least
+    efficient when `n` is prime.
+
+    Note that if ``x`` is real-valued, then ``A[j] == A[n-j].conjugate()``.
+    If ``x`` is real-valued and ``n`` is even, then ``A[n/2]`` is real.
+
+    If the data type of `x` is real, a "real FFT" algorithm is automatically
+    used, which roughly halves the computation time. To increase efficiency
+    a little further, use `rfft`, which does the same calculation, but only
+    outputs half of the symmetrical spectrum. If the data is both real and
+    symmetrical, the `dct` can again double the efficiency by generating
+    half of the spectrum from half of the signal.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fftpack import fft, ifft
+    >>> x = np.arange(5)
+    >>> np.allclose(fft(ifft(x)), x, atol=1e-15)  # within numerical accuracy.
+    True
+
+    """
+    return _pocketfft.fft(x, n, axis, None, overwrite_x)
+
+
+def ifft(x, n=None, axis=-1, overwrite_x=False):
+    """
+    Return discrete inverse Fourier transform of real or complex sequence.
+
+    The returned complex array contains ``y(0), y(1),..., y(n-1)``, where
+
+    ``y(j) = (x * exp(2*pi*sqrt(-1)*j*np.arange(n)/n)).mean()``.
+
+    Parameters
+    ----------
+    x : array_like
+        Transformed data to invert.
+    n : int, optional
+        Length of the inverse Fourier transform.  If ``n < x.shape[axis]``,
+        `x` is truncated. If ``n > x.shape[axis]``, `x` is zero-padded.
+        The default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the ifft's are computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    ifft : ndarray of floats
+        The inverse discrete Fourier transform.
+
+    See Also
+    --------
+    fft : Forward FFT
+
+    Notes
+    -----
+    Both single and double precision routines are implemented. Half precision
+    inputs will be converted to single precision. Non-floating-point inputs
+    will be converted to double precision. Long-double precision inputs are
+    not supported.
+
+    This function is most efficient when `n` is a power of two, and least
+    efficient when `n` is prime.
+
+    If the data type of `x` is real, a "real IFFT" algorithm is automatically
+    used, which roughly halves the computation time.
+
+    Examples
+    --------
+    >>> from scipy.fftpack import fft, ifft
+    >>> import numpy as np
+    >>> x = np.arange(5)
+    >>> np.allclose(ifft(fft(x)), x, atol=1e-15)  # within numerical accuracy.
+    True
+
+    """
+    return _pocketfft.ifft(x, n, axis, None, overwrite_x)
+
+
+def rfft(x, n=None, axis=-1, overwrite_x=False):
+    """
+    Discrete Fourier transform of a real sequence.
+
+    Parameters
+    ----------
+    x : array_like, real-valued
+        The data to transform.
+    n : int, optional
+        Defines the length of the Fourier transform. If `n` is not specified
+        (the default) then ``n = x.shape[axis]``. If ``n < x.shape[axis]``,
+        `x` is truncated, if ``n > x.shape[axis]``, `x` is zero-padded.
+    axis : int, optional
+        The axis along which the transform is applied. The default is the
+        last axis.
+    overwrite_x : bool, optional
+        If set to true, the contents of `x` can be overwritten. Default is
+        False.
+
+    Returns
+    -------
+    z : real ndarray
+        The returned real array contains::
+
+          [y(0),Re(y(1)),Im(y(1)),...,Re(y(n/2))]              if n is even
+          [y(0),Re(y(1)),Im(y(1)),...,Re(y(n/2)),Im(y(n/2))]   if n is odd
+
+        where::
+
+          y(j) = sum[k=0..n-1] x[k] * exp(-sqrt(-1)*j*k*2*pi/n)
+          j = 0..n-1
+
+    See Also
+    --------
+    fft, irfft, scipy.fft.rfft
+
+    Notes
+    -----
+    Within numerical accuracy, ``y == rfft(irfft(y))``.
+
+    Both single and double precision routines are implemented. Half precision
+    inputs will be converted to single precision. Non-floating-point inputs
+    will be converted to double precision. Long-double precision inputs are
+    not supported.
+
+    To get an output with a complex datatype, consider using the newer
+    function `scipy.fft.rfft`.
+
+    Examples
+    --------
+    >>> from scipy.fftpack import fft, rfft
+    >>> a = [9, -9, 1, 3]
+    >>> fft(a)
+    array([  4. +0.j,   8.+12.j,  16. +0.j,   8.-12.j])
+    >>> rfft(a)
+    array([  4.,   8.,  12.,  16.])
+
+    """
+    return _pocketfft.rfft_fftpack(x, n, axis, None, overwrite_x)
+
+
+def irfft(x, n=None, axis=-1, overwrite_x=False):
+    """
+    Return inverse discrete Fourier transform of real sequence x.
+
+    The contents of `x` are interpreted as the output of the `rfft`
+    function.
+
+    Parameters
+    ----------
+    x : array_like
+        Transformed data to invert.
+    n : int, optional
+        Length of the inverse Fourier transform.
+        If n < x.shape[axis], x is truncated.
+        If n > x.shape[axis], x is zero-padded.
+        The default results in n = x.shape[axis].
+    axis : int, optional
+        Axis along which the ifft's are computed; the default is over
+        the last axis (i.e., axis=-1).
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    irfft : ndarray of floats
+        The inverse discrete Fourier transform.
+
+    See Also
+    --------
+    rfft, ifft, scipy.fft.irfft
+
+    Notes
+    -----
+    The returned real array contains::
+
+        [y(0),y(1),...,y(n-1)]
+
+    where for n is even::
+
+        y(j) = 1/n (sum[k=1..n/2-1] (x[2*k-1]+sqrt(-1)*x[2*k])
+                                     * exp(sqrt(-1)*j*k* 2*pi/n)
+                    + c.c. + x[0] + (-1)**(j) x[n-1])
+
+    and for n is odd::
+
+        y(j) = 1/n (sum[k=1..(n-1)/2] (x[2*k-1]+sqrt(-1)*x[2*k])
+                                     * exp(sqrt(-1)*j*k* 2*pi/n)
+                    + c.c. + x[0])
+
+    c.c. denotes complex conjugate of preceding expression.
+
+    For details on input parameters, see `rfft`.
+
+    To process (conjugate-symmetric) frequency-domain data with a complex
+    datatype, consider using the newer function `scipy.fft.irfft`.
+
+    Examples
+    --------
+    >>> from scipy.fftpack import rfft, irfft
+    >>> a = [1.0, 2.0, 3.0, 4.0, 5.0]
+    >>> irfft(a)
+    array([ 2.6       , -3.16405192,  1.24398433, -1.14955713,  1.46962473])
+    >>> irfft(rfft(a))
+    array([1., 2., 3., 4., 5.])
+
+    """
+    return _pocketfft.irfft_fftpack(x, n, axis, None, overwrite_x)
+
+
+def fftn(x, shape=None, axes=None, overwrite_x=False):
+    """
+    Return multidimensional discrete Fourier transform.
+
+    The returned array contains::
+
+      y[j_1,..,j_d] = sum[k_1=0..n_1-1, ..., k_d=0..n_d-1]
+         x[k_1,..,k_d] * prod[i=1..d] exp(-sqrt(-1)*2*pi/n_i * j_i * k_i)
+
+    where d = len(x.shape) and n = x.shape.
+
+    Parameters
+    ----------
+    x : array_like
+        The (N-D) array to transform.
+    shape : int or array_like of ints or None, optional
+        The shape of the result. If both `shape` and `axes` (see below) are
+        None, `shape` is ``x.shape``; if `shape` is None but `axes` is
+        not None, then `shape` is ``numpy.take(x.shape, axes, axis=0)``.
+        If ``shape[i] > x.shape[i]``, the ith dimension is padded with zeros.
+        If ``shape[i] < x.shape[i]``, the ith dimension is truncated to
+        length ``shape[i]``.
+        If any element of `shape` is -1, the size of the corresponding
+        dimension of `x` is used.
+    axes : int or array_like of ints or None, optional
+        The axes of `x` (`y` if `shape` is not None) along which the
+        transform is applied.
+        The default is over all axes.
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed. Default is False.
+
+    Returns
+    -------
+    y : complex-valued N-D NumPy array
+        The (N-D) DFT of the input array.
+
+    See Also
+    --------
+    ifftn
+
+    Notes
+    -----
+    If ``x`` is real-valued, then
+    ``y[..., j_i, ...] == y[..., n_i-j_i, ...].conjugate()``.
+
+    Both single and double precision routines are implemented. Half precision
+    inputs will be converted to single precision. Non-floating-point inputs
+    will be converted to double precision. Long-double precision inputs are
+    not supported.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fftpack import fftn, ifftn
+    >>> y = (-np.arange(16), 8 - np.arange(16), np.arange(16))
+    >>> np.allclose(y, fftn(ifftn(y)))
+    True
+
+    """
+    shape = _good_shape(x, shape, axes)
+    return _pocketfft.fftn(x, shape, axes, None, overwrite_x)
+
+
+def ifftn(x, shape=None, axes=None, overwrite_x=False):
+    """
+    Return inverse multidimensional discrete Fourier transform.
+
+    The sequence can be of an arbitrary type.
+
+    The returned array contains::
+
+      y[j_1,..,j_d] = 1/p * sum[k_1=0..n_1-1, ..., k_d=0..n_d-1]
+         x[k_1,..,k_d] * prod[i=1..d] exp(sqrt(-1)*2*pi/n_i * j_i * k_i)
+
+    where ``d = len(x.shape)``, ``n = x.shape``, and ``p = prod[i=1..d] n_i``.
+
+    For description of parameters see `fftn`.
+
+    See Also
+    --------
+    fftn : for detailed information.
+
+    Examples
+    --------
+    >>> from scipy.fftpack import fftn, ifftn
+    >>> import numpy as np
+    >>> y = (-np.arange(16), 8 - np.arange(16), np.arange(16))
+    >>> np.allclose(y, ifftn(fftn(y)))
+    True
+
+    """
+    shape = _good_shape(x, shape, axes)
+    return _pocketfft.ifftn(x, shape, axes, None, overwrite_x)
+
+
+def fft2(x, shape=None, axes=(-2,-1), overwrite_x=False):
+    """
+    2-D discrete Fourier transform.
+
+    Return the 2-D discrete Fourier transform of the 2-D argument
+    `x`.
+
+    See Also
+    --------
+    fftn : for detailed information.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fftpack import fft2, ifft2
+    >>> y = np.mgrid[:5, :5][0]
+    >>> y
+    array([[0, 0, 0, 0, 0],
+           [1, 1, 1, 1, 1],
+           [2, 2, 2, 2, 2],
+           [3, 3, 3, 3, 3],
+           [4, 4, 4, 4, 4]])
+    >>> np.allclose(y, ifft2(fft2(y)))
+    True
+    """
+    return fftn(x,shape,axes,overwrite_x)
+
+
+def ifft2(x, shape=None, axes=(-2,-1), overwrite_x=False):
+    """
+    2-D discrete inverse Fourier transform of real or complex sequence.
+
+    Return inverse 2-D discrete Fourier transform of
+    arbitrary type sequence x.
+
+    See `ifft` for more information.
+
+    See Also
+    --------
+    fft2, ifft
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fftpack import fft2, ifft2
+    >>> y = np.mgrid[:5, :5][0]
+    >>> y
+    array([[0, 0, 0, 0, 0],
+           [1, 1, 1, 1, 1],
+           [2, 2, 2, 2, 2],
+           [3, 3, 3, 3, 3],
+           [4, 4, 4, 4, 4]])
+    >>> np.allclose(y, fft2(ifft2(y)))
+    True
+
+    """
+    return ifftn(x,shape,axes,overwrite_x)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_helper.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_helper.py
new file mode 100644
index 0000000000000000000000000000000000000000..7892543732906dcd86b4c1aa9c1f249af701c137
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_helper.py
@@ -0,0 +1,115 @@
+import operator
+
+import numpy as np
+from numpy.fft import fftshift, ifftshift, fftfreq
+
+import scipy.fft._pocketfft.helper as _helper
+
+__all__ = ['fftshift', 'ifftshift', 'fftfreq', 'rfftfreq', 'next_fast_len']
+
+
+def rfftfreq(n, d=1.0):
+    """DFT sample frequencies (for usage with rfft, irfft).
+
+    The returned float array contains the frequency bins in
+    cycles/unit (with zero at the start) given a window length `n` and a
+    sample spacing `d`::
+
+      f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2]/(d*n)   if n is even
+      f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2,n/2]/(d*n)   if n is odd
+
+    Parameters
+    ----------
+    n : int
+        Window length.
+    d : scalar, optional
+        Sample spacing. Default is 1.
+
+    Returns
+    -------
+    out : ndarray
+        The array of length `n`, containing the sample frequencies.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy import fftpack
+    >>> sig = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
+    >>> sig_fft = fftpack.rfft(sig)
+    >>> n = sig_fft.size
+    >>> timestep = 0.1
+    >>> freq = fftpack.rfftfreq(n, d=timestep)
+    >>> freq
+    array([ 0.  ,  1.25,  1.25,  2.5 ,  2.5 ,  3.75,  3.75,  5.  ])
+
+    """
+    n = operator.index(n)
+    if n < 0:
+        raise ValueError(f"n = {n} is not valid. "
+                         "n must be a nonnegative integer.")
+
+    return (np.arange(1, n + 1, dtype=int) // 2) / float(n * d)
+
+
+def next_fast_len(target):
+    """
+    Find the next fast size of input data to `fft`, for zero-padding, etc.
+
+    SciPy's FFTPACK has efficient functions for radix {2, 3, 4, 5}, so this
+    returns the next composite of the prime factors 2, 3, and 5 which is
+    greater than or equal to `target`. (These are also known as 5-smooth
+    numbers, regular numbers, or Hamming numbers.)
+
+    Parameters
+    ----------
+    target : int
+        Length to start searching from. Must be a positive integer.
+
+    Returns
+    -------
+    out : int
+        The first 5-smooth number greater than or equal to `target`.
+
+    Notes
+    -----
+    .. versionadded:: 0.18.0
+
+    Examples
+    --------
+    On a particular machine, an FFT of prime length takes 133 ms:
+
+    >>> from scipy import fftpack
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> min_len = 10007  # prime length is worst case for speed
+    >>> a = rng.standard_normal(min_len)
+    >>> b = fftpack.fft(a)
+
+    Zero-padding to the next 5-smooth length reduces computation time to
+    211 us, a speedup of 630 times:
+
+    >>> fftpack.next_fast_len(min_len)
+    10125
+    >>> b = fftpack.fft(a, 10125)
+
+    Rounding up to the next power of 2 is not optimal, taking 367 us to
+    compute, 1.7 times as long as the 5-smooth size:
+
+    >>> b = fftpack.fft(a, 16384)
+
+    """
+    # Real transforms use regular sizes so this is backwards compatible
+    return _helper.good_size(target, True)
+
+
+def _good_shape(x, shape, axes):
+    """Ensure that shape argument is valid for scipy.fftpack
+
+    scipy.fftpack does not support len(shape) < x.ndim when axes is not given.
+    """
+    if shape is not None and axes is None:
+        shape = _helper._iterable_of_int(shape, 'shape')
+        if len(shape) != np.ndim(x):
+            raise ValueError("when given, axes and shape arguments"
+                             " have to be of the same length")
+    return shape
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_pseudo_diffs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_pseudo_diffs.py
new file mode 100644
index 0000000000000000000000000000000000000000..6dbcc8d3979b35c1497266fea34cf565cd3d11d7
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_pseudo_diffs.py
@@ -0,0 +1,554 @@
+"""
+Differential and pseudo-differential operators.
+"""
+# Created by Pearu Peterson, September 2002
+
+__all__ = ['diff',
+           'tilbert','itilbert','hilbert','ihilbert',
+           'cs_diff','cc_diff','sc_diff','ss_diff',
+           'shift']
+
+import threading
+
+from numpy import pi, asarray, sin, cos, sinh, cosh, tanh, iscomplexobj
+from . import convolve
+
+from scipy.fft._pocketfft.helper import _datacopied
+
+
+_cache = threading.local()
+
+
+def diff(x,order=1,period=None, _cache=_cache):
+    """
+    Return kth derivative (or integral) of a periodic sequence x.
+
+    If x_j and y_j are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+      y_j = pow(sqrt(-1)*j*2*pi/period, order) * x_j
+      y_0 = 0 if order is not 0.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    order : int, optional
+        The order of differentiation. Default order is 1. If order is
+        negative, then integration is carried out under the assumption
+        that ``x_0 == 0``.
+    period : float, optional
+        The assumed period of the sequence. Default is ``2*pi``.
+
+    Notes
+    -----
+    If ``sum(x, axis=0) = 0`` then ``diff(diff(x, k), -k) == x`` (within
+    numerical accuracy).
+
+    For odd order and even ``len(x)``, the Nyquist mode is taken zero.
+
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'diff_cache'):
+            _cache.diff_cache = {}
+        _cache = _cache.diff_cache
+
+    tmp = asarray(x)
+    if order == 0:
+        return tmp
+    if iscomplexobj(tmp):
+        return diff(tmp.real, order, period, _cache)+1j*diff(
+            tmp.imag, order, period, _cache)
+    if period is not None:
+        c = 2*pi/period
+    else:
+        c = 1.0
+    n = len(x)
+    omega = _cache.get((n,order,c))
+    if omega is None:
+        if len(_cache) > 20:
+            while _cache:
+                _cache.popitem()
+
+        def kernel(k,order=order,c=c):
+            if k:
+                return pow(c*k,order)
+            return 0
+        omega = convolve.init_convolution_kernel(n,kernel,d=order,
+                                                 zero_nyquist=1)
+        _cache[(n,order,c)] = omega
+    overwrite_x = _datacopied(tmp, x)
+    return convolve.convolve(tmp,omega,swap_real_imag=order % 2,
+                             overwrite_x=overwrite_x)
+
+
+def tilbert(x, h, period=None, _cache=_cache):
+    """
+    Return h-Tilbert transform of a periodic sequence x.
+
+    If x_j and y_j are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+        y_j = sqrt(-1)*coth(j*h*2*pi/period) * x_j
+        y_0 = 0
+
+    Parameters
+    ----------
+    x : array_like
+        The input array to transform.
+    h : float
+        Defines the parameter of the Tilbert transform.
+    period : float, optional
+        The assumed period of the sequence. Default period is ``2*pi``.
+
+    Returns
+    -------
+    tilbert : ndarray
+        The result of the transform.
+
+    Notes
+    -----
+    If ``sum(x, axis=0) == 0`` and ``n = len(x)`` is odd, then
+    ``tilbert(itilbert(x)) == x``.
+
+    If ``2 * pi * h / period`` is approximately 10 or larger, then
+    numerically ``tilbert == hilbert``
+    (theoretically oo-Tilbert == Hilbert).
+
+    For even ``len(x)``, the Nyquist mode of ``x`` is taken zero.
+
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'tilbert_cache'):
+            _cache.tilbert_cache = {}
+        _cache = _cache.tilbert_cache
+
+    tmp = asarray(x)
+    if iscomplexobj(tmp):
+        return tilbert(tmp.real, h, period, _cache) + \
+               1j * tilbert(tmp.imag, h, period, _cache)
+
+    if period is not None:
+        h = h * 2 * pi / period
+
+    n = len(x)
+    omega = _cache.get((n, h))
+    if omega is None:
+        if len(_cache) > 20:
+            while _cache:
+                _cache.popitem()
+
+        def kernel(k, h=h):
+            if k:
+                return 1.0/tanh(h*k)
+
+            return 0
+
+        omega = convolve.init_convolution_kernel(n, kernel, d=1)
+        _cache[(n,h)] = omega
+
+    overwrite_x = _datacopied(tmp, x)
+    return convolve.convolve(tmp,omega,swap_real_imag=1,overwrite_x=overwrite_x)
+
+
+def itilbert(x,h,period=None, _cache=_cache):
+    """
+    Return inverse h-Tilbert transform of a periodic sequence x.
+
+    If ``x_j`` and ``y_j`` are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+      y_j = -sqrt(-1)*tanh(j*h*2*pi/period) * x_j
+      y_0 = 0
+
+    For more details, see `tilbert`.
+
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'itilbert_cache'):
+            _cache.itilbert_cache = {}
+        _cache = _cache.itilbert_cache
+
+    tmp = asarray(x)
+    if iscomplexobj(tmp):
+        return itilbert(tmp.real, h, period, _cache) + \
+               1j*itilbert(tmp.imag, h, period, _cache)
+    if period is not None:
+        h = h*2*pi/period
+    n = len(x)
+    omega = _cache.get((n,h))
+    if omega is None:
+        if len(_cache) > 20:
+            while _cache:
+                _cache.popitem()
+
+        def kernel(k,h=h):
+            if k:
+                return -tanh(h*k)
+            return 0
+        omega = convolve.init_convolution_kernel(n,kernel,d=1)
+        _cache[(n,h)] = omega
+    overwrite_x = _datacopied(tmp, x)
+    return convolve.convolve(tmp,omega,swap_real_imag=1,overwrite_x=overwrite_x)
+
+
+def hilbert(x, _cache=_cache):
+    """
+    Return Hilbert transform of a periodic sequence x.
+
+    If x_j and y_j are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+      y_j = sqrt(-1)*sign(j) * x_j
+      y_0 = 0
+
+    Parameters
+    ----------
+    x : array_like
+        The input array, should be periodic.
+    _cache : dict, optional
+        Dictionary that contains the kernel used to do a convolution with.
+
+    Returns
+    -------
+    y : ndarray
+        The transformed input.
+
+    See Also
+    --------
+    scipy.signal.hilbert : Compute the analytic signal, using the Hilbert
+                           transform.
+
+    Notes
+    -----
+    If ``sum(x, axis=0) == 0`` then ``hilbert(ihilbert(x)) == x``.
+
+    For even len(x), the Nyquist mode of x is taken zero.
+
+    The sign of the returned transform does not have a factor -1 that is more
+    often than not found in the definition of the Hilbert transform. Note also
+    that `scipy.signal.hilbert` does have an extra -1 factor compared to this
+    function.
+
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'hilbert_cache'):
+            _cache.hilbert_cache = {}
+        _cache = _cache.hilbert_cache
+
+    tmp = asarray(x)
+    if iscomplexobj(tmp):
+        return hilbert(tmp.real, _cache) + 1j * hilbert(tmp.imag, _cache)
+    n = len(x)
+    omega = _cache.get(n)
+    if omega is None:
+        if len(_cache) > 20:
+            while _cache:
+                _cache.popitem()
+
+        def kernel(k):
+            if k > 0:
+                return 1.0
+            elif k < 0:
+                return -1.0
+            return 0.0
+        omega = convolve.init_convolution_kernel(n,kernel,d=1)
+        _cache[n] = omega
+    overwrite_x = _datacopied(tmp, x)
+    return convolve.convolve(tmp,omega,swap_real_imag=1,overwrite_x=overwrite_x)
+
+
+def ihilbert(x, _cache=_cache):
+    """
+    Return inverse Hilbert transform of a periodic sequence x.
+
+    If ``x_j`` and ``y_j`` are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+      y_j = -sqrt(-1)*sign(j) * x_j
+      y_0 = 0
+
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'ihilbert_cache'):
+            _cache.ihilbert_cache = {}
+        _cache = _cache.ihilbert_cache
+    return -hilbert(x, _cache)
+
+
+def cs_diff(x, a, b, period=None, _cache=_cache):
+    """
+    Return (a,b)-cosh/sinh pseudo-derivative of a periodic sequence.
+
+    If ``x_j`` and ``y_j`` are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+      y_j = -sqrt(-1)*cosh(j*a*2*pi/period)/sinh(j*b*2*pi/period) * x_j
+      y_0 = 0
+
+    Parameters
+    ----------
+    x : array_like
+        The array to take the pseudo-derivative from.
+    a, b : float
+        Defines the parameters of the cosh/sinh pseudo-differential
+        operator.
+    period : float, optional
+        The period of the sequence. Default period is ``2*pi``.
+
+    Returns
+    -------
+    cs_diff : ndarray
+        Pseudo-derivative of periodic sequence `x`.
+
+    Notes
+    -----
+    For even len(`x`), the Nyquist mode of `x` is taken as zero.
+
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'cs_diff_cache'):
+            _cache.cs_diff_cache = {}
+        _cache = _cache.cs_diff_cache
+
+    tmp = asarray(x)
+    if iscomplexobj(tmp):
+        return cs_diff(tmp.real, a, b, period, _cache) + \
+               1j*cs_diff(tmp.imag, a, b, period, _cache)
+    if period is not None:
+        a = a*2*pi/period
+        b = b*2*pi/period
+    n = len(x)
+    omega = _cache.get((n,a,b))
+    if omega is None:
+        if len(_cache) > 20:
+            while _cache:
+                _cache.popitem()
+
+        def kernel(k,a=a,b=b):
+            if k:
+                return -cosh(a*k)/sinh(b*k)
+            return 0
+        omega = convolve.init_convolution_kernel(n,kernel,d=1)
+        _cache[(n,a,b)] = omega
+    overwrite_x = _datacopied(tmp, x)
+    return convolve.convolve(tmp,omega,swap_real_imag=1,overwrite_x=overwrite_x)
+
+
+def sc_diff(x, a, b, period=None, _cache=_cache):
+    """
+    Return (a,b)-sinh/cosh pseudo-derivative of a periodic sequence x.
+
+    If x_j and y_j are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+      y_j = sqrt(-1)*sinh(j*a*2*pi/period)/cosh(j*b*2*pi/period) * x_j
+      y_0 = 0
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    a,b : float
+        Defines the parameters of the sinh/cosh pseudo-differential
+        operator.
+    period : float, optional
+        The period of the sequence x. Default is 2*pi.
+
+    Notes
+    -----
+    ``sc_diff(cs_diff(x,a,b),b,a) == x``
+    For even ``len(x)``, the Nyquist mode of x is taken as zero.
+
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'sc_diff_cache'):
+            _cache.sc_diff_cache = {}
+        _cache = _cache.sc_diff_cache
+
+    tmp = asarray(x)
+    if iscomplexobj(tmp):
+        return sc_diff(tmp.real, a, b, period, _cache) + \
+               1j * sc_diff(tmp.imag, a, b, period, _cache)
+    if period is not None:
+        a = a*2*pi/period
+        b = b*2*pi/period
+    n = len(x)
+    omega = _cache.get((n,a,b))
+    if omega is None:
+        if len(_cache) > 20:
+            while _cache:
+                _cache.popitem()
+
+        def kernel(k,a=a,b=b):
+            if k:
+                return sinh(a*k)/cosh(b*k)
+            return 0
+        omega = convolve.init_convolution_kernel(n,kernel,d=1)
+        _cache[(n,a,b)] = omega
+    overwrite_x = _datacopied(tmp, x)
+    return convolve.convolve(tmp,omega,swap_real_imag=1,overwrite_x=overwrite_x)
+
+
+def ss_diff(x, a, b, period=None, _cache=_cache):
+    """
+    Return (a,b)-sinh/sinh pseudo-derivative of a periodic sequence x.
+
+    If x_j and y_j are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+      y_j = sinh(j*a*2*pi/period)/sinh(j*b*2*pi/period) * x_j
+      y_0 = a/b * x_0
+
+    Parameters
+    ----------
+    x : array_like
+        The array to take the pseudo-derivative from.
+    a,b
+        Defines the parameters of the sinh/sinh pseudo-differential
+        operator.
+    period : float, optional
+        The period of the sequence x. Default is ``2*pi``.
+
+    Notes
+    -----
+    ``ss_diff(ss_diff(x,a,b),b,a) == x``
+
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'ss_diff_cache'):
+            _cache.ss_diff_cache = {}
+        _cache = _cache.ss_diff_cache
+
+    tmp = asarray(x)
+    if iscomplexobj(tmp):
+        return ss_diff(tmp.real, a, b, period, _cache) + \
+               1j*ss_diff(tmp.imag, a, b, period, _cache)
+    if period is not None:
+        a = a*2*pi/period
+        b = b*2*pi/period
+    n = len(x)
+    omega = _cache.get((n,a,b))
+    if omega is None:
+        if len(_cache) > 20:
+            while _cache:
+                _cache.popitem()
+
+        def kernel(k,a=a,b=b):
+            if k:
+                return sinh(a*k)/sinh(b*k)
+            return float(a)/b
+        omega = convolve.init_convolution_kernel(n,kernel)
+        _cache[(n,a,b)] = omega
+    overwrite_x = _datacopied(tmp, x)
+    return convolve.convolve(tmp,omega,overwrite_x=overwrite_x)
+
+
+def cc_diff(x, a, b, period=None, _cache=_cache):
+    """
+    Return (a,b)-cosh/cosh pseudo-derivative of a periodic sequence.
+
+    If x_j and y_j are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+      y_j = cosh(j*a*2*pi/period)/cosh(j*b*2*pi/period) * x_j
+
+    Parameters
+    ----------
+    x : array_like
+        The array to take the pseudo-derivative from.
+    a,b : float
+        Defines the parameters of the sinh/sinh pseudo-differential
+        operator.
+    period : float, optional
+        The period of the sequence x. Default is ``2*pi``.
+
+    Returns
+    -------
+    cc_diff : ndarray
+        Pseudo-derivative of periodic sequence `x`.
+
+    Notes
+    -----
+    ``cc_diff(cc_diff(x,a,b),b,a) == x``
+
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'cc_diff_cache'):
+            _cache.cc_diff_cache = {}
+        _cache = _cache.cc_diff_cache
+
+    tmp = asarray(x)
+    if iscomplexobj(tmp):
+        return cc_diff(tmp.real, a, b, period, _cache) + \
+               1j * cc_diff(tmp.imag, a, b, period, _cache)
+    if period is not None:
+        a = a*2*pi/period
+        b = b*2*pi/period
+    n = len(x)
+    omega = _cache.get((n,a,b))
+    if omega is None:
+        if len(_cache) > 20:
+            while _cache:
+                _cache.popitem()
+
+        def kernel(k,a=a,b=b):
+            return cosh(a*k)/cosh(b*k)
+        omega = convolve.init_convolution_kernel(n,kernel)
+        _cache[(n,a,b)] = omega
+    overwrite_x = _datacopied(tmp, x)
+    return convolve.convolve(tmp,omega,overwrite_x=overwrite_x)
+
+
+def shift(x, a, period=None, _cache=_cache):
+    """
+    Shift periodic sequence x by a: y(u) = x(u+a).
+
+    If x_j and y_j are Fourier coefficients of periodic functions x
+    and y, respectively, then::
+
+          y_j = exp(j*a*2*pi/period*sqrt(-1)) * x_f
+
+    Parameters
+    ----------
+    x : array_like
+        The array to take the pseudo-derivative from.
+    a : float
+        Defines the parameters of the sinh/sinh pseudo-differential
+    period : float, optional
+        The period of the sequences x and y. Default period is ``2*pi``.
+    """
+    if isinstance(_cache, threading.local):
+        if not hasattr(_cache, 'shift_cache'):
+            _cache.shift_cache = {}
+        _cache = _cache.shift_cache
+
+    tmp = asarray(x)
+    if iscomplexobj(tmp):
+        return shift(tmp.real, a, period, _cache) + 1j * shift(
+            tmp.imag, a, period, _cache)
+    if period is not None:
+        a = a*2*pi/period
+    n = len(x)
+    omega = _cache.get((n,a))
+    if omega is None:
+        if len(_cache) > 20:
+            while _cache:
+                _cache.popitem()
+
+        def kernel_real(k,a=a):
+            return cos(a*k)
+
+        def kernel_imag(k,a=a):
+            return sin(a*k)
+        omega_real = convolve.init_convolution_kernel(n,kernel_real,d=0,
+                                                      zero_nyquist=0)
+        omega_imag = convolve.init_convolution_kernel(n,kernel_imag,d=1,
+                                                      zero_nyquist=0)
+        _cache[(n,a)] = omega_real,omega_imag
+    else:
+        omega_real,omega_imag = omega
+    overwrite_x = _datacopied(tmp, x)
+    return convolve.convolve_z(tmp,omega_real,omega_imag,
+                               overwrite_x=overwrite_x)
+
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_realtransforms.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_realtransforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..ad71d517b0ac829ab71850bf67f7dc38636161f2
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/_realtransforms.py
@@ -0,0 +1,598 @@
+"""
+Real spectrum transforms (DCT, DST, MDCT)
+"""
+
+__all__ = ['dct', 'idct', 'dst', 'idst', 'dctn', 'idctn', 'dstn', 'idstn']
+
+from scipy.fft import _pocketfft
+from ._helper import _good_shape
+
+_inverse_typemap = {1: 1, 2: 3, 3: 2, 4: 4}
+
+
+def dctn(x, type=2, shape=None, axes=None, norm=None, overwrite_x=False):
+    """
+    Return multidimensional Discrete Cosine Transform along the specified axes.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DCT (see Notes). Default type is 2.
+    shape : int or array_like of ints or None, optional
+        The shape of the result. If both `shape` and `axes` (see below) are
+        None, `shape` is ``x.shape``; if `shape` is None but `axes` is
+        not None, then `shape` is ``numpy.take(x.shape, axes, axis=0)``.
+        If ``shape[i] > x.shape[i]``, the ith dimension is padded with zeros.
+        If ``shape[i] < x.shape[i]``, the ith dimension is truncated to
+        length ``shape[i]``.
+        If any element of `shape` is -1, the size of the corresponding
+        dimension of `x` is used.
+    axes : int or array_like of ints or None, optional
+        Axes along which the DCT is computed.
+        The default is over all axes.
+    norm : {None, 'ortho'}, optional
+        Normalization mode (see Notes). Default is None.
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    idctn : Inverse multidimensional DCT
+
+    Notes
+    -----
+    For full details of the DCT types and normalization modes, as well as
+    references, see `dct`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fftpack import dctn, idctn
+    >>> rng = np.random.default_rng()
+    >>> y = rng.standard_normal((16, 16))
+    >>> np.allclose(y, idctn(dctn(y, norm='ortho'), norm='ortho'))
+    True
+
+    """
+    shape = _good_shape(x, shape, axes)
+    return _pocketfft.dctn(x, type, shape, axes, norm, overwrite_x)
+
+
+def idctn(x, type=2, shape=None, axes=None, norm=None, overwrite_x=False):
+    """
+    Return multidimensional Discrete Cosine Transform along the specified axes.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DCT (see Notes). Default type is 2.
+    shape : int or array_like of ints or None, optional
+        The shape of the result.  If both `shape` and `axes` (see below) are
+        None, `shape` is ``x.shape``; if `shape` is None but `axes` is
+        not None, then `shape` is ``numpy.take(x.shape, axes, axis=0)``.
+        If ``shape[i] > x.shape[i]``, the ith dimension is padded with zeros.
+        If ``shape[i] < x.shape[i]``, the ith dimension is truncated to
+        length ``shape[i]``.
+        If any element of `shape` is -1, the size of the corresponding
+        dimension of `x` is used.
+    axes : int or array_like of ints or None, optional
+        Axes along which the IDCT is computed.
+        The default is over all axes.
+    norm : {None, 'ortho'}, optional
+        Normalization mode (see Notes). Default is None.
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    dctn : multidimensional DCT
+
+    Notes
+    -----
+    For full details of the IDCT types and normalization modes, as well as
+    references, see `idct`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fftpack import dctn, idctn
+    >>> rng = np.random.default_rng()
+    >>> y = rng.standard_normal((16, 16))
+    >>> np.allclose(y, idctn(dctn(y, norm='ortho'), norm='ortho'))
+    True
+
+    """
+    type = _inverse_typemap[type]
+    shape = _good_shape(x, shape, axes)
+    return _pocketfft.dctn(x, type, shape, axes, norm, overwrite_x)
+
+
+def dstn(x, type=2, shape=None, axes=None, norm=None, overwrite_x=False):
+    """
+    Return multidimensional Discrete Sine Transform along the specified axes.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DST (see Notes). Default type is 2.
+    shape : int or array_like of ints or None, optional
+        The shape of the result.  If both `shape` and `axes` (see below) are
+        None, `shape` is ``x.shape``; if `shape` is None but `axes` is
+        not None, then `shape` is ``numpy.take(x.shape, axes, axis=0)``.
+        If ``shape[i] > x.shape[i]``, the ith dimension is padded with zeros.
+        If ``shape[i] < x.shape[i]``, the ith dimension is truncated to
+        length ``shape[i]``.
+        If any element of `shape` is -1, the size of the corresponding
+        dimension of `x` is used.
+    axes : int or array_like of ints or None, optional
+        Axes along which the DCT is computed.
+        The default is over all axes.
+    norm : {None, 'ortho'}, optional
+        Normalization mode (see Notes). Default is None.
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    idstn : Inverse multidimensional DST
+
+    Notes
+    -----
+    For full details of the DST types and normalization modes, as well as
+    references, see `dst`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fftpack import dstn, idstn
+    >>> rng = np.random.default_rng()
+    >>> y = rng.standard_normal((16, 16))
+    >>> np.allclose(y, idstn(dstn(y, norm='ortho'), norm='ortho'))
+    True
+
+    """
+    shape = _good_shape(x, shape, axes)
+    return _pocketfft.dstn(x, type, shape, axes, norm, overwrite_x)
+
+
+def idstn(x, type=2, shape=None, axes=None, norm=None, overwrite_x=False):
+    """
+    Return multidimensional Discrete Sine Transform along the specified axes.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DST (see Notes). Default type is 2.
+    shape : int or array_like of ints or None, optional
+        The shape of the result.  If both `shape` and `axes` (see below) are
+        None, `shape` is ``x.shape``; if `shape` is None but `axes` is
+        not None, then `shape` is ``numpy.take(x.shape, axes, axis=0)``.
+        If ``shape[i] > x.shape[i]``, the ith dimension is padded with zeros.
+        If ``shape[i] < x.shape[i]``, the ith dimension is truncated to
+        length ``shape[i]``.
+        If any element of `shape` is -1, the size of the corresponding
+        dimension of `x` is used.
+    axes : int or array_like of ints or None, optional
+        Axes along which the IDST is computed.
+        The default is over all axes.
+    norm : {None, 'ortho'}, optional
+        Normalization mode (see Notes). Default is None.
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    dstn : multidimensional DST
+
+    Notes
+    -----
+    For full details of the IDST types and normalization modes, as well as
+    references, see `idst`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.fftpack import dstn, idstn
+    >>> rng = np.random.default_rng()
+    >>> y = rng.standard_normal((16, 16))
+    >>> np.allclose(y, idstn(dstn(y, norm='ortho'), norm='ortho'))
+    True
+
+    """
+    type = _inverse_typemap[type]
+    shape = _good_shape(x, shape, axes)
+    return _pocketfft.dstn(x, type, shape, axes, norm, overwrite_x)
+
+
+def dct(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False):
+    r"""
+    Return the Discrete Cosine Transform of arbitrary type sequence x.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DCT (see Notes). Default type is 2.
+    n : int, optional
+        Length of the transform.  If ``n < x.shape[axis]``, `x` is
+        truncated.  If ``n > x.shape[axis]``, `x` is zero-padded. The
+        default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the dct is computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    norm : {None, 'ortho'}, optional
+        Normalization mode (see Notes). Default is None.
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    y : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    idct : Inverse DCT
+
+    Notes
+    -----
+    For a single dimension array ``x``, ``dct(x, norm='ortho')`` is equal to
+    MATLAB ``dct(x)``.
+
+    There are, theoretically, 8 types of the DCT, only the first 4 types are
+    implemented in scipy. 'The' DCT generally refers to DCT type 2, and 'the'
+    Inverse DCT generally refers to DCT type 3.
+
+    **Type I**
+
+    There are several definitions of the DCT-I; we use the following
+    (for ``norm=None``)
+
+    .. math::
+
+       y_k = x_0 + (-1)^k x_{N-1} + 2 \sum_{n=1}^{N-2} x_n \cos\left(
+       \frac{\pi k n}{N-1} \right)
+
+    If ``norm='ortho'``, ``x[0]`` and ``x[N-1]`` are multiplied by a scaling
+    factor of :math:`\sqrt{2}`, and ``y[k]`` is multiplied by a scaling factor
+    ``f``
+
+    .. math::
+
+        f = \begin{cases}
+         \frac{1}{2}\sqrt{\frac{1}{N-1}} & \text{if }k=0\text{ or }N-1, \\
+         \frac{1}{2}\sqrt{\frac{2}{N-1}} & \text{otherwise} \end{cases}
+
+    .. versionadded:: 1.2.0
+       Orthonormalization in DCT-I.
+
+    .. note::
+       The DCT-I is only supported for input size > 1.
+
+    **Type II**
+
+    There are several definitions of the DCT-II; we use the following
+    (for ``norm=None``)
+
+    .. math::
+
+       y_k = 2 \sum_{n=0}^{N-1} x_n \cos\left(\frac{\pi k(2n+1)}{2N} \right)
+
+    If ``norm='ortho'``, ``y[k]`` is multiplied by a scaling factor ``f``
+
+    .. math::
+       f = \begin{cases}
+       \sqrt{\frac{1}{4N}} & \text{if }k=0, \\
+       \sqrt{\frac{1}{2N}} & \text{otherwise} \end{cases}
+
+    which makes the corresponding matrix of coefficients orthonormal
+    (``O @ O.T = np.eye(N)``).
+
+    **Type III**
+
+    There are several definitions, we use the following (for ``norm=None``)
+
+    .. math::
+
+       y_k = x_0 + 2 \sum_{n=1}^{N-1} x_n \cos\left(\frac{\pi(2k+1)n}{2N}\right)
+
+    or, for ``norm='ortho'``
+
+    .. math::
+
+       y_k = \frac{x_0}{\sqrt{N}} + \sqrt{\frac{2}{N}} \sum_{n=1}^{N-1} x_n
+       \cos\left(\frac{\pi(2k+1)n}{2N}\right)
+
+    The (unnormalized) DCT-III is the inverse of the (unnormalized) DCT-II, up
+    to a factor ``2N``. The orthonormalized DCT-III is exactly the inverse of
+    the orthonormalized DCT-II.
+
+    **Type IV**
+
+    There are several definitions of the DCT-IV; we use the following
+    (for ``norm=None``)
+
+    .. math::
+
+       y_k = 2 \sum_{n=0}^{N-1} x_n \cos\left(\frac{\pi(2k+1)(2n+1)}{4N} \right)
+
+    If ``norm='ortho'``, ``y[k]`` is multiplied by a scaling factor ``f``
+
+    .. math::
+
+        f = \frac{1}{\sqrt{2N}}
+
+    .. versionadded:: 1.2.0
+       Support for DCT-IV.
+
+    References
+    ----------
+    .. [1] 'A Fast Cosine Transform in One and Two Dimensions', by J.
+           Makhoul, `IEEE Transactions on acoustics, speech and signal
+           processing` vol. 28(1), pp. 27-34,
+           :doi:`10.1109/TASSP.1980.1163351` (1980).
+    .. [2] Wikipedia, "Discrete cosine transform",
+           https://en.wikipedia.org/wiki/Discrete_cosine_transform
+
+    Examples
+    --------
+    The Type 1 DCT is equivalent to the FFT (though faster) for real,
+    even-symmetrical inputs. The output is also real and even-symmetrical.
+    Half of the FFT input is used to generate half of the FFT output:
+
+    >>> from scipy.fftpack import fft, dct
+    >>> import numpy as np
+    >>> fft(np.array([4., 3., 5., 10., 5., 3.])).real
+    array([ 30.,  -8.,   6.,  -2.,   6.,  -8.])
+    >>> dct(np.array([4., 3., 5., 10.]), 1)
+    array([ 30.,  -8.,   6.,  -2.])
+
+    """
+    return _pocketfft.dct(x, type, n, axis, norm, overwrite_x)
+
+
+def idct(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False):
+    """
+    Return the Inverse Discrete Cosine Transform of an arbitrary type sequence.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DCT (see Notes). Default type is 2.
+    n : int, optional
+        Length of the transform.  If ``n < x.shape[axis]``, `x` is
+        truncated.  If ``n > x.shape[axis]``, `x` is zero-padded. The
+        default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the idct is computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    norm : {None, 'ortho'}, optional
+        Normalization mode (see Notes). Default is None.
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    idct : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    dct : Forward DCT
+
+    Notes
+    -----
+    For a single dimension array `x`, ``idct(x, norm='ortho')`` is equal to
+    MATLAB ``idct(x)``.
+
+    'The' IDCT is the IDCT of type 2, which is the same as DCT of type 3.
+
+    IDCT of type 1 is the DCT of type 1, IDCT of type 2 is the DCT of type
+    3, and IDCT of type 3 is the DCT of type 2. IDCT of type 4 is the DCT
+    of type 4. For the definition of these types, see `dct`.
+
+    Examples
+    --------
+    The Type 1 DCT is equivalent to the DFT for real, even-symmetrical
+    inputs. The output is also real and even-symmetrical. Half of the IFFT
+    input is used to generate half of the IFFT output:
+
+    >>> from scipy.fftpack import ifft, idct
+    >>> import numpy as np
+    >>> ifft(np.array([ 30.,  -8.,   6.,  -2.,   6.,  -8.])).real
+    array([  4.,   3.,   5.,  10.,   5.,   3.])
+    >>> idct(np.array([ 30.,  -8.,   6.,  -2.]), 1) / 6
+    array([  4.,   3.,   5.,  10.])
+
+    """
+    type = _inverse_typemap[type]
+    return _pocketfft.dct(x, type, n, axis, norm, overwrite_x)
+
+
+def dst(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False):
+    r"""
+    Return the Discrete Sine Transform of arbitrary type sequence x.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DST (see Notes). Default type is 2.
+    n : int, optional
+        Length of the transform.  If ``n < x.shape[axis]``, `x` is
+        truncated.  If ``n > x.shape[axis]``, `x` is zero-padded. The
+        default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the dst is computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    norm : {None, 'ortho'}, optional
+        Normalization mode (see Notes). Default is None.
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    dst : ndarray of reals
+        The transformed input array.
+
+    See Also
+    --------
+    idst : Inverse DST
+
+    Notes
+    -----
+    For a single dimension array ``x``.
+
+    There are, theoretically, 8 types of the DST for different combinations of
+    even/odd boundary conditions and boundary off sets [1]_, only the first
+    4 types are implemented in scipy.
+
+    **Type I**
+
+    There are several definitions of the DST-I; we use the following
+    for ``norm=None``. DST-I assumes the input is odd around `n=-1` and `n=N`.
+
+    .. math::
+
+        y_k = 2 \sum_{n=0}^{N-1} x_n \sin\left(\frac{\pi(k+1)(n+1)}{N+1}\right)
+
+    Note that the DST-I is only supported for input size > 1.
+    The (unnormalized) DST-I is its own inverse, up to a factor ``2(N+1)``.
+    The orthonormalized DST-I is exactly its own inverse.
+
+    **Type II**
+
+    There are several definitions of the DST-II; we use the following for
+    ``norm=None``. DST-II assumes the input is odd around `n=-1/2` and
+    `n=N-1/2`; the output is odd around :math:`k=-1` and even around `k=N-1`
+
+    .. math::
+
+        y_k = 2 \sum_{n=0}^{N-1} x_n \sin\left(\frac{\pi(k+1)(2n+1)}{2N}\right)
+
+    if ``norm='ortho'``, ``y[k]`` is multiplied by a scaling factor ``f``
+
+    .. math::
+
+        f = \begin{cases}
+        \sqrt{\frac{1}{4N}} & \text{if }k = 0, \\
+        \sqrt{\frac{1}{2N}} & \text{otherwise} \end{cases}
+
+    **Type III**
+
+    There are several definitions of the DST-III, we use the following (for
+    ``norm=None``). DST-III assumes the input is odd around `n=-1` and even
+    around `n=N-1`
+
+    .. math::
+
+        y_k = (-1)^k x_{N-1} + 2 \sum_{n=0}^{N-2} x_n \sin\left(
+        \frac{\pi(2k+1)(n+1)}{2N}\right)
+
+    The (unnormalized) DST-III is the inverse of the (unnormalized) DST-II, up
+    to a factor ``2N``. The orthonormalized DST-III is exactly the inverse of the
+    orthonormalized DST-II.
+
+    .. versionadded:: 0.11.0
+
+    **Type IV**
+
+    There are several definitions of the DST-IV, we use the following (for
+    ``norm=None``). DST-IV assumes the input is odd around `n=-0.5` and even
+    around `n=N-0.5`
+
+    .. math::
+
+        y_k = 2 \sum_{n=0}^{N-1} x_n \sin\left(\frac{\pi(2k+1)(2n+1)}{4N}\right)
+
+    The (unnormalized) DST-IV is its own inverse, up to a factor ``2N``. The
+    orthonormalized DST-IV is exactly its own inverse.
+
+    .. versionadded:: 1.2.0
+       Support for DST-IV.
+
+    References
+    ----------
+    .. [1] Wikipedia, "Discrete sine transform",
+           https://en.wikipedia.org/wiki/Discrete_sine_transform
+
+    """
+    return _pocketfft.dst(x, type, n, axis, norm, overwrite_x)
+
+
+def idst(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False):
+    """
+    Return the Inverse Discrete Sine Transform of an arbitrary type sequence.
+
+    Parameters
+    ----------
+    x : array_like
+        The input array.
+    type : {1, 2, 3, 4}, optional
+        Type of the DST (see Notes). Default type is 2.
+    n : int, optional
+        Length of the transform.  If ``n < x.shape[axis]``, `x` is
+        truncated. If ``n > x.shape[axis]``, `x` is zero-padded. The
+        default results in ``n = x.shape[axis]``.
+    axis : int, optional
+        Axis along which the idst is computed; the default is over the
+        last axis (i.e., ``axis=-1``).
+    norm : {None, 'ortho'}, optional
+        Normalization mode (see Notes). Default is None.
+    overwrite_x : bool, optional
+        If True, the contents of `x` can be destroyed; the default is False.
+
+    Returns
+    -------
+    idst : ndarray of real
+        The transformed input array.
+
+    See Also
+    --------
+    dst : Forward DST
+
+    Notes
+    -----
+    'The' IDST is the IDST of type 2, which is the same as DST of type 3.
+
+    IDST of type 1 is the DST of type 1, IDST of type 2 is the DST of type
+    3, and IDST of type 3 is the DST of type 2. For the definition of these
+    types, see `dst`.
+
+    .. versionadded:: 0.11.0
+
+    """
+    type = _inverse_typemap[type]
+    return _pocketfft.dst(x, type, n, axis, norm, overwrite_x)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/basic.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/basic.py
new file mode 100644
index 0000000000000000000000000000000000000000..553f456fe1561c28928ecc4ebe2238459cc60443
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/basic.py
@@ -0,0 +1,20 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.fftpack` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'fft','ifft','fftn','ifftn','rfft','irfft',
+    'fft2','ifft2'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="fftpack", module="basic",
+                                   private_modules=["_basic"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/convolve.cpython-312-darwin.so b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/convolve.cpython-312-darwin.so
new file mode 100644
index 0000000000000000000000000000000000000000..c0121ba2a9a180c6a38ab4e3fdd577e5476d1b75
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/convolve.cpython-312-darwin.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:81235f0f79327d643366b65b5074526c83d83cf3393fd1fed8c70766214654ed
+size 114288
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/helper.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/helper.py
new file mode 100644
index 0000000000000000000000000000000000000000..fcc7000c215f8a7605a2a59b5767b27b2fcd969d
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/helper.py
@@ -0,0 +1,19 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.fftpack` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'fftshift', 'ifftshift', 'fftfreq', 'rfftfreq', 'next_fast_len'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="fftpack", module="helper",
+                                   private_modules=["_helper"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/pseudo_diffs.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/pseudo_diffs.py
new file mode 100644
index 0000000000000000000000000000000000000000..ecf71ad3256d48d2131c8058072da724cb001af9
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/pseudo_diffs.py
@@ -0,0 +1,22 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.fftpack` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'diff',
+    'tilbert', 'itilbert', 'hilbert', 'ihilbert',
+    'cs_diff', 'cc_diff', 'sc_diff', 'ss_diff',
+    'shift', 'convolve'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="fftpack", module="pseudo_diffs",
+                                   private_modules=["_pseudo_diffs"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/realtransforms.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/realtransforms.py
new file mode 100644
index 0000000000000000000000000000000000000000..9a392198fccf213bc988a79058bd69515e39f510
--- /dev/null
+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/realtransforms.py
@@ -0,0 +1,19 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.fftpack` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__ = [  # noqa: F822
+    'dct', 'idct', 'dst', 'idst', 'dctn', 'idctn', 'dstn', 'idstn'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="fftpack", module="realtransforms",
+                                   private_modules=["_realtransforms"], all=__all__,
+                                   attribute=name)
diff --git a/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/tests/.___init__.py b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/tests/.___init__.py
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+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/tests/._fftw_double_ref.npz
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+++ b/.venv_haddock/lib/python3.12/site-packages/scipy/fftpack/tests/._fftw_single_ref.npz
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+version https://git-lfs.github.com/spec/v1
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